Cavity Solitons in VCSEL Devices

S. Barbay; R. Kuszelewicz; J. R. Tredicce

doi:10.1155/2011/628761

Cavity Solitons in VCSEL Devices

Barbay, S.;Kuszelewicz, R.;Tredicce, J. R. 2011-10-23 00:00:00 Hindawi Publishing Corporation Advances in Optical Technologies Volume 2011, Article ID 628761, 23 pages doi:10.1155/2011/628761 Review Article 1 1 2 S. Barbay, R. Kuszelewicz, and J. R. Tredicce LaboratoiredePhotoniqueetdeNanostructures, CNRS-UPR20, RoutedeNozay,91460 Marcoussis, France Institut Non Lin´eaire de Nice, UMR6618 CNRS-Universit´e de Nice Sophia-Antipolis, 1361 Route de Lucioles, 06 560 Valbonne, France Correspondence should be addressed to S. Barbay, sylvain.barbay@lpn.cnrs.fr Received 20 June 2011; Accepted 9 August 2011 Academic Editor: Krassimir Panajotov Copyright © 2011 S. Barbay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We review advances on the experimental study of cavity solitons in VCSELs in the past decade. We emphasize on the design and fabrication of electrically or optically pumped broad-area VCSELs used for CSs formation and review diﬀerent experimental conﬁgurations. Potential applications of CSs in the ﬁeld of photonics are discussed, in particular the use of CSs for all-optical processing of information and for VCSELs characterization. Prospects on self-localization studies based on vertical cavity devices involving new physical mechanisms are also given. 1. Introduction e.g., [7–9]). Optics was not an exception. After the report of period doubling and chaos in a modulated laser [10], several In this paper we address experimental results on Cavity Sol- papers showed theoretically and experimentally the appear- itons (CS) in VCSEL devices and focus on recent studies and ance of instabilities in optical systems [11]. In particular, developments. We emphasize on the design and fabrication laser with injected signal and optical ampliﬁers have been of electrically or optically pumped broad-area VCSELs used exhaustively studied [12–17]. Dynamics of semiconductor for CS formation and review diﬀerent experimental conﬁg- lasers under injection and delayed optical feedback were urations. Applications of CS in the ﬁeld of photonics are also objects of interests mainly because of the possible discussed, in particular the potential use of CS for all-optical applications of such devices in optical communication processing of information and for VCSEL characterization. systems [18–20]. Later, mainly during the 90s, the interest Prospects on self-localization studies based on vertical cavity shifted towards spatiotemporal instabilities. The possibility devices involving new physical mechanisms are also given. of observing optical vortices [21] and ﬁnally reach optical The reader interested in the theory of CS formation in turbulence was very attractive, because optical systems were semiconductor devices can refer to recent reviews on the somehow easier to model than hydrodynamical ones. Thus, subject [1, 2] and also to [3]which provides ageneral review the comparison between experimental and theoretical results on CSs and their applications to photonics from a more was simpler than in other more complex systems. Several fundamental viewpoint. A collection of articles on the most studies reported the appearance of complex spatio-temporal recent developments in the ﬁeld can also be found in [4]. Our dynamics in optics [22–24] and in particular in laser systems goal is to provide a complete and accessible review on past [25–28]. Most of the experiments realized with broad area and most recent experimental results on CSs using vertical lasers, thus with a large transverse section or high Fresnel cavity semiconductor devices, while giving a prospect on number, showed the appearance of large structures more future directions. or less complex but almost always with long correlation During the 80s, the main focus of experimental studies length in the transverse plane and, therefore, avoiding the on nonlinear dynamics was on temporal dynamics (see, e.g., appearance of a complex or turbulent behavior [29]. The [5, 6]). Observation of period doubling, quasiperiodicity, reasons for such long correlation order is mainly that it is intermittency, and chaos in a variety of systems ranging from somehow diﬃcult in lasers to reach a really high Fresnel ﬂuids to chemical reactions appeared in the literature (see, number, because cavity lengths are usually too long. In 2 Advances in Optical Technologies that sense, VCSEL represents an ideal laser to study spatio- Swift-Hohenberg equation, a model equation that describes temporal dynamics. Eﬀective cavity lengths of the order of pattern forming systems and applicable in nonlinear optics 10 μm, active medium lengths of the order of a quarter-wave- [39]. The stability conditions for localized structures in 1D length, almost planar mirrors, and the possibility of having were theoretically studied in [43]. The authors then proved more than 150 μm in diameter makes this device an ideal theoretically that an inﬁnity of localized structures present- candidate to observe structures with very short correlation ing an arbitrary number of intensity peaks coexist and may length and, therefore, complex optical spatio-temporal struc- be stable for a ﬁnite range of parameter values. Later, a sim- tures. Several theoretical studies were centered around the ilar method was used to study the region of coexistence and formation of patterns in VCSELs [30–32]aswellassome the order of the solutions in parameter space [44, 45]. experimental ones [33–36]. The potential of CSs for applications to parallel infor- However, the most interesting results have been obtained mation processing was then recognized and demonstrated in in general models of lasers with saturable absorbers [37–39] [40] and analyzed in the context of a model suited for semi- or opticalabsorberorampliﬁer[32, 40, 41]. Numerical and conductor systems in [30]. CS can be excited and erased by a analytical results showed that it is possible to observe local- local perturbation at any transverse location of a nonlinear, ized structures in these optical systems. The main property broad-area cavity and as such play the role of pixels or spatial of a localized structure is that its correlation length is much logical bits. They can be manipulated in phase or intensity smaller than the size of the system. Thus, each localized gradients, where they can be moved or controlled, a property structure will behave as an independent object. In optics, that relaxes considerably the addressing constrains if one localized structures with a single intensity peak have been wished to arrange them into 2D matrices. called cavity solitons (CSs). Cavity solitons are self-localized The main advantages of semiconductor systems over states of light appearing in the transverse plane of a cavity as other optical systems, where CS were predicted and observed bright spots sitting on a dark background. Experimentally, lie in the fast timescales and small spatial scales associated they can be characterized by the following properties: (1) with CS formation in semiconductor materials. Indeed, the CSs are self-localized states, independent of the system characteristic timescale for CS formation in semiconductor boundaries whose shape and size is ﬁxed by the system systems is of the order of the carrier recombination time, parameters and do not depend on the excitation that gave which is in the nanosecond range, much shorter than other birth to them; (2) CSs can exist in several (ideally arbitrary) competing macroscopic systems based on photorefractive transverse locations of the cavity and can be independently media [48], liquid crystals [49], or atomic vapors [46]in manipulated (written, erased, ...); (3) CS can be “moved” which CS were also found. Moreover, the characteristic size or set into motion. At ﬁrst sight, they possess characteristics of aCSisgovernedbythe diﬀraction length a ∝ LλF , resembling those of self-trapped beams [42] but constrained where L is the cavity length, λ the wavelength of light and within a cavity whose propagation path is folded by the cavity F the resonator ﬁnesse and is of the order of 10 μmin mirrors. However, it is worthwhile to notice that single peak microcavities, at least one order of magnitude smaller than localized structures are diﬀerent from self-trapped beams, in other macroscopic systems. CS necessitate a large and uni- because they are created by two fronts connecting two form aspect ratio system: a cavity whose transverse extent is diﬀerent spatial solutions in a dissipative system. This feature much larger than the longitudinal extent such that it can host introduces important physical diﬀerences; however, that can many transverse modes and allow for spatial decorrelation be fully appreciated only when considering rather subtle between diﬀerent cavity locations. Therefore, broad-area theories on CS formation [43, 44]. Some of these physical VCSELs appear then as ideal devices to implement CS in diﬀerences were experimentally observed in a semiconduct- semiconductor material systems. The ﬁrst demonstration of or-based system in [45]. On the other hand, the presence CS in a broad-area VCSEL that stimulated all the ensuing of a cavity is not necessary either as demonstrated by the investigations was reported in [50]. observation of single peak localized structures in [46]ina This paper is organized as follows. We present in Section single feedback mirror experiment performed in Na vapour. 2 the characteristics of broad-area VCSELs with electrical Thus, CS may be better called single peak localized structure injection and optical pumping designed for CS studies. In (SPLS), but we will use both names in this review. Section 3, we then describe experimental results obtained in CS arise usually under the condition of coexistence of a the amplifying regime, with a cavity driven by an external homogeneous and a patterned stationary state; for the same coherent beam (holding beam). An important new concep- control parameter values, the solution may approach one or tual and applicative step was obtained by the demonstration the other state depending upon the initial condition. Lo- of a CS laser, that is, a system that does not require a coherent calized structures are thus somehow intermediate, control- optical injection and emits self-localized microlasers having lable states between the homogeneous state and the fully the properties of the CSs described earlier, as explained developed pattern. SPLS may also exist in optical systems, in Section 4. Possible applications of CS to photonics are where two uniform states coexist, as a result of the locking presented in Section 5 with the experimental demonstrations of two fronts. This mechanism was ﬁrst studied theoretically of an optical delay line and of a soliton force microscope. and numerically in [47] where self-localized states (then The role of device defects and the applications of CS to called “diﬀractive autosolitons”) were demonstrated to exist device homogeneity characterization are also demonstrated. in a nonlinear, bistable, interferometer. Self-localized states Finally, new directions in the ﬁeld of self-localized states were also found in the more general framework of the using VCSELs are presented in Section 6. We analyze CS Advances in Optical Technologies 3 side of the VCSEL, the substrate is thinned down to 180 μm p-type bragg reﬂector Cu heat sink and antireﬂection coated in order to avoid back reﬂection TiPtAu contact Active QWs from the air-semiconductor interface into the gain medium. The diamond can then be attached to a copper submount Diamond heat spreader with a thermal paste. This design ensures a very good over- Oxide aperture AuSn solder all thermal conductivity of the VCSEL, compulsory for cw operation with large active areas. Cw operation was indeed GaAs substrate obtained for 200 μm or even higher diameter VCSELs with Al O 2 3 very good conversion eﬃciency and low threshold at room AR coating passivation layer GeNiAu contact temperature. In [53], the group at the University of Ulm re- n-type bragg reﬂector ported room-temperature, cw operation of 320 μmVCSELs Light output in diameter with a maximum output power of 0.89 W and a Figure 1: Schematic representation of a broad-area bottom emitter 2 current density at threshold of 1 kA/cm . VCSEL structure with diamond heat spreader, after [51]( c 2011 This VCSEL design has been successfully employed for IEEE). the ﬁrst demonstration of cavity solitons in a semiconductor optical ampliﬁer [50], and subsequent studies on cavity soli- tonlasersinanextendedconﬁgurationwithafeedback grat- ing [54] or face-to-face conﬁguration [55] (see Section 4). in polarization, Cavity Light Bullets which are 3D-localized While a VCSEL possesses in theory a translational sym- states of light traveling in a cavity and CS polaritons which metry across its useful aperture, this is not the case in prac- explore new material nonlinearities. tice, and this has important consequences for CS studies. There are indeed two main types of spatial nonuniformities 2. VCSEL Fabrication and Design for to consider: extended nonuniformities such as those of the CS Formation cavity resonance wavelength and of the pump, and localized nonuniformities. Because of the growth conditions, layer Broad-area VCSELs play an important role in the develop- thicknesses vary over the substrate that results in the appear- ment of CS studies in semiconductor systems. However, it ance of a wedge along a given direction. This wedge does not was necessary to develop adequate devices, and there were aﬀect much the spectral characteristics of the Bragg mirrors; major challenges to deal with, namely, uniformity (concern- however, the gradient in the cavity thickness translates into ing pumping and cavity resonance) and thermal manage- a cavity resonance wavelength gradient. The eﬀect is all the ment. In the following, we review two solutions that have more important when dealing with broad area devices, be- been proposed and used for CS experimental studies, one causethencavityresonance canvaryappreciablyacrossthe with electrical injection and the other with optical injection. VCSEL optical aperture. Since CS are sensitive to any pa- The two approaches are presented and the various pros and rameter gradients [40, 56, 57], this may have major impact cons are discussed. on their observation and control. In the seminal experiment on CS in VCSELs [50, 58], a large cavity resonance gra- 2.1. Electrically Pumped Broad-Area Devices. The bottom dient of 2.34 GHz/μm was measured which prevented the emitter VCSEL structure is represented on Figure 1,ade- observation of cavity solitons over the entire VCSEL surface. Later, improvements in the growth conditions enhanced tailed description and characterization of which can be found in [51, 52]. The VCSEL is designed for laser operation around the VCSEL uniformity of about one order of magnitude 980 nm and optimized for high-power, cw emission. The (0.4 GHz/μm[59]) and allowed the manipulation of CS active zone is composed of three InGaAs/GaAs quantum over the whole transverse extent of the VCSEL. As for the wells, embedded in an AlGaAs spacer to fabricate the one- pump uniformity, the bottom emitting structure allows to wavelength thick cavity. Two high reﬂectivity Al Ga As/ achieve a very good uniformity at the center of the device, 0.9 0.1 GaAs Bragg mirrors close the cavity. The top mirror is p- whereas the borders suﬀer the well-known current crowding doped with Carbon, while the back mirror is n-doped with eﬀect [60]. This manifests itself through the appearance of a high-order ﬂower-like pattern [35] just above the laser silicon. The back and front mirrors have respectively, 30 and 24.5 pairs of quarter wavelength-thick layers at the targeted threshold and limits the available area for CS manipulation. cavity resonance of 980 nm. The whole cavity is grown on However, since bottom emitting devices grown on a GaAs substrate are limited to wavelengths above 900 nm to avoid a GaAs substrate using molecular beam epithaxy (MBE). Circular mesas of diameter ranging from 100 to 250 μmare absorption, shorter emission devices may require adopting then etched in the structure before oxidization of the current other techniques. As an example, electrode patterning and aperture down to the beginning of the back mirror, where use of semitransparent ITO electrodes were considered for a thin (30 nm) AlAs layer has been included. This layer is the design of 850 nm, broad-area top emitting devices [61] and proved promising for improving electrical injection oxidized in a water-nitrogen environment at high temper- ature, leaving an oxidized ring of 25 μm width. A TiPtAu uniformity of top-emitters. A by-product of this technique contact is then deposited on top of the mesa and the device would also be the possibility to address CS electrically with local electrodes. Electrode patterning was also used in [62] is soldered on the heat sink. Heat sinking is provided by metalized diamond sinks soldered with AuSn. On the other on a 960 nm top emitting VCSEL in the optical ampliﬁer 4 Advances in Optical Technologies regime. Bistability and optical pattern formation which are the crystal lattice (see Figure 2). At the end of the process, all prerequisites for CS formation were observed. However, the the excess energy is transformed into heat and transferred to insuﬃcient transverse extension of the VCSEL together with the lattice. There is very little to do against this fundamental the rather large grid period (4 μm) prevented CS formation mechanism except reducing the photon energy excess by on a uniformly injected background. choosing a proper wavelength. The spatially localized sources of nonuniformity that As a result, an eﬃcient optical design must minimize heat have also to be taken into account for CS studies are often production and optimize pump absorption into the gain termed as defects, and may precisely arise from crystallo- region. Such a design has been proposed in [67]and suc- graphic defects in the Bragg mirror materials or in the Quan- cessfully applied to CS studies in [68] in the AlGaAs material tum wells, and lead to CS pinning. More detailed studies on system. the sample uniformity have been conducted in [63], where The design relies on the creation of a window at the pump CS were used as a spatial probe for defects, and in [64], where wavelength around 800 nm. The pump window corresponds localized defects where used as a source of drifting CS. These to a region in the optical spectrum of the cavity where trans- aspects are detailed in Section 5.2. mission is minimized and pump absorption is maximized, while keeping the cavity properties at the operating wave- 2.2. Optically Pumped Broad-Area Devices. An alternative length of 870 nm unchanged. This is accomplished by an op- timization procedure on the layer thicknesses composing the scheme for CS studies relies on the use of optically pumped devices. It may seem at ﬁrst rather incongruous to deal multilayer mirrors of the cavity. Target values of the trans- with optically pumped VCSELs while electrical injection has mission, reﬂection, and absorption spectra in given spectral regions are chosen. The procedure starts with a quarter- always represented the ultimate goal in devices. However, the advent of high-power low-cost sources could make it a wavelength Al Ga As/AlAs multilayer stack centered at 0.225 0.775 reasonable choice, all the more that integrated and compact 870 nm. Then, all the layers composing the back and front sources can be fabricated. There are several advantages in multilayer mirrors are allowed to vary in order to reach the using optical pumping for CS formation and studies. The desired spectral targets. This is simply done by minimizing an error function that measures the deviation from the ideal ﬁrst one is that optical pumping allows to easily shape the pump beam using conventional optics and to get rid of target and the actual values, depending on all the layer current crowding eﬀects by using, for example, a top-hat thicknesses. A Simplex algorithm is used as a minimization algorithm. The algorithm eventually converges towards a set shape illumination. Since the processing steps after the device growth are reduced, the second advantage one can expect is of layer thicknesses values (see Figure 2(b)). As can be readily to reduce the number of defects, and thereby the stress on the seen, all the layer thicknesses have diﬀerent values and the ﬁnal sample, hence the number of pinning sources. The third initial periodic structure is lost. but not the least advantage is that the pump ﬁeld may be The calculated structure has been grown by metal- shaped not only in the transverse but also in the propagation organic chemical vapor deposition and the reﬂectivity and directions, as will be described further in the text and used calculated spectra are shown on Figure 3. There is a very in Section 4 to design new compact devices. Note also that good agreement between the calculated and the measured reﬂectivity spectra. The pump window is easily seen on the optical pumping is commonly used in VECSELs for high power lasers [65, 66] and may also be used in the framework left around 800 nm, where absorption is maximized and of studies on CLB (see Section 6.2). There are, however, at the same time pump transmission into the substrate is minimized. The cavity resonance structure at 890 nm is kept. problems to be circumvented in order for optical pumping to be a viable solution. The most important problem is the This design ensures that very few pump photons will be thermal management, to be addressed along its two com- absorbed into the substrate and contribute to heating while ponents: heat production and heat dissipation. It is all the optimizing the pumping eﬃciency. The width of the pump more important here as we consider broad area devices. Heat window is 20 nm which introduces immunity against even- tual temperature induced shifts of the reﬂectivity spectra dissipation is common to the electrical pumping case and the same techniques can be somehow applied. On the converse, through temperature-induced index change and subsequent heat production is largely speciﬁc and depends on the dramatic eﬀects on the pumping level. It also allows pumping with a large numerical aperture microscope objective or lens. material system considered. In some systems where all the pump power is not absorbed in the gain region, the substrate The VCSEL can then be processed with other techniques absorption at the pump wavelength may represent the major to enhanceheatremoval,suchassubstrate removaland replacement with a high thermal conductivity substrate such part of the heat production. Therefore, a special care has to be taken to avoid it while optimizing the pump absorption in as SiC substrate or diamond substrate. Note that this tech- the gain medium. The second contribution to heat produc- nique does not prevents heat absorption into the substrate, tion (and to pump energy waste) is the so-called quantum since, in general, the bonding layers absorb very eﬃciently defect, that is, the energy diﬀerence between the pump the pump photons. Substrate removal and SiC bonding with Ti-InAu bonding has been employed in the sample used in energy and the laser transition (usually close to the bandgap of the semiconductor material). Pump photons absorbed by [68]. the semiconductor material produce electron-hole pairs at The same design technique has been used and reﬁned to fabricate a monolithic VCSEL with intracavity saturable an energy higher than that of the band gap that cascade to the bottom of the bands through phonon exchange with absorber. VCSELs with intracavity saturable absorbers were Advances in Optical Technologies 5 Active medium Back mirror Front mirror p 100 0 20 40 60 80 100 υ Layer number (a) (b) Figure 2: (a) Schematic representation of optical pumping in a semiconductor material: a pump photon of energy ω is absorbed in the semiconductor material creating an electron-hole pair. The electron and hole cascade to the bottom of the bands releasing extra energy to the lattice and eventually recombine either radiatively or nonradiatively. (b) (after [67]): Layer widths of the optimized structure. The substrate is on the left side of the ﬁgure. The cavity is ﬁlled by two absorbing Al Ga As spacers (layers 61 and 63) white bars around a bulk GaAs 0.07 0.93 active layer (layer 62, in black). The back and front Bragg mirrors are composed of alternating Al Ga As (dark gray) and AlAs (light 0.22 0.78 gray) layers. suited for CS studies. An original design for a vertical cavity laser with intracavity saturable absorber has been proposed in [73]. Using the same technique as explained before, a 0.8 cavity having a saturable absorber section and a gain section is designed. The gain region has two InGaAs/GaAs QW for 0.6 lasing around 980 nm. The saturable absorber section has one InGaAs/AlGaAs QW. All the QWs are placed at the antin- ode of the resonant cavity ﬁeld targeted at 980 nm. The cavity 0.4 is designed for optimized optical pumping around 800 nm. Therefore, in addition to the previous optimizations, the 0.2 multilayer mirror widths have also to be calculated in order to satisfy a condition on the pump ﬁeld intensity inside the active zone of the cavity. The pump ﬁeld in almost zero in the 780 800 820 840 860 880 900 920 940 whole pump window at the location of the SA QW. The gain λ (nm) QW barriers absorb the 800 nm pump ﬁeld, whereas the SA QW barriers are made transparent to the pump wavelength Figure 3: Calculated and measured spectra of the optimized cavity. in the pumping window by aluminium incorporation inside Red line: experimental reﬂectivity spectra. Black line: correspond- the barriers. The design is depicted in Figure 4 and has been ing calculated reﬂectivity spectrum. Brown: calculated absorption. successfully used to demonstrate bistability, self-pulsing, and Dashed blue: calculated cavity transmission. a compact cavity soliton laser (see Section 4). 3. CS in Semiconductor Optical Ampliﬁers already considered in the prospect of building self-pulsing or bistable vertical-cavity lasers. Several designs have been The most studied system in optics is represented in Figure proposed for electrically injected devices. A quantum well 5. A nonlinear medium inside an optical cavity is driven by may for example be placed in the upper or lower mirror a homogeneous optical beam covering the whole transverse stack with a shorter carrier lifetime [69] or with an additional section of the device. The system can be set such that the contact for controllable operation [70]. Self-pulsing have also output intensity is zero and all the incoming beam is ab- been observed in small area, oxyde-conﬁned VCSELs thanks sorbed by the saturable medium. If the condition for the to the diﬀerence between the carrier and the optical mode bistable behavior is fulﬁlled, then a short and narrow optical conﬁnement [71]. A double cavity may also be used for pulse may ignite a small region of the device. Such an optical controllable self-pulsing or bistable operation [72]. These pulse is called the writing beam. If it is in phase with the hold- techniques necessitate either a small area cavity, a fast sat- ing beam, a CS is created at the location where it impinges urable absorber, or a complex electrical design and are not that persists after the writing pulse disappears. In a similar Layer width (nm) 6 Advances in Optical Technologies second output coming from the external cavity laser was then used as a coherent writing beam (WB). This beam was prepared so as to obtain a 10 μm waist; its power was con- trolled by an acousto-optic modulator. The phase relation between the writing beam and the holding beam was con- trolled by piezo-positioning a mirror on its own path. The reﬂected output of the VCSEL was monitored globally by a CCD camera or locally using a fast photodetector. The observation of CS in an electrically pumped VCSEL ampliﬁer [50, 58] and the demonstration of their mutual independence is explained in Figure 6. Similar results have been obtained in optically pumped VCSEL ampliﬁers [68]. The demonstration relies on the independent writing and 6400 6600 6800 7000 7200 7400 erasure of two CS at two diﬀerent locations of the VCSEL. Z (nm) In the ﬁrst demonstrations, the locations where the indepen- Figure 4: Active zone of the VCSEL-SA and ﬁeld intensities dent manipulation of the CS could be obtained in practice at the cavity resonance (black, divided by 400) and at the were limited by the presence of a strong cavity resonance gra- pump wavelengths (in red, between 795 nm and 805 nm) ver- dient. In the following experiments, new devices with much sus the growth depth. The active zone is composed of two smaller gradients were provided and allowed manipulation regions (in yellow and green): the SA region (yellow) with one over almost the whole transverse extent of the device, that is, InGaAs/Al Ga As quantum well and the amplifying region 0.22 0.78 200 μm. The switching characteristics were analyzed in [76]. (green) with two InGaAs/Al Ga As quantum wells. The ﬁrst 0.05 0.95 A sequence of independent control of two CSs using in-phase few layers composing the the front and back mirrors is visible on the local excitation with the holding beam (writing beam) or π- right and left respectively. of the active zone. Light grey: AlAs. Dark phase shifted beam (erasure beam) is shown in Figure 6. grey: Al Ga As. Note that the SA quantum well is at a node of the 0.22 78 The use of the phase parameter to control the writing pump ﬁelds in the whole range of possible pump wavelength while being at an antinode of the ﬁeld at cavity resonance. After [73]. or erasure process of a CS reveals in fact quite cumbersome in practical applications. However, an incoherent switching technique has been demonstrated by Barbay et al. in [68]. Using a specially designed optically pumped VCSOA as de- way, another CS can be created in any other location pro- scribed earlier, they have shown that CS writing and erasure vided the correlation length of the localized structure is can be achieved by short pulses (60 ps duration), at a wave- signiﬁcantly smaller than the transverse size of the device. CS length far from that of the holding beam, demonstrating a written in the way described above can be erased by sending a mechanism free of phase relationship. This technique relies pulse quite similarly to the writing pulse at the same location on the observation that CS in semiconductor devices are but with phase opposite to that the holding beam. compound objects. While a localized structure is formed in the intracavity ﬁeld distribution, a counterpart forms in the Experimentally, CS have been observed in several systems based on photorefractive crystals [48], Na vapors [46], liquid carrier density. Hence, it is possible to excite CS by locally crystal light valves [49, 74], semiconductor optical ampliﬁers adding carriers. The fact that both writing and erasure are possible by local carrier injection, with slightly diﬀerent HB [50, 68], and lasers [54, 55, 73, 75]. In the latter, most experiments have been done in VCSELs, because their short parameters though, is intriguing and has been explained in cavity and large diameter insure a Fresnel number large terms of local temperature eﬀects in [77]. As in the coherent enough to avoid the formation of patterns correlated over the case however, a delay is observed in the writing process which whole extension of the system. CS have been observed in depends on the operating conditions and which is of the ampliﬁers both electrically [50]and opticallypumped[68]. order of 100–200 ns (against several ns in the coherent case). The pumping rate was set high enough to provide gain in the The erasure process is faster and occurs without delay in a active medium but low enough to maintain the VCSEL below timescale of a few ns or less. The writing delay can be reduced by increasing the writing power. the laser threshold. However, it must be noted that similar results have been obtained with an injected VCSEL pumped In theory, one needs a translationally invariant system slightly above threshold [59]. for CS formation and control. In practice, the presence of A typical experimental setup is shown in Figure 5.Abot- gradients in the system is unavoidable. They arise from tom emitter VCSEL with a diameter of 150 μm was injected diﬀerent sources. by a coherent optical beam produced by an edge emitter laser with an external cavity in a Littrow conﬁguration. Thus, the (i) Device growth and fabrication: the VCSEL cavity holding beam can be ﬁne tuned in the range 960–980 nm. resonance used in [50] had a linear variation along This beam was spatially ﬁltered such that the intensity could one diameter of the device. This variation creates a be considered as almost uniform across the whole section of linear gradient of one of the most important control the VCSEL, and thus not introducing an additional gradient parameters in the experiment: the detuning between component. The holding beam power was controlled by the cavity resonance frequency and the frequency an acousto-optic modulator together with a polarizer. The of the holding beam. Though generating important n(λ)∗|E| (a.u.) Advances in Optical Technologies 7 CCD OF BS PD BS FP1 MONO BS BS S FP2 PM SF 1 I AOM1 BS OI BS ◦ BS SF 2 PZT AOM2 P Figure 5: Experimental setup. M, high power edge emitter laser; I, current driver stabilized up to 0.01 mA; TO, temperature controller; G, grating; OI, optical diode; FP, Fabry-Perot resonators; AOM, Acousto-optic modulators; SF1, beam expander conﬁgurator with spatial ﬁltering; SF2, beam reducer conﬁgurator with spatial ﬁltering; S, broad-area vertical cavity surface emitting laser; C, collimator; CCD, camera; PD, Photodetector; PZT, piezoelectric ceramic; M and BS, mirrors and beam splitters; PM, power meter (optional); λ/4, λ/2wave plates; P, polarizers; OF and MONO, optical ﬁber and monochromator. consequences, it can be controlled by the growth con- Later, cavity solitons have been observed in electrically ditions. pumped VCSEL above threshold (see Section 4). The main properties of localized structures in optical ampliﬁers are the (ii) Nonuniform distributions of carrier injection in elec- intensity and phase stability. The good stability in intensity trically injected devices. Usually, electrically pumped is deﬁned by the fact that the low and high intensity of the broad area devices present a current density higher bistable cycle are very well deﬁned at all positions and remain at the borders than in the center of the active zone the same as much as the parameters are kept constant over (current crowding eﬀect). For this reason, a bottom the whole transverse section of the device. If the optically emitter structure was preferred in the ﬁrst demon- injected VCSEL is driven above threshold instead, the lower stration of the generation of localized structures in a branch of the bistable cycle is usually unstable and the CS VCSEL because the longer distance between the ring intensity ﬂuctuates in time. The holding beam deﬁnes the electrode and the active medium translates into a phase of the CS so that the phase is ﬁxed all across the more uniform current distribution. transverse section of the device. Thus, a possible transverse (iii) Misalignment of the holding beam with respect to the phase wave generated by the fast change in intensity at the optical axis of the VCSEL. position of the CS will not propagate. If a phase wave is created, then it will act as a phase gradient for a second CS (iv) Not completely uniform intensity distribution of the and it will move towards the border of the device as explained holding beam. in [78]. (v) Defects in the VCSEL structure. Some defects may In all cases, the experimental results have been compared repel the localized structure while others tend to pin with numerical ones showing very good qualitative agree- them (see Section 5.2). ment and in some cases even quantitative agreement with semiclassical models. All these gradients could aﬀect the generation and the sta- bility of CSs. Localized structures move under the eﬀect of a gradient and in semiconductor devices can move fast enough 4. CS Lasers to prevent a CDD camera from detecting them. Fortunately, some defects or unwanted gradients of the device or induced Vertical cavity semiconductor optical ampliﬁers (VCSOAs) by the imperfections in the experiment would pin them so allowed to demonstrate many useful properties of CS for that they remain stable and steady. During the ﬁrst experi- possible applications to all-optical processing of information ments, CS appeared always at the same set of positions. The (see Section 5). However, they necessitate the use of a co- introduction of external intensity or phase gradients allowed herent holding beam for optical injection which makes to move them around in a controllable way demonstrating the experimental implementation more diﬃcult, bulky, and the independence from the boundaries and the possibility costly. Moreover,CSs in such acasesit on anonzero back- to observe them in the whole transverse plane of the device ground and the contrast between the CS peak intensity and which can be relevant for some applications as we will ex- the background intensity is reduced. This is why laser CS plain in Section 5. would be needed to circumvent all these problems. 8 Advances in Optical Technologies (a) (b) (c) (d) (e) (f) (g) (h) Figure 6: 3D representation of the VCSOA near-ﬁeld intensity distribution, after [58]. The holding beam is always on, and all parameters are kept constant in the sequence (a)–(g). (a) The writing beam (WB) is oﬀ; (b) the WB induces the appearance of a single CS; (c) the WB is oﬀ again, and the CS remains; (d) the WB is displaced in position, and switched-on again and generates a second CS; (e) the WB is oﬀ again and the two bright spots coexist; (f) the WB targets the second CS, but the relative phase of WB with respect to HB has been changed, and the CS is erased; (g) the WB targets the ﬁrst CS, and it is erased in the same manner as in (f). Once the WB is blocked, the intensity distribution is identical to (a). In (h) is shown the CS proﬁle. It is to be noted that contrarily to what was believed at the the self-imaging conﬁguration in order to keep a high Fresnel early stages of their studies, CS in the laser regime can indeed number cavity hence the possibility to have a high number of exist in a VCSOA. As a laser with injected signal is known transverse modes and allow for spatial decorrelation. A half- to develop temporal (Hopf) instabilities that can couple to wave plate is used to match the VCSEL polarization direction the spatial degrees of freedom and drive the system to a of the laser emission to those of the beam splitters—BS1 regime of spatio-temporal chaos, this seemed apriori not and BS2—and of the grating. The grating is tuned such that favorable to the formation of CS which require a stable back- its maximum reﬂection is red detuned with respect to the ground to form on. It was nevertheless shown in [59], both VCSEL longitudinal mode. Above a certain threshold in the experimentally and theoretically, that CS can be observed in injected current (lower than the solitary laser threshold), a driven VCSEL above threshold. The theoretical modeling the system starts to emit and displays several isolated spots indicate that CS can exist even on the oscillatory background whose characteristics are those of a CSL [54]. The spots generated by the onset of a Hopf instability. This is conﬁrmed are bistable, almost identical in shape and size (10 μm), in the experiment, where it is shown that CS can survive in individually controllable in certain transverse locations of a narrow parameter range. Still, the laser CS thus obtained the laser (see Figure 7(b)), and can be put into motion or is limited by the necessity of a coherent holding beam (HB), “dragged” by an appropriate intensity gradient obtained by which in addition to injecting energy, ﬁxes the phase of the inserting a comb ﬁlter in the cavity. The emission spectrum CS. This is in contrast to the case of a true, “free-running” of each spot is narrow as expected in a laser. The writing CS laser (CSL) which can be described as a self-conﬁned mi- beam that provides a temporary and localized excitation is crolaser for which the phase is not ﬁxed. This last point has not coherent with the spots. Further details on the diﬀerent important consequences regarding CS interactions. switching techniques are described in [81], and a model that Theoretically, CSL have been found in two-photon active qualitatively agrees very well with the observations is pro- media [79] or in dense two-level systems [80]. In the context posed in [82]. Interestingly, the switch-on and oﬀ are of semiconductor CSLs, two possible bistable laser schemes obtained with an incoherent beam and the function (writing have been studied. The ﬁrst one is the VCSEL with frequency or erasure) is controlled by the position of the localized exci- selective feedback, which led also to the ﬁrst demonstration tation with respect to CSL location. This position depends of CSL in a semiconductor system [54], and the second one on the grating orientation. The minimum writing beam is the VCSEL with saturable absorber, studied in a compact pulse width needed to ignite a CSL is below 15 ns (lower and an extended cavity conﬁguration. limit not known due to experimental limitations), while the The VCSEL with a frequency selective feedback scheme is shorter the writing beam pulse, the higher the intensity is depicted in Figure 7. A broad area VCSEL of 200 μm diameter required [83]. Spontaneous switch is also observed following emitting around 980 nm is used in an external cavity con- an uncontrolled perturbation (being of mechanical, thermal, ﬁguration where a grating in Littrow conﬁguration here, or a optical origin). In such a case, the switch on is accompanied volume Bragg grating in later experiments, is used to close by short transient pulses, a feature of interest with respect to the cavity. A pair of lenses is inserted inside the cavity in Section 6.2. Multipeak structures are also observed [84]and Advances in Optical Technologies 9 (a) (b) (c) (d) (e) (f) Detection Writing beam (g) (h) (i) f = 8mm f = 300 mm Grating BS1 BS2 VCSEL Comb ﬁlter HWP1 HWP2 (a) (b) Figure 7: (a) Experimental setup of a CSL consisting in a VCSEL with frequency selective feedback. One pair of lenses are inserted inside the cavity in the self-imaging conﬁguration. Beam splitters BS1 and BS2 are used for writing beam input port and for output detection. (b) Sequence of images (inverted contrast) of the VCSEL surface showing the independent writing and erasure of two CSL. Reprinted with permission from [54]. ( c 2011) by the American Physical Society. associated with a CS-splitting phenomenon reminiscent of the round-trip time of the external cavity, relevant in the the homoclinic snaking curve observed in ampliﬁer systems context of Section 6.2. Multistability among several, multi- [45]. colored monochromatic CSL is analyzed and modeled in It has been long known that semiconductor lasers with [86, 87]. The proposed model also explains the observation saturable absorbers can be bistable. They constitute thus the and control of bistable laser vortices reported in [88], that second system of choice for CSL studies. The ﬁrst demon- were predicted earlier in wide-aperture, class-A lasers with stration of a CSL with a saturable absorber has been reported saturable absorption in [89]. in [55]. The experimental setup consists of two mutually A compact CSL has been demonstrated in [73, 75]. The coupled, face-to-face, VCSELs depicted in Figure 8.Itiscom- device, a monolithic, optically pumped, vertical cavity laser posed of two broad area (200 μm diameter) 980 nm VCSELs, with intracavity saturable absorber, is described in Section provided by the same company (ULM Photonics) as in the 2.2.Atdiﬀerence with the previous demonstrations, this previous demonstration. The VCSELs are optically coupled system is purely single-longitudinal mode. Its theoretical by lenses in the self-imaging conﬁguration. A beam splitter is description is intrinsically simpler and laser CS models have used for detection and for localized excitation. One VCSEL is been studied in [90, 91] and in [92–94] for semiconductor biased above transparency and operated in the gain regime, laser models (see also [2]for arecenttheoretical review). while the other VCSEL is biased below transparency and The vertical-cavity is optically pumped uniformly on a 70 μm operates in the saturable absorption regime. The tempera- diameter. ture of the gain VCSEL is set such that its emission is slightly Fast and sequential independent and incoherent writ- (1 nm) blue detuned with respect to the below-threshold ing/erasure are demonstrated with short (60 ps) pulses at spontaneous emission of the second VCSEL. The output a maximum rate of 82 MHz (see Figure 9). Note that the detected when the gain laser current is varied is shown in switch-on time is very fast (several ns) and only limited by Figure 8. For low currents, light emitted by the gain device relaxation oscillations [75], while the switch-oﬀ time is of the is almost fully reﬂected by the second VCSEL because of the order of 1 or 2 ns, as expected in this kind of systems [95]. frequency mismatch. The system starts to lase with a thresh- The same beam characteristics were used for both switch-on old lower than that of the solitary laser (Figures 8(a) and and switch-oﬀ. Theoretical work [95] suggests the important 8(b)). When laser emission starts to saturate with increasing role played by the writing/erasure beam width in the spa- current, and because of its thermal red-shift, laser emission tiotemporal dynamics that may explain why the same inten- starts to decrease as its coupling with the second VCSEL sity distribution can allow exciting or erasing a laser CS. progressively increases. When enough intensity can enter the One important point in CSL with respect to CS in am- saturable-absorber cavity, absorption saturation takes place, plifying systems is that the phase of the localized state is not and a bistable characteristics is locally recorded. In the near- ﬁxed and may have apriori arbitrary value. Nevertheless, the ﬁeld image of the sample, bistable laser spots appear that can phase proﬁle of a laser CS is larger than its intensity proﬁle, be controlled independently with an external beam. Here, and it was shown in [94] that CSLs at a distance shorter than a localized excitation whose wavelength is close to that of 60 μm will interact and form a cluster. The practical value in the emitted light is used. The switching process is analyzed experimental systems above which LCS may be independent in [85]. Switch-on is accompanied by rather long (600 ns) is however, smaller because of system’s inhomogeneities that transients composed of 150 ps pulses with a period equal to destroy the long-range interactions. If the distance between 10 Advances in Optical Technologies Detection L L L1 L1 L2 BS Coll. Coll. Detection L2 L2on L1on heatsink heatsink (a) 0.9 (A) (B) 0.8 0.7 0.6 0.5 (A) (B) (C) (D) (C) (D) 0.4 0.3 0.2 0.1 (E) (F) 0 50 100 150 200 250 300 350 400 450 IL1 (mA) Increasing I 50 μm Decreasing I (b) (c) Figure 8: Experimental setup (a) and experimental results (b) and (c) obtained in the face-to-face VCSELs conﬁguration (see text for details). Reprinted with permission from [55]. ( c 2011) by the American Physical Society. each laser CS is too small then laser CS shall not be independ- modulator [101] may prove interesting, at the expense of a ently controllable anymore [75]. The properties of clusters greater complexity of the experimental setup. Controlling the of laser localized structures and the associated motion is CSL motion remains therefore an important challenge. thoroughly studied in the theoretical paper of [96, 97]. Ex- perimentally, clusters arise either spontaneously [75]orfol- 5. Applications of CS to Photonics lowing a “splitting” process as the pump is increased as in [84, 98]. An experimental conﬁrmation that uncoupled, The main properties of localized structures or cavity solitons single-peaked Laser CS are mutually incoherent is given in in optical systems are twofold (1) They can be switched-on [84, 98], while clusters are found to have a well-deﬁned phase and oﬀ independently so that one can control their appear- relationship as reported in [98]. ance and disappearance. (2) If the system is homogeneous An important feature of CSL not yet clearly experimen- in the transverse plane, CSs are free to move, thus they tally demonstrated is related to the control of their motion. will feel the existence of any gradient. In other words, their In amplifying systems, motion can be induced either by a position and their velocity can be controlled by adjusting phase or intensity mask on the holding beam (see Section 5). a gradient of intensity and/or phase. These properties raise In laser systems, one cannot use the phase degree of freedom the idea that one can use localized structures in applications anymore. Motion can be induced by instabilities, as studied related to information processing. The most natural one is in [99, 100], where spontaneous motion is expected when an all optical memory [38, 40, 50, 102, 103] due to the the ratio of the carrier lifetimes in the active and passive controllability in position and switching capabilities of CSs. medium, respectively, is below a critical value. If boundaries However, there are several other possible applications not are included, for example, circular boundaries, CS move along the boundaries, an eﬀect that can be exploited for an so obvious at ﬁrst sight. In the following, we present two possible applications of cavity solitons: one in the optical optical clock [100]. Experimentally, techniques to control the index of refraction of the cavity by using a spatial light information processing context, an all optical delay line; and Intensity (a.u.) 6 Advances in Optical Technologies 11 150 150 100 100 50 50 0 0 0 24 8 0 24 8 Time (μs) Time (μs) (a) (b) 024 8 15 μm Time (μs) (c) (d) Figure 9: Independent and sequential writing-erasure of one cavity soliton while keeping the neighboring cavity soliton unchanged (a,b,c). The black trace corresponds to the incoming localized excitation pulse, and the middle (upper resp.) trace, green (red resp.) online, corresponds to the leftmost (rightmost resp.) cavity soliton. The zero intensity levels of the upper and middle traces (dashed lines) have been artiﬁcially oﬀset by 100 and 50, respectively for clarity. An averaged image of the two-cavity solitons considered is shown in (d). After [73]. another for material structure determination: a soliton force for some range of parameter values, is proportional to microscope. the gradient. The CS can be recovered later at a diﬀerent spatial position. This method was proposed for the ﬁrst time 5.1. All-Optical Delay Line. Apart from the existing elec- by Firth and Scroggie in 1996 [40, 57] and demonstrated tronic devices that are used today as shift registers, there has experimentally in Na vapors by Schap ¨ ers et al. in 2001 [109] been increasing interest in all optical delay lines in the last and by Pedaci et al. in 2008 in a VCSEL [110]. few years. Most of the proposed all-optical systems are based The optical system used in [110] is a bottom emitter on slowing down light by modifying the group velocity. Such VCSEL as described in Section 2.1. The broad area device variation can be a consequence of a nonlinear process like (200 microns in diameter) is injected by a collimated beam electromagnetically induced transparency (EIT), stimulated focused by a cylindrical lens. This allows the generation of Brillouin scattering (SBS), and so forth. In [104–108], it is a homogeneous injection beam along a line transverse to possible to ﬁnd several schemes based on slow-light in order the direction of propagation of light on the microresonator. to realize a delay line (Figure 10). The intensity of the injected ﬁeld, the detuning between the cavity resonance and the injected ﬁeld frequencies, and the Using localized structures, it is possible to propose a completely diﬀerent approach based on injecting a stream pumping current of the VCSEL were set at typical values for of optical pulses into a nonlinear device. Each injected pulse which the CS may exist in such devices (see [58]). Five fast will create a CS. If a linear gradient is somehow super- avalanche photodiode detectors are placed in the near-ﬁeld imposed, the CS will drift along this line at a speed which, image plane so as to detect the output intensity of the device Intensity (a.u.) Intensity (a.u.) Intensity (a.u.) 12 Advances in Optical Technologies also an all optical pulse reshaping of the incoming optical CCD pulse. Amplitude ﬂuctuations of the incoming pulse are eliminated because of the threshold response of the medium to generate a CS. This functionality may be very useful in Detectors VCSEL array order to avoid deterioration of the transmitted signal. 5.2. Soliton-Force Microscope/Role of Defects. As stated before CL the position of a CS or localized structure can be controlled by a gradient. In [103], it was shown that it is possible to Holding beam Master position the CS at the maximum of an intensity or phase laser gradient. On the other hand, CS can be pinned by defects in the structure of the device. The defects act by generating a gradient. If all other parameters are considered uniform, only Writing beam EOM the gradients generated by the defects will determine the ﬁnal position of the CS. One may distinguish between two types of Figure 10: Experimental setup. Vertical cavity surface emitting laser defects: those that are able to pin the CS and those that repel (VCSEL); cylindrical lens (CL); electro-optic modulator (EOM); them. Thus, in presence of gradients of diﬀerent origins, the tunable master laser (ML). Inset: transverse proﬁle emission stable positions of CSs will be those where the forces applied (negative image) of a 200 μm section VCSEL, in the regime of CS on them compensate. This view may however, be mitigated existence under injection by a broad holding beam. Four CSs are by the recent theoretical demonstration in [111] that CS may present in the image. (ﬁgure reproduced from [110]). also feel the boundaries, even if they are far from them, so that only a ﬁnite set of positions are allowed. This point lacks; however, a clear experimental demonstration. along the line deﬁned by the holding beam. A linear phase In [63], it was proposed to monitor the motion of CS gradient is generated by tilting the holding beam with respect under the eﬀects of externally applied gradients. Deviation of to the axis normal to the VCSEL. The amount of gradient the CS trajectory from the one imposed by external gradient is then controlled by the angle of incidence of the holding reﬂects the presence of a defect of the structure revealing its beam. A CS is then created by applying a 100 ns writing beam attractive or repulsive character. As a consequence, a map of pulse at some point of the microresonator. This CS drifts as the inhomogeneities of the device is given by the frequency a consequence of the presence of a phase gradient along the of visits of the areas of the device when the motion of CSs is line deﬁned by the cylindrical lens and its passage is detected imposed across the entire section of the system. by the fast photodiodes. The detected output intensity as The experimental setup used in [63] to record the map a function of time is displaced depending on the detector of inhomogeneities is similar to the one described in the considered, as can be seen in Figure 11. It is clear then that previous section. The motion of the CS is induced by creating the CS generated at one point in the transverse section of a gradient in the transverse direction to the propagation of the device is drifting along a line and detected sequentially light. In particular, a spatial modulation of the holding beam by the ﬁve fast detectors. Knowing the distance between intensity was introduced. In order to control the gradient the corresponding points detected by the fast photodiodes strength and position of the intensity maxima a Mach-Zen- (7 μm), the speed of the CS is measured as a function of der interferometer was inserted in the path of the holding the tilt-induced phase gradient. In the case represented in beam. The interferometer is set to generate an intensity Figure 11, the average speed of the CS is 4.7 μm/ns. The proﬁle on the VCSEL formed by fringes of 10 μmsize. The observation provides a proof-of-principle for an all optical pattern allows conﬁning the position of CSs along the direc- delay line based on the property of motion of the CS under tion perpendicular to the fringe. No gradient is present in the inﬂuence of a phase gradient. principle along each interference fringe. In such conditions, The experimental results obtained in [110] are in good only the imposed intensity gradient or intrinsic gradients in agreement with numerical ones obtained by integration of the device can induce a motion of the CS. The fringes are a semiclassical model. In Figure 12, numerical results are adiabatically shifted horizontally by just moving a mirror shown corresponding to the speed of CS as a function of of the Mach-Zender interferometer controlled by a PZT the gradient strength which are compatible with the experi- ceramics. The CS is expected to be dragged in a straight line mental ones. For a large interval of the gradient strength, the while the fringe is moved, but it was observed that it deviates velocity of the CS is almost linear and can be easily controlled from this line. The deviation is attributed to the presence between 1 and 4 micrometer/ns. This is much smaller than of internal gradients generated by defects in the device. those obtained on the devices based on slowing down the The procedure was repeated for diﬀerent orientation of the speed of light by changing the index of refraction of the fringes. For an ideal defect-free medium, such analysis would medium. Furthermore, those theoretical results indicate that result in a uniformly gray map. As long as inhomogeneities the speed of the CS can be increased by increasing the decay rate γ of the carrier density in the semiconductor device are present, some regions are visited very often by the CS while others are almost never visited. Thus, high-intensity (Figure 12(b)). The system proposed in [110]providesnot only an operation of the device as an all optical delay line but regions in the map correspond to attractive defects while Advances in Optical Technologies 13 0.12 0.1 0.08 AB CD E 0.06 0.04 0.02 80 90 100 110 120 130 Time (ns) (a) (b) Figure 11: Passage of a CS in front of a linear array of ﬁve detectors (A)–(E). (a) Time traces of these detectors, displaced vertically by 0.02 units for clarity. Detector A monitors the point addressed by the writing beam, applied at time t = 0. (b) Positions of the detectors in the transverse plane (indicated by squares). The area monitored by each detector has a diameter of less than 7.2 μm and the separation between neighboring detectors is 8.9 μm. Also shown is a time-averaged output image of the VCSEL during the CS drift (charge coupled device camera exposure time of about 1 ms). Figure reproduced from [110]. θ =−2 θ =−1.83 −1 −2 −4 −2 024 02468 10 12 14 Log (γ) 4 −1 K/(10 m ) Large gradient Small gradient Analytic (a) (b) Figure 12: (a) Drift speed versus phase gradient (wave-vector tilt of holding beam) for a scaled cavity photon to carrier recombination rate −1 γ = 0.01 (corresponding to a nonradiative carrier lifetime of 1 ns ) and two-cavity detuning values. The cavity photon lifetime is 10 ps. (b) 4 −1 Log-log plot of CS drift speed versus γ for a ﬁxed scaled detuning (θ =−2) and for two values of the gradient: (stars) K = 2.38 × 10 m ; 5 −1 (diamonds) K = 1.91 × 10 m . Here, the cavity photon lifetime is 1.5 ps. Figure reproduced from [110]. −1 Velocity (μmns ) Intensity (a.u.) −1 Log (velocity) (μmns ) 14 Advances in Optical Technologies (a) (b) (c) Figure 13: (a) Spontaneous emission proﬁle of the VCSEL. (b) CSs trajectories when dragged toward the left. (c) Map of the defects in the VCSEL structure as the result of the complete analysis of the CSs trajectories. After [62]. low-intensity regions to repulsive ones. The experimental 6. Prospects and New Developments map is shown in Figure 13 with an inverted contrast. [63] The previous demonstrations of CS using VCSEL devices, gives a clear proof of the possibility to use the motion either in the optical ampliﬁer or laser regimes, relied on properties of localized structures in order to determine the absorptive or gain nonlinearities. CS were observed in the position and strength of defects in semiconductor devices. optical ﬁeld intensity and carrier density components. Sev- The spatial resolution is determined by the size of the CS eral other interesting new directions have been stimulated by which is in this experiment of the order of 10 μm. Such a these ﬁndings, exploring self-localization of diﬀerent degrees spatial resolution could in principle be increased by working of freedom, using diﬀerent nonlinearities (see, e.g., [113– in a diﬀerent region of parameter space or using devices 115] for theoretical studies of CS in quantum dot materials) emitting at shorter wavelength. However, the strength of the or extrapolating the CS concept to three dimensions. In the proposed method lies in the sensitivity of the CS trajectory following, we describe the advances in the ﬁelds of polariza- to any gradient, should they be smaller than the CS size tion CS, cavity soliton polariton and cavity light bullets. itself. The practical limitation comes from the preparation of the external gradient and therefore, the quality of the optics that limits the uniformity of the holding beam. Moreover, 6.1. Polarization CS. Due to the generally circular aperture of the method not only allows to detect surface defects, but VCSELs, polarization of the emission is not constrained into also can probe bulk defects in the device. This technique a single direction as in edge-emitting lasers but rather may has been called soliton force microscopy, since it uses the vary in the whole output plane, depending on the operating various potentials felt by CSs in the VCSEL to reveal the conditions (temperature and injection level). This fact has map of defects. A similar dragging of CS has also been been long recognized and studied in real devices [116–118]. demonstrated in [54] in a CSL with ﬁltered feedback. In The understanding of the polarization dynamics in VCSELs this latter system, an attempt to control the inhomogeneities has been the subject of many theoretical studies and a model has also been undertaken in [101] using a Spatial Light [119] now well accepted has emerged, the so-called spin ﬂip Modulator. The idea is to create with an additional, spatially model (SFM). Whereas polarization control of VCSELs has patterned, control beam a gradient that counteracts the represented a major goal of research, polarization switches eﬀect of the local inhomogeneities by locally varying the can also be used in optical communications schemes [120, refractive index. This results in displaced hysteresis cycles for 121], where stochastic resonance in the polarization dynam- individual CSs allowing two CSs initially not simultaneously ics enhances transmission of binary information. The light bistable to become controllable in the same parameter emitted by a VCSEL is,s in general polarized along one of regions. the two crystallographic directions [110] or [110] because of Another interesting aspects of defects in VCSEL devices crystal anisotropies, and since these anisotropies are weak, it has been unveiled in [64, 112]. Indeed, defects can under is possible to control the state of emitted polarization. This is certain circumstances be the source of CSs that may subse- also true in broad-area devices [122], while the situation may quently drift under a gradient, being a controlled gradient or be more complex for highly divergent modes in even larger a cavity resonance gradient. This results in the appearance devices [123]. In VCSELs with cylindrical symmetry, optical of an almost periodic source of drifting localized states. The injection [124] or feedback [125, 126]can be employed average period can be controlled by the phase gradient or to control the polarization of light. Since polarized optical by the kind of defect itself. Drifting excitations were also injection or optical feedback can both induce bistability found in a CSL with ﬁltered feedback in [81], while the CS [127, 128], all the necessary ingredients are available for properties remained to be established. CS formation in large-aperture devices. Polarization CS Advances in Optical Technologies 15 0.3 0.2 0.1 (b) −0.1 −0.2 −0.3 −0.4 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 Ba i s current (mA) (a) (c) Figure 14: Near-ﬁeld image of the VCSEL surface when injected by an orthogonally polarized holding beam in the lower (c) and upper (b) branch of the bistability curve (a) obtained by ramping the injected current in the laser. Reprinted with permission from [131]. ( c 2011) by the American Physical Society. could oﬀer the practical advantage of ultrafast switching with Ginzburg-Landau equation [139, 140], a model used to de- low switching energy as was demonstrated in small polariza- scribe pulses in mode-locked lasers with a fast saturable tion-bistable devices [129]. Polarization CS were predicted absorber. Cavity light bullets share the same properties as theoretically in [130]inaKerr cavity with diﬀerent losses for dissipative light bullets, in the sense that they are 3D non- the two polarization components of the ﬁeld. They have been linearly localized states of light. However, CLBs form in a experimentally investigated in [131]ina40 μm diameter cavity and are thus not freely propagating. CLBs have been VCSEL. The laser, which is shown to emit in a well-deﬁned proposed and theoretically demonstrated in an extended polarization state just above the laser threshold, is injected cavity ﬁlled with a saturable absorber medium [141, 142] by an orthogonally polarized holding beam. A localized state injected by a holding beam. It was shown that under certain that sits in the center of the device spontaneously switches circumstances, spatial ﬁlament solitons can destabilize in the on and displays a bistable behavior when the injected propagation direction and form a 3D soliton (cf. Figure 15). current is ramped (see Figure 14). These results, though not These CLBs are addressable and independently controllable demonstrating the independence of the localized state from as their 2D counterpart. An important feature is that they sit the boundaries principally because of the moderate size of on a non zero background, the stable uniform steady-state. the laser used in the experiment, are encouraging steps to- CLBs have also been studied in a similar model including wards the demonstration of polarization CS in VCSELs. a Kerr focusing nonlinearity, showing that the unstable 3D localized structures then formed can be stabilized via higher- 6.2. Cavity Light Bullets. Self-localization of light in 3D order processes such as multiphoton absorption [143]. A remains an open challenge [132–136]. The idea of combining model more suitable for semiconductor systems was studied the characteristics of a spatial soliton with those of a temporal in [144] with MQWs as the nonlinear material. The model soliton has been proposed more than 20 years ago [137], showed that the formation of CLBs requires fast carrier and the corresponding object has been termed a light bullet. recombination times, since otherwise, the carrier dynamics Light bullets are self-localized states of light in space and lags behind the photon dynamics and prevents the formation time that keep their spatial and temporal proﬁle in the of a CLB. course of propagation: self-focusing can compensate for CLBs are a theoretical as well as experimental challenge. diﬀraction and at the same time group velocity dispersion While the choice of a VCSEL for CS studies in semiconductor systems seems obvious, a variety of semiconductor devices can be compensated by self-phase modulation. Because of the particle-like behavior of optical solitons, 3D self-localized may eventually be used for CLB studies. Among these, states of light would be intriguing objects possibly leading bisection edge-emitting lasers are good candidates [145]. to new application breakthroughs [138]. Dissipative light Freely propagating light bullets have also been investigated bullets are often considered in the context of the complex theoretically in nonlinear waveguide arrays, which can be Intensity (a.u.) 16 Advances in Optical Technologies yyyyy (a) (b) t.u. = 0.3 t.u. = 1.3 Regime (more than 600 t.u.) 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 z z z 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 2468 10 2468 10 2468 10 x x x (c) Figure 15: (a, b) Snapshot of 3D ﬁlaments and self-conﬁned states in an extended cavity with transverse directions (x, y) and propagation direction z. (c) Three snapshots of a 1D transverse cavity after injection of a writing beam: t = 0.3, initial injection; t = 1.3, destabilization of the longitudinally uniform solution; t> 600, two independent CLBs are formed and propagate in the cavity. Reprinted with permission from [141]. ( 2011) by the American Physical Society. easily realized in semiconductor materials, in [146–148]and the stability of multifrequency laser CSs. The observations in Bragg gratings [149]. can then be interpreted in terms of partially phase-locked However, the extended cavity conﬁgurations used in external cavity-modes giving rise to quasiperiodically or ir- Section 4 could reveal very interesting regarding CLB dem- regularly pulsing multifrequency laser CSs sitting on a non- onstration. The idea is to extend the VCSEL cavity to allow zero background. for multiple longitudinal modes and temporal mode-locking Self-pulsing localized laser structures are also observed in to take place, while preserving a high Fresnel number VCSEL-based schemes with a saturable absorber. In a mono- ensuring the possibility of multitransverse mode operation lithic vertical cavity laser with saturable absorber [73], self- [150]. In this conﬁguration, a CLB can be viewed as a mode- pulsing localized states are observed. The physical origin of locked 2D CS. In [83, 151, 152], using a VCSEL with a self-pulsing in that case has to be attributed to a Q-switching frequency selective feedback by a volume Bragg grating in instability since the cavity has a single-longitudinal mode. the self-imaging conﬁguration, it was shown that depending The observed behavior is consistent with the experimental on the writing pulse intensity a transient multiple frequency observations. In a face to face VCSEL conﬁguration, self- laser CS can be switched on. In most cases the transient pulsing optical structures have been observed [85]witha oscillations die away after several tens of ns and the ﬁnal pulsing period of 400 ps corresponding to the cavity round- state is a steady, cw laser CS. However, for a high writing trip time. The physical mechanism for self-pulsing is thus in pulse intensity an oscillating laser CS can stabilize with a that case similar to that of the frequency-selective feedback frequency of 3.8 GHz. Because of experimental limitations experiment describes earlier. In both cases, the self-pulsing the modulation depth of the oscillation is not known. state could not be controlled by an external beam and was not Numerical simulations of the system [153] are in fairly good bistable anymore. Control by an external beam of an irreg- qualitative agreement with the observed behavior and predict ular self-pulsing state has nevertheless been shown in [73]. Advances in Optical Technologies 17 It has been obtained on a structure composed of several localized spots but the physical mechanism at stake is not 0.4 clear at the moment. These states are, however, not CLBs, be- cause they develop in microcavities, but they probably con- stitute a good starting point for further investigation in an 0.2 extended conﬁguration. Research on VCSEL-based CLBs is thus concentrated for the moment on extended cavity schemes. While there has been some interesting and encouraging results so far, no conclusive result has been obtained though. One reason lies certainly in the theoretical and numerical diﬃculty in mod- eling semiconductor extended cavity systems, since they are nonlinear, multilongitudinal and—transverse mode systems. Moreover, the CLBs obtained this way seem rather diﬀerent 0 from the original theoretical proposition in [141], and the Figure 16: 2D self-localized bright CS polariton as predicted in link to the Ginzburg-Landau type approach to light bullets [170]. Reprinted with permission from [170]. ( c 2011) by the is not completely clear either. It is anticipated that further American Physical Society. studies in the ﬁeld will help clarify all the physics and the properties of these new self-localized objects and maybe help improve the theoretical comprehension and modeling of semiconductor-based mode-locked lasers [65, 66]. regime using the nonlinear bleaching of the Rabi-splitting [163] under high pumping excitation. However, there has 6.3. Cavity Soliton Polariton. Exciton polaritons (also called been no convincing experimental observations of such a more simply cavity polaritons or polaritons) are mixed light- mechanism so far. A few experimental observations are matter states arising when an exciton and a cavity-mode are associated with the simultaneous presence of the weak and strongly coupled ([154, 155] for a recent review). These states strong coupling signatures in the spectrum, and bistability appear when a photon coming from the recombination of is associated to the bare cavity mode [164, 165]. Bistability an exciton (a bound electron-hole pair) is reabsorbed and has also been observed in a polariton diode [166], where the reemitted several times before the photon escapes from the intracavity electric ﬁeld is responsible for the strong to weak microcavity. The cavity-exciton coupling gives rise to two coupling abrupt switching. resonances separated by the so-called Rabi splitting observed Bistability being again one key ingredient for CS for- in the reﬂectivity spectrum of the microcavity, through a mation, several authors have studied how nonlinear and mechanism analogous to the anticrossing in the eigenener- spatial eﬀects (diﬀraction in particular) can mix to allow self- gies of a system composed of two coupled oscillators. This localized states appearance. Indications of self-localization normal-mode coupling [156] is characterized by the disper- were reported in [167], where local bistability, as well as sion curve depicted, for example, in Figure 1(a) in [157]. localized bright and dark optical structures are reported in Exciton polaritons are fascinating quantum objects with a microcavity with several QWs as active medium, brought bosonic properties in which Bose-Einstein condensation was to low temperature (4 K). However, a clear demonstration of recently observed [158] at temperatures much higher than polariton CS is missing, since no demonstration of indepen- in atomic clouds (and even at room temperature in [159]). dent excitation has been reported. All these results stimulated An important feature in the context of CS is the giant theoretical work on polariton CS. In addition to the large χ -type nonlinearity exhibited by exciton polaritons due optical nonlinearity exhibited in this system, which is in- to the coherent polariton-polariton scattering: two pump teresting because it allows the realization of low pump- polaritons with in-plane wave vector k can scatter in one power nonlinear optical devices [168], exciton polariton- polariton with in-plane wave vector 2k and one with 0 in- based systems are expected to display very fast switching plane wave-vector. This coherent process must fulﬁll phase times too [169], a few orders of magnitude smaller than in matching and energy conservation conditions, and can be the weak-coupling regime. Moreover, the quantum nature of obtained in two diﬀerent ways. The ﬁrst one, in the degen- exciton polaritons could open new prospects in the ﬁeld of erate case, with normal incidence pump beam which gives CS applied to information processing or parallel compu- rise to an optical nonlinearity analogous to a Kerr nonlin- tation though practical schemes are not very clear at the earity, with the diﬀerence that the index of refraction no moment (Figure 16). longer depends on the input beam intensity but rather on Dark polariton solitons were ﬁrst predicted to appear the polariton density. The second one in the nondegenerate [171] in a cavity sustaining exciton polaritons, when the case in a parametric ampliﬁcation conﬁguration, at the so- lower polariton branch is excited at normal incidence. The called “magic-angle” (inﬂection point in the lower-polariton fact that bright CS polaritons were found to be unstable in dispersion curve) with nonzero pump wave vector [160]. that case is related to the defocusing nature of the exciton- Bistability has been observed in both the degenerate [161] polariton nonlinearity. Using the dispersion properties of the and the nondegenerate case [162]. Another mechanism is lower polariton branch near its inﬂection point (|k| 1in also predicted to lead to bistability in the strong coupling Figure 1(a)) in [157]), it was later shown [172] that 1D bright | Ψ | 18 Advances in Optical Technologies CS polaritons could be obtained. The stabilization of these saturableabsorber,”in Localized States in Physics: Solitons and Patterns, O. Descalzi, M. Clerc, S. Residori, and G. Assanto, states rely on the existence of higher-order spatial dispersion Eds., pp. 187–211, Springer, Berlin Heidelberg, Germany, terms that can counteract the repulsive nonlinearity. These CS polaritons are moving objects, since the ﬁrst order [3] T. Ackemann, W. J. Firth, and G. L. Oppo, “Fundamental- dispersion is nonzero at the inﬂection point. In 2D, use of sand applications of spatial dissipative solitons in photonic a conﬁning potential in the perpendicular direction to the devices,” in Advances in Atomic Molecular and Optical Physics, inclined pump beam has been proposed to obtain 2D P. R. B. E. Arimondo and C. C. Lin, Eds., vol. 57 of AdvancesIn localized states. The authors claim that their theoretical pre- Atomic,Molecular,and OpticalPhysics, chapter 6, pp. 323– dictions are in good agreement with the almost simultaneous 421, Academic Press, 2009. experimental observation reported in [157]ofmoving [4] R. Kuszelewicza, S. Barbay, G. Tissoni, and G. Almuneau, “quasilocalized” polaritons. The latter authors have however “Editorial on dissipative optical solitons,” European Physical adiﬀerent interpretation in terms of the straightening of the Journal D, vol. 59, no. 1, pp. 1–2, 2010. [5] H.G.Solari,M.Natiello, andG.Mindlin, Nonlinear Dynam- Bogolyubov dispersion in superﬂuids. ics: A Two-Way Trip from Physics to Math, IOP Publishers, In spite of the opposite signs of dispersion in polaritons London, UK, 1996. excited close to the magic angle, truly 2D self-conﬁned [6] R. Gilmore and M. Lefranc, The Topology of Chaos, Alice in polaritons have nevertheless been obtained numerically in a Stretch and Squeeze land, Wiley, New York, NY, USA, 2002. recent work [170]. Starting from the 1D bright CS polariton [7] F. Moss, L. A. Lugiato, and W. Schleigh, Eds., Noise and Chaos conditions demonstrated in [172], the authors show that in Nonlinear Dynamical Systems, Cambridge University Press, there exists a range of excitation intensities for which New York, NY, USA, 1990. the width of the localized state remains constant in both [8] B. Belousov, “A periodic reaction and its mechanism,” in directions. While in the propagation direction the explana- Oscillationsand Traveling Waves in Chemical Systems,R.Field tion for self-localization remains the same as in the 1D case, and M. Burger, Eds., pp. 605–613, Wiley, New York, NY, USA, in the perpendicular direction self-localization is attributed to the parametric nonlinearity: the 2D CS polariton is thus [9] J. C. Roux, R. H. Simoyi, and H. L. Swinney, “Observation of a strange attractor,” Physica D, vol. 8, no. 1-2, pp. 257–266, stable in both directions thanks to diﬀerent physical mecha- nisms, each of them sustaining their family of 1D self-local- [10] F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, “Exper- ized states. imental evidence of subharmonic bifurcations, multistability, Other theoretical studies have focused on diﬀerent phys- and turbulence in a Q-switched gas laser,” Physical Review ical mechanism for CS polariton formation. In [173], taking Letters, vol. 49, no. 17, pp. 1217–1220, 1982. into account the polarization degree of freedom of exciton [11] N. B. Abraham, P. Mandel, and L. M. Narducci, “I dynamical polaritons, the authors show 1D vectorial bright and dark instabilities and pulsations in lasers,” Progress in Optics, vol. CS polaritons formation. Exploring in [174] the saturation 25, pp. 1–190, 1988. of exciton-photon coupling, the author shows that normal [12] F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, incidence, resting CS polaritons may exist. 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Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2011 S. Barbay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ISSN: 1687-6393
DOI: 10.1155/2011/628761
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Abstract

Hindawi Publishing Corporation Advances in Optical Technologies Volume 2011, Article ID 628761, 23 pages doi:10.1155/2011/628761 Review Article 1 1 2 S. Barbay, R. Kuszelewicz, and J. R. Tredicce LaboratoiredePhotoniqueetdeNanostructures, CNRS-UPR20, RoutedeNozay,91460 Marcoussis, France Institut Non Lin´eaire de Nice, UMR6618 CNRS-Universit´e de Nice Sophia-Antipolis, 1361 Route de Lucioles, 06 560 Valbonne, France Correspondence should be addressed to S. Barbay, sylvain.barbay@lpn.cnrs.fr Received 20 June 2011; Accepted 9 August 2011 Academic Editor: Krassimir Panajotov Copyright © 2011 S. Barbay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We review advances on the experimental study of cavity solitons in VCSELs in the past decade. We emphasize on the design and fabrication of electrically or optically pumped broad-area VCSELs used for CSs formation and review diﬀerent experimental conﬁgurations. Potential applications of CSs in the ﬁeld of photonics are discussed, in particular the use of CSs for all-optical processing of information and for VCSELs characterization. Prospects on self-localization studies based on vertical cavity devices involving new physical mechanisms are also given. 1. Introduction e.g., [7–9]). Optics was not an exception. After the report of period doubling and chaos in a modulated laser [10], several In this paper we address experimental results on Cavity Sol- papers showed theoretically and experimentally the appear- itons (CS) in VCSEL devices and focus on recent studies and ance of instabilities in optical systems [11]. In particular, developments. We emphasize on the design and fabrication laser with injected signal and optical ampliﬁers have been of electrically or optically pumped broad-area VCSELs used exhaustively studied [12–17]. Dynamics of semiconductor for CS formation and review diﬀerent experimental conﬁg- lasers under injection and delayed optical feedback were urations. Applications of CS in the ﬁeld of photonics are also objects of interests mainly because of the possible discussed, in particular the potential use of CS for all-optical applications of such devices in optical communication processing of information and for VCSEL characterization. systems [18–20]. Later, mainly during the 90s, the interest Prospects on self-localization studies based on vertical cavity shifted towards spatiotemporal instabilities. The possibility devices involving new physical mechanisms are also given. of observing optical vortices [21] and ﬁnally reach optical The reader interested in the theory of CS formation in turbulence was very attractive, because optical systems were semiconductor devices can refer to recent reviews on the somehow easier to model than hydrodynamical ones. Thus, subject [1, 2] and also to [3]which provides ageneral review the comparison between experimental and theoretical results on CSs and their applications to photonics from a more was simpler than in other more complex systems. Several fundamental viewpoint. A collection of articles on the most studies reported the appearance of complex spatio-temporal recent developments in the ﬁeld can also be found in [4]. Our dynamics in optics [22–24] and in particular in laser systems goal is to provide a complete and accessible review on past [25–28]. Most of the experiments realized with broad area and most recent experimental results on CSs using vertical lasers, thus with a large transverse section or high Fresnel cavity semiconductor devices, while giving a prospect on number, showed the appearance of large structures more future directions. or less complex but almost always with long correlation During the 80s, the main focus of experimental studies length in the transverse plane and, therefore, avoiding the on nonlinear dynamics was on temporal dynamics (see, e.g., appearance of a complex or turbulent behavior [29]. The [5, 6]). Observation of period doubling, quasiperiodicity, reasons for such long correlation order is mainly that it is intermittency, and chaos in a variety of systems ranging from somehow diﬃcult in lasers to reach a really high Fresnel ﬂuids to chemical reactions appeared in the literature (see, number, because cavity lengths are usually too long. In 2 Advances in Optical Technologies that sense, VCSEL represents an ideal laser to study spatio- Swift-Hohenberg equation, a model equation that describes temporal dynamics. Eﬀective cavity lengths of the order of pattern forming systems and applicable in nonlinear optics 10 μm, active medium lengths of the order of a quarter-wave- [39]. The stability conditions for localized structures in 1D length, almost planar mirrors, and the possibility of having were theoretically studied in [43]. The authors then proved more than 150 μm in diameter makes this device an ideal theoretically that an inﬁnity of localized structures present- candidate to observe structures with very short correlation ing an arbitrary number of intensity peaks coexist and may length and, therefore, complex optical spatio-temporal struc- be stable for a ﬁnite range of parameter values. Later, a sim- tures. Several theoretical studies were centered around the ilar method was used to study the region of coexistence and formation of patterns in VCSELs [30–32]aswellassome the order of the solutions in parameter space [44, 45]. experimental ones [33–36]. The potential of CSs for applications to parallel infor- However, the most interesting results have been obtained mation processing was then recognized and demonstrated in in general models of lasers with saturable absorbers [37–39] [40] and analyzed in the context of a model suited for semi- or opticalabsorberorampliﬁer[32, 40, 41]. Numerical and conductor systems in [30]. CS can be excited and erased by a analytical results showed that it is possible to observe local- local perturbation at any transverse location of a nonlinear, ized structures in these optical systems. The main property broad-area cavity and as such play the role of pixels or spatial of a localized structure is that its correlation length is much logical bits. They can be manipulated in phase or intensity smaller than the size of the system. Thus, each localized gradients, where they can be moved or controlled, a property structure will behave as an independent object. In optics, that relaxes considerably the addressing constrains if one localized structures with a single intensity peak have been wished to arrange them into 2D matrices. called cavity solitons (CSs). Cavity solitons are self-localized The main advantages of semiconductor systems over states of light appearing in the transverse plane of a cavity as other optical systems, where CS were predicted and observed bright spots sitting on a dark background. Experimentally, lie in the fast timescales and small spatial scales associated they can be characterized by the following properties: (1) with CS formation in semiconductor materials. Indeed, the CSs are self-localized states, independent of the system characteristic timescale for CS formation in semiconductor boundaries whose shape and size is ﬁxed by the system systems is of the order of the carrier recombination time, parameters and do not depend on the excitation that gave which is in the nanosecond range, much shorter than other birth to them; (2) CSs can exist in several (ideally arbitrary) competing macroscopic systems based on photorefractive transverse locations of the cavity and can be independently media [48], liquid crystals [49], or atomic vapors [46]in manipulated (written, erased, ...); (3) CS can be “moved” which CS were also found. Moreover, the characteristic size or set into motion. At ﬁrst sight, they possess characteristics of aCSisgovernedbythe diﬀraction length a ∝ LλF , resembling those of self-trapped beams [42] but constrained where L is the cavity length, λ the wavelength of light and within a cavity whose propagation path is folded by the cavity F the resonator ﬁnesse and is of the order of 10 μmin mirrors. However, it is worthwhile to notice that single peak microcavities, at least one order of magnitude smaller than localized structures are diﬀerent from self-trapped beams, in other macroscopic systems. CS necessitate a large and uni- because they are created by two fronts connecting two form aspect ratio system: a cavity whose transverse extent is diﬀerent spatial solutions in a dissipative system. This feature much larger than the longitudinal extent such that it can host introduces important physical diﬀerences; however, that can many transverse modes and allow for spatial decorrelation be fully appreciated only when considering rather subtle between diﬀerent cavity locations. Therefore, broad-area theories on CS formation [43, 44]. Some of these physical VCSELs appear then as ideal devices to implement CS in diﬀerences were experimentally observed in a semiconduct- semiconductor material systems. The ﬁrst demonstration of or-based system in [45]. On the other hand, the presence CS in a broad-area VCSEL that stimulated all the ensuing of a cavity is not necessary either as demonstrated by the investigations was reported in [50]. observation of single peak localized structures in [46]ina This paper is organized as follows. We present in Section single feedback mirror experiment performed in Na vapour. 2 the characteristics of broad-area VCSELs with electrical Thus, CS may be better called single peak localized structure injection and optical pumping designed for CS studies. In (SPLS), but we will use both names in this review. Section 3, we then describe experimental results obtained in CS arise usually under the condition of coexistence of a the amplifying regime, with a cavity driven by an external homogeneous and a patterned stationary state; for the same coherent beam (holding beam). An important new concep- control parameter values, the solution may approach one or tual and applicative step was obtained by the demonstration the other state depending upon the initial condition. Lo- of a CS laser, that is, a system that does not require a coherent calized structures are thus somehow intermediate, control- optical injection and emits self-localized microlasers having lable states between the homogeneous state and the fully the properties of the CSs described earlier, as explained developed pattern. SPLS may also exist in optical systems, in Section 4. Possible applications of CS to photonics are where two uniform states coexist, as a result of the locking presented in Section 5 with the experimental demonstrations of two fronts. This mechanism was ﬁrst studied theoretically of an optical delay line and of a soliton force microscope. and numerically in [47] where self-localized states (then The role of device defects and the applications of CS to called “diﬀractive autosolitons”) were demonstrated to exist device homogeneity characterization are also demonstrated. in a nonlinear, bistable, interferometer. Self-localized states Finally, new directions in the ﬁeld of self-localized states were also found in the more general framework of the using VCSELs are presented in Section 6. We analyze CS Advances in Optical Technologies 3 side of the VCSEL, the substrate is thinned down to 180 μm p-type bragg reﬂector Cu heat sink and antireﬂection coated in order to avoid back reﬂection TiPtAu contact Active QWs from the air-semiconductor interface into the gain medium. The diamond can then be attached to a copper submount Diamond heat spreader with a thermal paste. This design ensures a very good over- Oxide aperture AuSn solder all thermal conductivity of the VCSEL, compulsory for cw operation with large active areas. Cw operation was indeed GaAs substrate obtained for 200 μm or even higher diameter VCSELs with Al O 2 3 very good conversion eﬃciency and low threshold at room AR coating passivation layer GeNiAu contact temperature. In [53], the group at the University of Ulm re- n-type bragg reﬂector ported room-temperature, cw operation of 320 μmVCSELs Light output in diameter with a maximum output power of 0.89 W and a Figure 1: Schematic representation of a broad-area bottom emitter 2 current density at threshold of 1 kA/cm . VCSEL structure with diamond heat spreader, after [51]( c 2011 This VCSEL design has been successfully employed for IEEE). the ﬁrst demonstration of cavity solitons in a semiconductor optical ampliﬁer [50], and subsequent studies on cavity soli- tonlasersinanextendedconﬁgurationwithafeedback grat- ing [54] or face-to-face conﬁguration [55] (see Section 4). in polarization, Cavity Light Bullets which are 3D-localized While a VCSEL possesses in theory a translational sym- states of light traveling in a cavity and CS polaritons which metry across its useful aperture, this is not the case in prac- explore new material nonlinearities. tice, and this has important consequences for CS studies. There are indeed two main types of spatial nonuniformities 2. VCSEL Fabrication and Design for to consider: extended nonuniformities such as those of the CS Formation cavity resonance wavelength and of the pump, and localized nonuniformities. Because of the growth conditions, layer Broad-area VCSELs play an important role in the develop- thicknesses vary over the substrate that results in the appear- ment of CS studies in semiconductor systems. However, it ance of a wedge along a given direction. This wedge does not was necessary to develop adequate devices, and there were aﬀect much the spectral characteristics of the Bragg mirrors; major challenges to deal with, namely, uniformity (concern- however, the gradient in the cavity thickness translates into ing pumping and cavity resonance) and thermal manage- a cavity resonance wavelength gradient. The eﬀect is all the ment. In the following, we review two solutions that have more important when dealing with broad area devices, be- been proposed and used for CS experimental studies, one causethencavityresonance canvaryappreciablyacrossthe with electrical injection and the other with optical injection. VCSEL optical aperture. Since CS are sensitive to any pa- The two approaches are presented and the various pros and rameter gradients [40, 56, 57], this may have major impact cons are discussed. on their observation and control. In the seminal experiment on CS in VCSELs [50, 58], a large cavity resonance gra- 2.1. Electrically Pumped Broad-Area Devices. The bottom dient of 2.34 GHz/μm was measured which prevented the emitter VCSEL structure is represented on Figure 1,ade- observation of cavity solitons over the entire VCSEL surface. Later, improvements in the growth conditions enhanced tailed description and characterization of which can be found in [51, 52]. The VCSEL is designed for laser operation around the VCSEL uniformity of about one order of magnitude 980 nm and optimized for high-power, cw emission. The (0.4 GHz/μm[59]) and allowed the manipulation of CS active zone is composed of three InGaAs/GaAs quantum over the whole transverse extent of the VCSEL. As for the wells, embedded in an AlGaAs spacer to fabricate the one- pump uniformity, the bottom emitting structure allows to wavelength thick cavity. Two high reﬂectivity Al Ga As/ achieve a very good uniformity at the center of the device, 0.9 0.1 GaAs Bragg mirrors close the cavity. The top mirror is p- whereas the borders suﬀer the well-known current crowding doped with Carbon, while the back mirror is n-doped with eﬀect [60]. This manifests itself through the appearance of a high-order ﬂower-like pattern [35] just above the laser silicon. The back and front mirrors have respectively, 30 and 24.5 pairs of quarter wavelength-thick layers at the targeted threshold and limits the available area for CS manipulation. cavity resonance of 980 nm. The whole cavity is grown on However, since bottom emitting devices grown on a GaAs substrate are limited to wavelengths above 900 nm to avoid a GaAs substrate using molecular beam epithaxy (MBE). Circular mesas of diameter ranging from 100 to 250 μmare absorption, shorter emission devices may require adopting then etched in the structure before oxidization of the current other techniques. As an example, electrode patterning and aperture down to the beginning of the back mirror, where use of semitransparent ITO electrodes were considered for a thin (30 nm) AlAs layer has been included. This layer is the design of 850 nm, broad-area top emitting devices [61] and proved promising for improving electrical injection oxidized in a water-nitrogen environment at high temper- ature, leaving an oxidized ring of 25 μm width. A TiPtAu uniformity of top-emitters. A by-product of this technique contact is then deposited on top of the mesa and the device would also be the possibility to address CS electrically with local electrodes. Electrode patterning was also used in [62] is soldered on the heat sink. Heat sinking is provided by metalized diamond sinks soldered with AuSn. On the other on a 960 nm top emitting VCSEL in the optical ampliﬁer 4 Advances in Optical Technologies regime. Bistability and optical pattern formation which are the crystal lattice (see Figure 2). At the end of the process, all prerequisites for CS formation were observed. However, the the excess energy is transformed into heat and transferred to insuﬃcient transverse extension of the VCSEL together with the lattice. There is very little to do against this fundamental the rather large grid period (4 μm) prevented CS formation mechanism except reducing the photon energy excess by on a uniformly injected background. choosing a proper wavelength. The spatially localized sources of nonuniformity that As a result, an eﬃcient optical design must minimize heat have also to be taken into account for CS studies are often production and optimize pump absorption into the gain termed as defects, and may precisely arise from crystallo- region. Such a design has been proposed in [67]and suc- graphic defects in the Bragg mirror materials or in the Quan- cessfully applied to CS studies in [68] in the AlGaAs material tum wells, and lead to CS pinning. More detailed studies on system. the sample uniformity have been conducted in [63], where The design relies on the creation of a window at the pump CS were used as a spatial probe for defects, and in [64], where wavelength around 800 nm. The pump window corresponds localized defects where used as a source of drifting CS. These to a region in the optical spectrum of the cavity where trans- aspects are detailed in Section 5.2. mission is minimized and pump absorption is maximized, while keeping the cavity properties at the operating wave- 2.2. Optically Pumped Broad-Area Devices. An alternative length of 870 nm unchanged. This is accomplished by an op- timization procedure on the layer thicknesses composing the scheme for CS studies relies on the use of optically pumped devices. It may seem at ﬁrst rather incongruous to deal multilayer mirrors of the cavity. Target values of the trans- with optically pumped VCSELs while electrical injection has mission, reﬂection, and absorption spectra in given spectral regions are chosen. The procedure starts with a quarter- always represented the ultimate goal in devices. However, the advent of high-power low-cost sources could make it a wavelength Al Ga As/AlAs multilayer stack centered at 0.225 0.775 reasonable choice, all the more that integrated and compact 870 nm. Then, all the layers composing the back and front sources can be fabricated. There are several advantages in multilayer mirrors are allowed to vary in order to reach the using optical pumping for CS formation and studies. The desired spectral targets. This is simply done by minimizing an error function that measures the deviation from the ideal ﬁrst one is that optical pumping allows to easily shape the pump beam using conventional optics and to get rid of target and the actual values, depending on all the layer current crowding eﬀects by using, for example, a top-hat thicknesses. A Simplex algorithm is used as a minimization algorithm. The algorithm eventually converges towards a set shape illumination. Since the processing steps after the device growth are reduced, the second advantage one can expect is of layer thicknesses values (see Figure 2(b)). As can be readily to reduce the number of defects, and thereby the stress on the seen, all the layer thicknesses have diﬀerent values and the ﬁnal sample, hence the number of pinning sources. The third initial periodic structure is lost. but not the least advantage is that the pump ﬁeld may be The calculated structure has been grown by metal- shaped not only in the transverse but also in the propagation organic chemical vapor deposition and the reﬂectivity and directions, as will be described further in the text and used calculated spectra are shown on Figure 3. There is a very in Section 4 to design new compact devices. Note also that good agreement between the calculated and the measured reﬂectivity spectra. The pump window is easily seen on the optical pumping is commonly used in VECSELs for high power lasers [65, 66] and may also be used in the framework left around 800 nm, where absorption is maximized and of studies on CLB (see Section 6.2). There are, however, at the same time pump transmission into the substrate is minimized. The cavity resonance structure at 890 nm is kept. problems to be circumvented in order for optical pumping to be a viable solution. The most important problem is the This design ensures that very few pump photons will be thermal management, to be addressed along its two com- absorbed into the substrate and contribute to heating while ponents: heat production and heat dissipation. It is all the optimizing the pumping eﬃciency. The width of the pump more important here as we consider broad area devices. Heat window is 20 nm which introduces immunity against even- tual temperature induced shifts of the reﬂectivity spectra dissipation is common to the electrical pumping case and the same techniques can be somehow applied. On the converse, through temperature-induced index change and subsequent heat production is largely speciﬁc and depends on the dramatic eﬀects on the pumping level. It also allows pumping with a large numerical aperture microscope objective or lens. material system considered. In some systems where all the pump power is not absorbed in the gain region, the substrate The VCSEL can then be processed with other techniques absorption at the pump wavelength may represent the major to enhanceheatremoval,suchassubstrate removaland replacement with a high thermal conductivity substrate such part of the heat production. Therefore, a special care has to be taken to avoid it while optimizing the pump absorption in as SiC substrate or diamond substrate. Note that this tech- the gain medium. The second contribution to heat produc- nique does not prevents heat absorption into the substrate, tion (and to pump energy waste) is the so-called quantum since, in general, the bonding layers absorb very eﬃciently defect, that is, the energy diﬀerence between the pump the pump photons. Substrate removal and SiC bonding with Ti-InAu bonding has been employed in the sample used in energy and the laser transition (usually close to the bandgap of the semiconductor material). Pump photons absorbed by [68]. the semiconductor material produce electron-hole pairs at The same design technique has been used and reﬁned to fabricate a monolithic VCSEL with intracavity saturable an energy higher than that of the band gap that cascade to the bottom of the bands through phonon exchange with absorber. VCSELs with intracavity saturable absorbers were Advances in Optical Technologies 5 Active medium Back mirror Front mirror p 100 0 20 40 60 80 100 υ Layer number (a) (b) Figure 2: (a) Schematic representation of optical pumping in a semiconductor material: a pump photon of energy ω is absorbed in the semiconductor material creating an electron-hole pair. The electron and hole cascade to the bottom of the bands releasing extra energy to the lattice and eventually recombine either radiatively or nonradiatively. (b) (after [67]): Layer widths of the optimized structure. The substrate is on the left side of the ﬁgure. The cavity is ﬁlled by two absorbing Al Ga As spacers (layers 61 and 63) white bars around a bulk GaAs 0.07 0.93 active layer (layer 62, in black). The back and front Bragg mirrors are composed of alternating Al Ga As (dark gray) and AlAs (light 0.22 0.78 gray) layers. suited for CS studies. An original design for a vertical cavity laser with intracavity saturable absorber has been proposed in [73]. Using the same technique as explained before, a 0.8 cavity having a saturable absorber section and a gain section is designed. The gain region has two InGaAs/GaAs QW for 0.6 lasing around 980 nm. The saturable absorber section has one InGaAs/AlGaAs QW. All the QWs are placed at the antin- ode of the resonant cavity ﬁeld targeted at 980 nm. The cavity 0.4 is designed for optimized optical pumping around 800 nm. Therefore, in addition to the previous optimizations, the 0.2 multilayer mirror widths have also to be calculated in order to satisfy a condition on the pump ﬁeld intensity inside the active zone of the cavity. The pump ﬁeld in almost zero in the 780 800 820 840 860 880 900 920 940 whole pump window at the location of the SA QW. The gain λ (nm) QW barriers absorb the 800 nm pump ﬁeld, whereas the SA QW barriers are made transparent to the pump wavelength Figure 3: Calculated and measured spectra of the optimized cavity. in the pumping window by aluminium incorporation inside Red line: experimental reﬂectivity spectra. Black line: correspond- the barriers. The design is depicted in Figure 4 and has been ing calculated reﬂectivity spectrum. Brown: calculated absorption. successfully used to demonstrate bistability, self-pulsing, and Dashed blue: calculated cavity transmission. a compact cavity soliton laser (see Section 4). 3. CS in Semiconductor Optical Ampliﬁers already considered in the prospect of building self-pulsing or bistable vertical-cavity lasers. Several designs have been The most studied system in optics is represented in Figure proposed for electrically injected devices. A quantum well 5. A nonlinear medium inside an optical cavity is driven by may for example be placed in the upper or lower mirror a homogeneous optical beam covering the whole transverse stack with a shorter carrier lifetime [69] or with an additional section of the device. The system can be set such that the contact for controllable operation [70]. Self-pulsing have also output intensity is zero and all the incoming beam is ab- been observed in small area, oxyde-conﬁned VCSELs thanks sorbed by the saturable medium. If the condition for the to the diﬀerence between the carrier and the optical mode bistable behavior is fulﬁlled, then a short and narrow optical conﬁnement [71]. A double cavity may also be used for pulse may ignite a small region of the device. Such an optical controllable self-pulsing or bistable operation [72]. These pulse is called the writing beam. If it is in phase with the hold- techniques necessitate either a small area cavity, a fast sat- ing beam, a CS is created at the location where it impinges urable absorber, or a complex electrical design and are not that persists after the writing pulse disappears. In a similar Layer width (nm) 6 Advances in Optical Technologies second output coming from the external cavity laser was then used as a coherent writing beam (WB). This beam was prepared so as to obtain a 10 μm waist; its power was con- trolled by an acousto-optic modulator. The phase relation between the writing beam and the holding beam was con- trolled by piezo-positioning a mirror on its own path. The reﬂected output of the VCSEL was monitored globally by a CCD camera or locally using a fast photodetector. The observation of CS in an electrically pumped VCSEL ampliﬁer [50, 58] and the demonstration of their mutual independence is explained in Figure 6. Similar results have been obtained in optically pumped VCSEL ampliﬁers [68]. The demonstration relies on the independent writing and 6400 6600 6800 7000 7200 7400 erasure of two CS at two diﬀerent locations of the VCSEL. Z (nm) In the ﬁrst demonstrations, the locations where the indepen- Figure 4: Active zone of the VCSEL-SA and ﬁeld intensities dent manipulation of the CS could be obtained in practice at the cavity resonance (black, divided by 400) and at the were limited by the presence of a strong cavity resonance gra- pump wavelengths (in red, between 795 nm and 805 nm) ver- dient. In the following experiments, new devices with much sus the growth depth. The active zone is composed of two smaller gradients were provided and allowed manipulation regions (in yellow and green): the SA region (yellow) with one over almost the whole transverse extent of the device, that is, InGaAs/Al Ga As quantum well and the amplifying region 0.22 0.78 200 μm. The switching characteristics were analyzed in [76]. (green) with two InGaAs/Al Ga As quantum wells. The ﬁrst 0.05 0.95 A sequence of independent control of two CSs using in-phase few layers composing the the front and back mirrors is visible on the local excitation with the holding beam (writing beam) or π- right and left respectively. of the active zone. Light grey: AlAs. Dark phase shifted beam (erasure beam) is shown in Figure 6. grey: Al Ga As. Note that the SA quantum well is at a node of the 0.22 78 The use of the phase parameter to control the writing pump ﬁelds in the whole range of possible pump wavelength while being at an antinode of the ﬁeld at cavity resonance. After [73]. or erasure process of a CS reveals in fact quite cumbersome in practical applications. However, an incoherent switching technique has been demonstrated by Barbay et al. in [68]. Using a specially designed optically pumped VCSOA as de- way, another CS can be created in any other location pro- scribed earlier, they have shown that CS writing and erasure vided the correlation length of the localized structure is can be achieved by short pulses (60 ps duration), at a wave- signiﬁcantly smaller than the transverse size of the device. CS length far from that of the holding beam, demonstrating a written in the way described above can be erased by sending a mechanism free of phase relationship. This technique relies pulse quite similarly to the writing pulse at the same location on the observation that CS in semiconductor devices are but with phase opposite to that the holding beam. compound objects. While a localized structure is formed in the intracavity ﬁeld distribution, a counterpart forms in the Experimentally, CS have been observed in several systems based on photorefractive crystals [48], Na vapors [46], liquid carrier density. Hence, it is possible to excite CS by locally crystal light valves [49, 74], semiconductor optical ampliﬁers adding carriers. The fact that both writing and erasure are possible by local carrier injection, with slightly diﬀerent HB [50, 68], and lasers [54, 55, 73, 75]. In the latter, most experiments have been done in VCSELs, because their short parameters though, is intriguing and has been explained in cavity and large diameter insure a Fresnel number large terms of local temperature eﬀects in [77]. As in the coherent enough to avoid the formation of patterns correlated over the case however, a delay is observed in the writing process which whole extension of the system. CS have been observed in depends on the operating conditions and which is of the ampliﬁers both electrically [50]and opticallypumped[68]. order of 100–200 ns (against several ns in the coherent case). The pumping rate was set high enough to provide gain in the The erasure process is faster and occurs without delay in a active medium but low enough to maintain the VCSEL below timescale of a few ns or less. The writing delay can be reduced by increasing the writing power. the laser threshold. However, it must be noted that similar results have been obtained with an injected VCSEL pumped In theory, one needs a translationally invariant system slightly above threshold [59]. for CS formation and control. In practice, the presence of A typical experimental setup is shown in Figure 5.Abot- gradients in the system is unavoidable. They arise from tom emitter VCSEL with a diameter of 150 μm was injected diﬀerent sources. by a coherent optical beam produced by an edge emitter laser with an external cavity in a Littrow conﬁguration. Thus, the (i) Device growth and fabrication: the VCSEL cavity holding beam can be ﬁne tuned in the range 960–980 nm. resonance used in [50] had a linear variation along This beam was spatially ﬁltered such that the intensity could one diameter of the device. This variation creates a be considered as almost uniform across the whole section of linear gradient of one of the most important control the VCSEL, and thus not introducing an additional gradient parameters in the experiment: the detuning between component. The holding beam power was controlled by the cavity resonance frequency and the frequency an acousto-optic modulator together with a polarizer. The of the holding beam. Though generating important n(λ)∗|E| (a.u.) Advances in Optical Technologies 7 CCD OF BS PD BS FP1 MONO BS BS S FP2 PM SF 1 I AOM1 BS OI BS ◦ BS SF 2 PZT AOM2 P Figure 5: Experimental setup. M, high power edge emitter laser; I, current driver stabilized up to 0.01 mA; TO, temperature controller; G, grating; OI, optical diode; FP, Fabry-Perot resonators; AOM, Acousto-optic modulators; SF1, beam expander conﬁgurator with spatial ﬁltering; SF2, beam reducer conﬁgurator with spatial ﬁltering; S, broad-area vertical cavity surface emitting laser; C, collimator; CCD, camera; PD, Photodetector; PZT, piezoelectric ceramic; M and BS, mirrors and beam splitters; PM, power meter (optional); λ/4, λ/2wave plates; P, polarizers; OF and MONO, optical ﬁber and monochromator. consequences, it can be controlled by the growth con- Later, cavity solitons have been observed in electrically ditions. pumped VCSEL above threshold (see Section 4). The main properties of localized structures in optical ampliﬁers are the (ii) Nonuniform distributions of carrier injection in elec- intensity and phase stability. The good stability in intensity trically injected devices. Usually, electrically pumped is deﬁned by the fact that the low and high intensity of the broad area devices present a current density higher bistable cycle are very well deﬁned at all positions and remain at the borders than in the center of the active zone the same as much as the parameters are kept constant over (current crowding eﬀect). For this reason, a bottom the whole transverse section of the device. If the optically emitter structure was preferred in the ﬁrst demon- injected VCSEL is driven above threshold instead, the lower stration of the generation of localized structures in a branch of the bistable cycle is usually unstable and the CS VCSEL because the longer distance between the ring intensity ﬂuctuates in time. The holding beam deﬁnes the electrode and the active medium translates into a phase of the CS so that the phase is ﬁxed all across the more uniform current distribution. transverse section of the device. Thus, a possible transverse (iii) Misalignment of the holding beam with respect to the phase wave generated by the fast change in intensity at the optical axis of the VCSEL. position of the CS will not propagate. If a phase wave is created, then it will act as a phase gradient for a second CS (iv) Not completely uniform intensity distribution of the and it will move towards the border of the device as explained holding beam. in [78]. (v) Defects in the VCSEL structure. Some defects may In all cases, the experimental results have been compared repel the localized structure while others tend to pin with numerical ones showing very good qualitative agree- them (see Section 5.2). ment and in some cases even quantitative agreement with semiclassical models. All these gradients could aﬀect the generation and the sta- bility of CSs. Localized structures move under the eﬀect of a gradient and in semiconductor devices can move fast enough 4. CS Lasers to prevent a CDD camera from detecting them. Fortunately, some defects or unwanted gradients of the device or induced Vertical cavity semiconductor optical ampliﬁers (VCSOAs) by the imperfections in the experiment would pin them so allowed to demonstrate many useful properties of CS for that they remain stable and steady. During the ﬁrst experi- possible applications to all-optical processing of information ments, CS appeared always at the same set of positions. The (see Section 5). However, they necessitate the use of a co- introduction of external intensity or phase gradients allowed herent holding beam for optical injection which makes to move them around in a controllable way demonstrating the experimental implementation more diﬃcult, bulky, and the independence from the boundaries and the possibility costly. Moreover,CSs in such acasesit on anonzero back- to observe them in the whole transverse plane of the device ground and the contrast between the CS peak intensity and which can be relevant for some applications as we will ex- the background intensity is reduced. This is why laser CS plain in Section 5. would be needed to circumvent all these problems. 8 Advances in Optical Technologies (a) (b) (c) (d) (e) (f) (g) (h) Figure 6: 3D representation of the VCSOA near-ﬁeld intensity distribution, after [58]. The holding beam is always on, and all parameters are kept constant in the sequence (a)–(g). (a) The writing beam (WB) is oﬀ; (b) the WB induces the appearance of a single CS; (c) the WB is oﬀ again, and the CS remains; (d) the WB is displaced in position, and switched-on again and generates a second CS; (e) the WB is oﬀ again and the two bright spots coexist; (f) the WB targets the second CS, but the relative phase of WB with respect to HB has been changed, and the CS is erased; (g) the WB targets the ﬁrst CS, and it is erased in the same manner as in (f). Once the WB is blocked, the intensity distribution is identical to (a). In (h) is shown the CS proﬁle. It is to be noted that contrarily to what was believed at the the self-imaging conﬁguration in order to keep a high Fresnel early stages of their studies, CS in the laser regime can indeed number cavity hence the possibility to have a high number of exist in a VCSOA. As a laser with injected signal is known transverse modes and allow for spatial decorrelation. A half- to develop temporal (Hopf) instabilities that can couple to wave plate is used to match the VCSEL polarization direction the spatial degrees of freedom and drive the system to a of the laser emission to those of the beam splitters—BS1 regime of spatio-temporal chaos, this seemed apriori not and BS2—and of the grating. The grating is tuned such that favorable to the formation of CS which require a stable back- its maximum reﬂection is red detuned with respect to the ground to form on. It was nevertheless shown in [59], both VCSEL longitudinal mode. Above a certain threshold in the experimentally and theoretically, that CS can be observed in injected current (lower than the solitary laser threshold), a driven VCSEL above threshold. The theoretical modeling the system starts to emit and displays several isolated spots indicate that CS can exist even on the oscillatory background whose characteristics are those of a CSL [54]. The spots generated by the onset of a Hopf instability. This is conﬁrmed are bistable, almost identical in shape and size (10 μm), in the experiment, where it is shown that CS can survive in individually controllable in certain transverse locations of a narrow parameter range. Still, the laser CS thus obtained the laser (see Figure 7(b)), and can be put into motion or is limited by the necessity of a coherent holding beam (HB), “dragged” by an appropriate intensity gradient obtained by which in addition to injecting energy, ﬁxes the phase of the inserting a comb ﬁlter in the cavity. The emission spectrum CS. This is in contrast to the case of a true, “free-running” of each spot is narrow as expected in a laser. The writing CS laser (CSL) which can be described as a self-conﬁned mi- beam that provides a temporary and localized excitation is crolaser for which the phase is not ﬁxed. This last point has not coherent with the spots. Further details on the diﬀerent important consequences regarding CS interactions. switching techniques are described in [81], and a model that Theoretically, CSL have been found in two-photon active qualitatively agrees very well with the observations is pro- media [79] or in dense two-level systems [80]. In the context posed in [82]. Interestingly, the switch-on and oﬀ are of semiconductor CSLs, two possible bistable laser schemes obtained with an incoherent beam and the function (writing have been studied. The ﬁrst one is the VCSEL with frequency or erasure) is controlled by the position of the localized exci- selective feedback, which led also to the ﬁrst demonstration tation with respect to CSL location. This position depends of CSL in a semiconductor system [54], and the second one on the grating orientation. The minimum writing beam is the VCSEL with saturable absorber, studied in a compact pulse width needed to ignite a CSL is below 15 ns (lower and an extended cavity conﬁguration. limit not known due to experimental limitations), while the The VCSEL with a frequency selective feedback scheme is shorter the writing beam pulse, the higher the intensity is depicted in Figure 7. A broad area VCSEL of 200 μm diameter required [83]. Spontaneous switch is also observed following emitting around 980 nm is used in an external cavity con- an uncontrolled perturbation (being of mechanical, thermal, ﬁguration where a grating in Littrow conﬁguration here, or a optical origin). In such a case, the switch on is accompanied volume Bragg grating in later experiments, is used to close by short transient pulses, a feature of interest with respect to the cavity. A pair of lenses is inserted inside the cavity in Section 6.2. Multipeak structures are also observed [84]and Advances in Optical Technologies 9 (a) (b) (c) (d) (e) (f) Detection Writing beam (g) (h) (i) f = 8mm f = 300 mm Grating BS1 BS2 VCSEL Comb ﬁlter HWP1 HWP2 (a) (b) Figure 7: (a) Experimental setup of a CSL consisting in a VCSEL with frequency selective feedback. One pair of lenses are inserted inside the cavity in the self-imaging conﬁguration. Beam splitters BS1 and BS2 are used for writing beam input port and for output detection. (b) Sequence of images (inverted contrast) of the VCSEL surface showing the independent writing and erasure of two CSL. Reprinted with permission from [54]. ( c 2011) by the American Physical Society. associated with a CS-splitting phenomenon reminiscent of the round-trip time of the external cavity, relevant in the the homoclinic snaking curve observed in ampliﬁer systems context of Section 6.2. Multistability among several, multi- [45]. colored monochromatic CSL is analyzed and modeled in It has been long known that semiconductor lasers with [86, 87]. The proposed model also explains the observation saturable absorbers can be bistable. They constitute thus the and control of bistable laser vortices reported in [88], that second system of choice for CSL studies. The ﬁrst demon- were predicted earlier in wide-aperture, class-A lasers with stration of a CSL with a saturable absorber has been reported saturable absorption in [89]. in [55]. The experimental setup consists of two mutually A compact CSL has been demonstrated in [73, 75]. The coupled, face-to-face, VCSELs depicted in Figure 8.Itiscom- device, a monolithic, optically pumped, vertical cavity laser posed of two broad area (200 μm diameter) 980 nm VCSELs, with intracavity saturable absorber, is described in Section provided by the same company (ULM Photonics) as in the 2.2.Atdiﬀerence with the previous demonstrations, this previous demonstration. The VCSELs are optically coupled system is purely single-longitudinal mode. Its theoretical by lenses in the self-imaging conﬁguration. A beam splitter is description is intrinsically simpler and laser CS models have used for detection and for localized excitation. One VCSEL is been studied in [90, 91] and in [92–94] for semiconductor biased above transparency and operated in the gain regime, laser models (see also [2]for arecenttheoretical review). while the other VCSEL is biased below transparency and The vertical-cavity is optically pumped uniformly on a 70 μm operates in the saturable absorption regime. The tempera- diameter. ture of the gain VCSEL is set such that its emission is slightly Fast and sequential independent and incoherent writ- (1 nm) blue detuned with respect to the below-threshold ing/erasure are demonstrated with short (60 ps) pulses at spontaneous emission of the second VCSEL. The output a maximum rate of 82 MHz (see Figure 9). Note that the detected when the gain laser current is varied is shown in switch-on time is very fast (several ns) and only limited by Figure 8. For low currents, light emitted by the gain device relaxation oscillations [75], while the switch-oﬀ time is of the is almost fully reﬂected by the second VCSEL because of the order of 1 or 2 ns, as expected in this kind of systems [95]. frequency mismatch. The system starts to lase with a thresh- The same beam characteristics were used for both switch-on old lower than that of the solitary laser (Figures 8(a) and and switch-oﬀ. Theoretical work [95] suggests the important 8(b)). When laser emission starts to saturate with increasing role played by the writing/erasure beam width in the spa- current, and because of its thermal red-shift, laser emission tiotemporal dynamics that may explain why the same inten- starts to decrease as its coupling with the second VCSEL sity distribution can allow exciting or erasing a laser CS. progressively increases. When enough intensity can enter the One important point in CSL with respect to CS in am- saturable-absorber cavity, absorption saturation takes place, plifying systems is that the phase of the localized state is not and a bistable characteristics is locally recorded. In the near- ﬁxed and may have apriori arbitrary value. Nevertheless, the ﬁeld image of the sample, bistable laser spots appear that can phase proﬁle of a laser CS is larger than its intensity proﬁle, be controlled independently with an external beam. Here, and it was shown in [94] that CSLs at a distance shorter than a localized excitation whose wavelength is close to that of 60 μm will interact and form a cluster. The practical value in the emitted light is used. The switching process is analyzed experimental systems above which LCS may be independent in [85]. Switch-on is accompanied by rather long (600 ns) is however, smaller because of system’s inhomogeneities that transients composed of 150 ps pulses with a period equal to destroy the long-range interactions. If the distance between 10 Advances in Optical Technologies Detection L L L1 L1 L2 BS Coll. Coll. Detection L2 L2on L1on heatsink heatsink (a) 0.9 (A) (B) 0.8 0.7 0.6 0.5 (A) (B) (C) (D) (C) (D) 0.4 0.3 0.2 0.1 (E) (F) 0 50 100 150 200 250 300 350 400 450 IL1 (mA) Increasing I 50 μm Decreasing I (b) (c) Figure 8: Experimental setup (a) and experimental results (b) and (c) obtained in the face-to-face VCSELs conﬁguration (see text for details). Reprinted with permission from [55]. ( c 2011) by the American Physical Society. each laser CS is too small then laser CS shall not be independ- modulator [101] may prove interesting, at the expense of a ently controllable anymore [75]. The properties of clusters greater complexity of the experimental setup. Controlling the of laser localized structures and the associated motion is CSL motion remains therefore an important challenge. thoroughly studied in the theoretical paper of [96, 97]. Ex- perimentally, clusters arise either spontaneously [75]orfol- 5. Applications of CS to Photonics lowing a “splitting” process as the pump is increased as in [84, 98]. An experimental conﬁrmation that uncoupled, The main properties of localized structures or cavity solitons single-peaked Laser CS are mutually incoherent is given in in optical systems are twofold (1) They can be switched-on [84, 98], while clusters are found to have a well-deﬁned phase and oﬀ independently so that one can control their appear- relationship as reported in [98]. ance and disappearance. (2) If the system is homogeneous An important feature of CSL not yet clearly experimen- in the transverse plane, CSs are free to move, thus they tally demonstrated is related to the control of their motion. will feel the existence of any gradient. In other words, their In amplifying systems, motion can be induced either by a position and their velocity can be controlled by adjusting phase or intensity mask on the holding beam (see Section 5). a gradient of intensity and/or phase. These properties raise In laser systems, one cannot use the phase degree of freedom the idea that one can use localized structures in applications anymore. Motion can be induced by instabilities, as studied related to information processing. The most natural one is in [99, 100], where spontaneous motion is expected when an all optical memory [38, 40, 50, 102, 103] due to the the ratio of the carrier lifetimes in the active and passive controllability in position and switching capabilities of CSs. medium, respectively, is below a critical value. If boundaries However, there are several other possible applications not are included, for example, circular boundaries, CS move along the boundaries, an eﬀect that can be exploited for an so obvious at ﬁrst sight. In the following, we present two possible applications of cavity solitons: one in the optical optical clock [100]. Experimentally, techniques to control the index of refraction of the cavity by using a spatial light information processing context, an all optical delay line; and Intensity (a.u.) 6 Advances in Optical Technologies 11 150 150 100 100 50 50 0 0 0 24 8 0 24 8 Time (μs) Time (μs) (a) (b) 024 8 15 μm Time (μs) (c) (d) Figure 9: Independent and sequential writing-erasure of one cavity soliton while keeping the neighboring cavity soliton unchanged (a,b,c). The black trace corresponds to the incoming localized excitation pulse, and the middle (upper resp.) trace, green (red resp.) online, corresponds to the leftmost (rightmost resp.) cavity soliton. The zero intensity levels of the upper and middle traces (dashed lines) have been artiﬁcially oﬀset by 100 and 50, respectively for clarity. An averaged image of the two-cavity solitons considered is shown in (d). After [73]. another for material structure determination: a soliton force for some range of parameter values, is proportional to microscope. the gradient. The CS can be recovered later at a diﬀerent spatial position. This method was proposed for the ﬁrst time 5.1. All-Optical Delay Line. Apart from the existing elec- by Firth and Scroggie in 1996 [40, 57] and demonstrated tronic devices that are used today as shift registers, there has experimentally in Na vapors by Schap ¨ ers et al. in 2001 [109] been increasing interest in all optical delay lines in the last and by Pedaci et al. in 2008 in a VCSEL [110]. few years. Most of the proposed all-optical systems are based The optical system used in [110] is a bottom emitter on slowing down light by modifying the group velocity. Such VCSEL as described in Section 2.1. The broad area device variation can be a consequence of a nonlinear process like (200 microns in diameter) is injected by a collimated beam electromagnetically induced transparency (EIT), stimulated focused by a cylindrical lens. This allows the generation of Brillouin scattering (SBS), and so forth. In [104–108], it is a homogeneous injection beam along a line transverse to possible to ﬁnd several schemes based on slow-light in order the direction of propagation of light on the microresonator. to realize a delay line (Figure 10). The intensity of the injected ﬁeld, the detuning between the cavity resonance and the injected ﬁeld frequencies, and the Using localized structures, it is possible to propose a completely diﬀerent approach based on injecting a stream pumping current of the VCSEL were set at typical values for of optical pulses into a nonlinear device. Each injected pulse which the CS may exist in such devices (see [58]). Five fast will create a CS. If a linear gradient is somehow super- avalanche photodiode detectors are placed in the near-ﬁeld imposed, the CS will drift along this line at a speed which, image plane so as to detect the output intensity of the device Intensity (a.u.) Intensity (a.u.) Intensity (a.u.) 12 Advances in Optical Technologies also an all optical pulse reshaping of the incoming optical CCD pulse. Amplitude ﬂuctuations of the incoming pulse are eliminated because of the threshold response of the medium to generate a CS. This functionality may be very useful in Detectors VCSEL array order to avoid deterioration of the transmitted signal. 5.2. Soliton-Force Microscope/Role of Defects. As stated before CL the position of a CS or localized structure can be controlled by a gradient. In [103], it was shown that it is possible to Holding beam Master position the CS at the maximum of an intensity or phase laser gradient. On the other hand, CS can be pinned by defects in the structure of the device. The defects act by generating a gradient. If all other parameters are considered uniform, only Writing beam EOM the gradients generated by the defects will determine the ﬁnal position of the CS. One may distinguish between two types of Figure 10: Experimental setup. Vertical cavity surface emitting laser defects: those that are able to pin the CS and those that repel (VCSEL); cylindrical lens (CL); electro-optic modulator (EOM); them. Thus, in presence of gradients of diﬀerent origins, the tunable master laser (ML). Inset: transverse proﬁle emission stable positions of CSs will be those where the forces applied (negative image) of a 200 μm section VCSEL, in the regime of CS on them compensate. This view may however, be mitigated existence under injection by a broad holding beam. Four CSs are by the recent theoretical demonstration in [111] that CS may present in the image. (ﬁgure reproduced from [110]). also feel the boundaries, even if they are far from them, so that only a ﬁnite set of positions are allowed. This point lacks; however, a clear experimental demonstration. along the line deﬁned by the holding beam. A linear phase In [63], it was proposed to monitor the motion of CS gradient is generated by tilting the holding beam with respect under the eﬀects of externally applied gradients. Deviation of to the axis normal to the VCSEL. The amount of gradient the CS trajectory from the one imposed by external gradient is then controlled by the angle of incidence of the holding reﬂects the presence of a defect of the structure revealing its beam. A CS is then created by applying a 100 ns writing beam attractive or repulsive character. As a consequence, a map of pulse at some point of the microresonator. This CS drifts as the inhomogeneities of the device is given by the frequency a consequence of the presence of a phase gradient along the of visits of the areas of the device when the motion of CSs is line deﬁned by the cylindrical lens and its passage is detected imposed across the entire section of the system. by the fast photodiodes. The detected output intensity as The experimental setup used in [63] to record the map a function of time is displaced depending on the detector of inhomogeneities is similar to the one described in the considered, as can be seen in Figure 11. It is clear then that previous section. The motion of the CS is induced by creating the CS generated at one point in the transverse section of a gradient in the transverse direction to the propagation of the device is drifting along a line and detected sequentially light. In particular, a spatial modulation of the holding beam by the ﬁve fast detectors. Knowing the distance between intensity was introduced. In order to control the gradient the corresponding points detected by the fast photodiodes strength and position of the intensity maxima a Mach-Zen- (7 μm), the speed of the CS is measured as a function of der interferometer was inserted in the path of the holding the tilt-induced phase gradient. In the case represented in beam. The interferometer is set to generate an intensity Figure 11, the average speed of the CS is 4.7 μm/ns. The proﬁle on the VCSEL formed by fringes of 10 μmsize. The observation provides a proof-of-principle for an all optical pattern allows conﬁning the position of CSs along the direc- delay line based on the property of motion of the CS under tion perpendicular to the fringe. No gradient is present in the inﬂuence of a phase gradient. principle along each interference fringe. In such conditions, The experimental results obtained in [110] are in good only the imposed intensity gradient or intrinsic gradients in agreement with numerical ones obtained by integration of the device can induce a motion of the CS. The fringes are a semiclassical model. In Figure 12, numerical results are adiabatically shifted horizontally by just moving a mirror shown corresponding to the speed of CS as a function of of the Mach-Zender interferometer controlled by a PZT the gradient strength which are compatible with the experi- ceramics. The CS is expected to be dragged in a straight line mental ones. For a large interval of the gradient strength, the while the fringe is moved, but it was observed that it deviates velocity of the CS is almost linear and can be easily controlled from this line. The deviation is attributed to the presence between 1 and 4 micrometer/ns. This is much smaller than of internal gradients generated by defects in the device. those obtained on the devices based on slowing down the The procedure was repeated for diﬀerent orientation of the speed of light by changing the index of refraction of the fringes. For an ideal defect-free medium, such analysis would medium. Furthermore, those theoretical results indicate that result in a uniformly gray map. As long as inhomogeneities the speed of the CS can be increased by increasing the decay rate γ of the carrier density in the semiconductor device are present, some regions are visited very often by the CS while others are almost never visited. Thus, high-intensity (Figure 12(b)). The system proposed in [110]providesnot only an operation of the device as an all optical delay line but regions in the map correspond to attractive defects while Advances in Optical Technologies 13 0.12 0.1 0.08 AB CD E 0.06 0.04 0.02 80 90 100 110 120 130 Time (ns) (a) (b) Figure 11: Passage of a CS in front of a linear array of ﬁve detectors (A)–(E). (a) Time traces of these detectors, displaced vertically by 0.02 units for clarity. Detector A monitors the point addressed by the writing beam, applied at time t = 0. (b) Positions of the detectors in the transverse plane (indicated by squares). The area monitored by each detector has a diameter of less than 7.2 μm and the separation between neighboring detectors is 8.9 μm. Also shown is a time-averaged output image of the VCSEL during the CS drift (charge coupled device camera exposure time of about 1 ms). Figure reproduced from [110]. θ =−2 θ =−1.83 −1 −2 −4 −2 024 02468 10 12 14 Log (γ) 4 −1 K/(10 m ) Large gradient Small gradient Analytic (a) (b) Figure 12: (a) Drift speed versus phase gradient (wave-vector tilt of holding beam) for a scaled cavity photon to carrier recombination rate −1 γ = 0.01 (corresponding to a nonradiative carrier lifetime of 1 ns ) and two-cavity detuning values. The cavity photon lifetime is 10 ps. (b) 4 −1 Log-log plot of CS drift speed versus γ for a ﬁxed scaled detuning (θ =−2) and for two values of the gradient: (stars) K = 2.38 × 10 m ; 5 −1 (diamonds) K = 1.91 × 10 m . Here, the cavity photon lifetime is 1.5 ps. Figure reproduced from [110]. −1 Velocity (μmns ) Intensity (a.u.) −1 Log (velocity) (μmns ) 14 Advances in Optical Technologies (a) (b) (c) Figure 13: (a) Spontaneous emission proﬁle of the VCSEL. (b) CSs trajectories when dragged toward the left. (c) Map of the defects in the VCSEL structure as the result of the complete analysis of the CSs trajectories. After [62]. low-intensity regions to repulsive ones. The experimental 6. Prospects and New Developments map is shown in Figure 13 with an inverted contrast. [63] The previous demonstrations of CS using VCSEL devices, gives a clear proof of the possibility to use the motion either in the optical ampliﬁer or laser regimes, relied on properties of localized structures in order to determine the absorptive or gain nonlinearities. CS were observed in the position and strength of defects in semiconductor devices. optical ﬁeld intensity and carrier density components. Sev- The spatial resolution is determined by the size of the CS eral other interesting new directions have been stimulated by which is in this experiment of the order of 10 μm. Such a these ﬁndings, exploring self-localization of diﬀerent degrees spatial resolution could in principle be increased by working of freedom, using diﬀerent nonlinearities (see, e.g., [113– in a diﬀerent region of parameter space or using devices 115] for theoretical studies of CS in quantum dot materials) emitting at shorter wavelength. However, the strength of the or extrapolating the CS concept to three dimensions. In the proposed method lies in the sensitivity of the CS trajectory following, we describe the advances in the ﬁelds of polariza- to any gradient, should they be smaller than the CS size tion CS, cavity soliton polariton and cavity light bullets. itself. The practical limitation comes from the preparation of the external gradient and therefore, the quality of the optics that limits the uniformity of the holding beam. Moreover, 6.1. Polarization CS. Due to the generally circular aperture of the method not only allows to detect surface defects, but VCSELs, polarization of the emission is not constrained into also can probe bulk defects in the device. This technique a single direction as in edge-emitting lasers but rather may has been called soliton force microscopy, since it uses the vary in the whole output plane, depending on the operating various potentials felt by CSs in the VCSEL to reveal the conditions (temperature and injection level). This fact has map of defects. A similar dragging of CS has also been been long recognized and studied in real devices [116–118]. demonstrated in [54] in a CSL with ﬁltered feedback. In The understanding of the polarization dynamics in VCSELs this latter system, an attempt to control the inhomogeneities has been the subject of many theoretical studies and a model has also been undertaken in [101] using a Spatial Light [119] now well accepted has emerged, the so-called spin ﬂip Modulator. The idea is to create with an additional, spatially model (SFM). Whereas polarization control of VCSELs has patterned, control beam a gradient that counteracts the represented a major goal of research, polarization switches eﬀect of the local inhomogeneities by locally varying the can also be used in optical communications schemes [120, refractive index. This results in displaced hysteresis cycles for 121], where stochastic resonance in the polarization dynam- individual CSs allowing two CSs initially not simultaneously ics enhances transmission of binary information. The light bistable to become controllable in the same parameter emitted by a VCSEL is,s in general polarized along one of regions. the two crystallographic directions [110] or [110] because of Another interesting aspects of defects in VCSEL devices crystal anisotropies, and since these anisotropies are weak, it has been unveiled in [64, 112]. Indeed, defects can under is possible to control the state of emitted polarization. This is certain circumstances be the source of CSs that may subse- also true in broad-area devices [122], while the situation may quently drift under a gradient, being a controlled gradient or be more complex for highly divergent modes in even larger a cavity resonance gradient. This results in the appearance devices [123]. In VCSELs with cylindrical symmetry, optical of an almost periodic source of drifting localized states. The injection [124] or feedback [125, 126]can be employed average period can be controlled by the phase gradient or to control the polarization of light. Since polarized optical by the kind of defect itself. Drifting excitations were also injection or optical feedback can both induce bistability found in a CSL with ﬁltered feedback in [81], while the CS [127, 128], all the necessary ingredients are available for properties remained to be established. CS formation in large-aperture devices. Polarization CS Advances in Optical Technologies 15 0.3 0.2 0.1 (b) −0.1 −0.2 −0.3 −0.4 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 Ba i s current (mA) (a) (c) Figure 14: Near-ﬁeld image of the VCSEL surface when injected by an orthogonally polarized holding beam in the lower (c) and upper (b) branch of the bistability curve (a) obtained by ramping the injected current in the laser. Reprinted with permission from [131]. ( c 2011) by the American Physical Society. could oﬀer the practical advantage of ultrafast switching with Ginzburg-Landau equation [139, 140], a model used to de- low switching energy as was demonstrated in small polariza- scribe pulses in mode-locked lasers with a fast saturable tion-bistable devices [129]. Polarization CS were predicted absorber. Cavity light bullets share the same properties as theoretically in [130]inaKerr cavity with diﬀerent losses for dissipative light bullets, in the sense that they are 3D non- the two polarization components of the ﬁeld. They have been linearly localized states of light. However, CLBs form in a experimentally investigated in [131]ina40 μm diameter cavity and are thus not freely propagating. CLBs have been VCSEL. The laser, which is shown to emit in a well-deﬁned proposed and theoretically demonstrated in an extended polarization state just above the laser threshold, is injected cavity ﬁlled with a saturable absorber medium [141, 142] by an orthogonally polarized holding beam. A localized state injected by a holding beam. It was shown that under certain that sits in the center of the device spontaneously switches circumstances, spatial ﬁlament solitons can destabilize in the on and displays a bistable behavior when the injected propagation direction and form a 3D soliton (cf. Figure 15). current is ramped (see Figure 14). These results, though not These CLBs are addressable and independently controllable demonstrating the independence of the localized state from as their 2D counterpart. An important feature is that they sit the boundaries principally because of the moderate size of on a non zero background, the stable uniform steady-state. the laser used in the experiment, are encouraging steps to- CLBs have also been studied in a similar model including wards the demonstration of polarization CS in VCSELs. a Kerr focusing nonlinearity, showing that the unstable 3D localized structures then formed can be stabilized via higher- 6.2. Cavity Light Bullets. Self-localization of light in 3D order processes such as multiphoton absorption [143]. A remains an open challenge [132–136]. The idea of combining model more suitable for semiconductor systems was studied the characteristics of a spatial soliton with those of a temporal in [144] with MQWs as the nonlinear material. The model soliton has been proposed more than 20 years ago [137], showed that the formation of CLBs requires fast carrier and the corresponding object has been termed a light bullet. recombination times, since otherwise, the carrier dynamics Light bullets are self-localized states of light in space and lags behind the photon dynamics and prevents the formation time that keep their spatial and temporal proﬁle in the of a CLB. course of propagation: self-focusing can compensate for CLBs are a theoretical as well as experimental challenge. diﬀraction and at the same time group velocity dispersion While the choice of a VCSEL for CS studies in semiconductor systems seems obvious, a variety of semiconductor devices can be compensated by self-phase modulation. Because of the particle-like behavior of optical solitons, 3D self-localized may eventually be used for CLB studies. Among these, states of light would be intriguing objects possibly leading bisection edge-emitting lasers are good candidates [145]. to new application breakthroughs [138]. Dissipative light Freely propagating light bullets have also been investigated bullets are often considered in the context of the complex theoretically in nonlinear waveguide arrays, which can be Intensity (a.u.) 16 Advances in Optical Technologies yyyyy (a) (b) t.u. = 0.3 t.u. = 1.3 Regime (more than 600 t.u.) 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 z z z 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 2468 10 2468 10 2468 10 x x x (c) Figure 15: (a, b) Snapshot of 3D ﬁlaments and self-conﬁned states in an extended cavity with transverse directions (x, y) and propagation direction z. (c) Three snapshots of a 1D transverse cavity after injection of a writing beam: t = 0.3, initial injection; t = 1.3, destabilization of the longitudinally uniform solution; t> 600, two independent CLBs are formed and propagate in the cavity. Reprinted with permission from [141]. ( 2011) by the American Physical Society. easily realized in semiconductor materials, in [146–148]and the stability of multifrequency laser CSs. The observations in Bragg gratings [149]. can then be interpreted in terms of partially phase-locked However, the extended cavity conﬁgurations used in external cavity-modes giving rise to quasiperiodically or ir- Section 4 could reveal very interesting regarding CLB dem- regularly pulsing multifrequency laser CSs sitting on a non- onstration. The idea is to extend the VCSEL cavity to allow zero background. for multiple longitudinal modes and temporal mode-locking Self-pulsing localized laser structures are also observed in to take place, while preserving a high Fresnel number VCSEL-based schemes with a saturable absorber. In a mono- ensuring the possibility of multitransverse mode operation lithic vertical cavity laser with saturable absorber [73], self- [150]. In this conﬁguration, a CLB can be viewed as a mode- pulsing localized states are observed. The physical origin of locked 2D CS. In [83, 151, 152], using a VCSEL with a self-pulsing in that case has to be attributed to a Q-switching frequency selective feedback by a volume Bragg grating in instability since the cavity has a single-longitudinal mode. the self-imaging conﬁguration, it was shown that depending The observed behavior is consistent with the experimental on the writing pulse intensity a transient multiple frequency observations. In a face to face VCSEL conﬁguration, self- laser CS can be switched on. In most cases the transient pulsing optical structures have been observed [85]witha oscillations die away after several tens of ns and the ﬁnal pulsing period of 400 ps corresponding to the cavity round- state is a steady, cw laser CS. However, for a high writing trip time. The physical mechanism for self-pulsing is thus in pulse intensity an oscillating laser CS can stabilize with a that case similar to that of the frequency-selective feedback frequency of 3.8 GHz. Because of experimental limitations experiment describes earlier. In both cases, the self-pulsing the modulation depth of the oscillation is not known. state could not be controlled by an external beam and was not Numerical simulations of the system [153] are in fairly good bistable anymore. Control by an external beam of an irreg- qualitative agreement with the observed behavior and predict ular self-pulsing state has nevertheless been shown in [73]. Advances in Optical Technologies 17 It has been obtained on a structure composed of several localized spots but the physical mechanism at stake is not 0.4 clear at the moment. These states are, however, not CLBs, be- cause they develop in microcavities, but they probably con- stitute a good starting point for further investigation in an 0.2 extended conﬁguration. Research on VCSEL-based CLBs is thus concentrated for the moment on extended cavity schemes. While there has been some interesting and encouraging results so far, no conclusive result has been obtained though. One reason lies certainly in the theoretical and numerical diﬃculty in mod- eling semiconductor extended cavity systems, since they are nonlinear, multilongitudinal and—transverse mode systems. Moreover, the CLBs obtained this way seem rather diﬀerent 0 from the original theoretical proposition in [141], and the Figure 16: 2D self-localized bright CS polariton as predicted in link to the Ginzburg-Landau type approach to light bullets [170]. Reprinted with permission from [170]. ( c 2011) by the is not completely clear either. It is anticipated that further American Physical Society. studies in the ﬁeld will help clarify all the physics and the properties of these new self-localized objects and maybe help improve the theoretical comprehension and modeling of semiconductor-based mode-locked lasers [65, 66]. regime using the nonlinear bleaching of the Rabi-splitting [163] under high pumping excitation. However, there has 6.3. Cavity Soliton Polariton. Exciton polaritons (also called been no convincing experimental observations of such a more simply cavity polaritons or polaritons) are mixed light- mechanism so far. A few experimental observations are matter states arising when an exciton and a cavity-mode are associated with the simultaneous presence of the weak and strongly coupled ([154, 155] for a recent review). These states strong coupling signatures in the spectrum, and bistability appear when a photon coming from the recombination of is associated to the bare cavity mode [164, 165]. Bistability an exciton (a bound electron-hole pair) is reabsorbed and has also been observed in a polariton diode [166], where the reemitted several times before the photon escapes from the intracavity electric ﬁeld is responsible for the strong to weak microcavity. The cavity-exciton coupling gives rise to two coupling abrupt switching. resonances separated by the so-called Rabi splitting observed Bistability being again one key ingredient for CS for- in the reﬂectivity spectrum of the microcavity, through a mation, several authors have studied how nonlinear and mechanism analogous to the anticrossing in the eigenener- spatial eﬀects (diﬀraction in particular) can mix to allow self- gies of a system composed of two coupled oscillators. This localized states appearance. Indications of self-localization normal-mode coupling [156] is characterized by the disper- were reported in [167], where local bistability, as well as sion curve depicted, for example, in Figure 1(a) in [157]. localized bright and dark optical structures are reported in Exciton polaritons are fascinating quantum objects with a microcavity with several QWs as active medium, brought bosonic properties in which Bose-Einstein condensation was to low temperature (4 K). However, a clear demonstration of recently observed [158] at temperatures much higher than polariton CS is missing, since no demonstration of indepen- in atomic clouds (and even at room temperature in [159]). dent excitation has been reported. All these results stimulated An important feature in the context of CS is the giant theoretical work on polariton CS. In addition to the large χ -type nonlinearity exhibited by exciton polaritons due optical nonlinearity exhibited in this system, which is in- to the coherent polariton-polariton scattering: two pump teresting because it allows the realization of low pump- polaritons with in-plane wave vector k can scatter in one power nonlinear optical devices [168], exciton polariton- polariton with in-plane wave vector 2k and one with 0 in- based systems are expected to display very fast switching plane wave-vector. This coherent process must fulﬁll phase times too [169], a few orders of magnitude smaller than in matching and energy conservation conditions, and can be the weak-coupling regime. Moreover, the quantum nature of obtained in two diﬀerent ways. The ﬁrst one, in the degen- exciton polaritons could open new prospects in the ﬁeld of erate case, with normal incidence pump beam which gives CS applied to information processing or parallel compu- rise to an optical nonlinearity analogous to a Kerr nonlin- tation though practical schemes are not very clear at the earity, with the diﬀerence that the index of refraction no moment (Figure 16). longer depends on the input beam intensity but rather on Dark polariton solitons were ﬁrst predicted to appear the polariton density. The second one in the nondegenerate [171] in a cavity sustaining exciton polaritons, when the case in a parametric ampliﬁcation conﬁguration, at the so- lower polariton branch is excited at normal incidence. The called “magic-angle” (inﬂection point in the lower-polariton fact that bright CS polaritons were found to be unstable in dispersion curve) with nonzero pump wave vector [160]. that case is related to the defocusing nature of the exciton- Bistability has been observed in both the degenerate [161] polariton nonlinearity. Using the dispersion properties of the and the nondegenerate case [162]. Another mechanism is lower polariton branch near its inﬂection point (|k| 1in also predicted to lead to bistability in the strong coupling Figure 1(a)) in [157]), it was later shown [172] that 1D bright | Ψ | 18 Advances in Optical Technologies CS polaritons could be obtained. The stabilization of these saturableabsorber,”in Localized States in Physics: Solitons and Patterns, O. Descalzi, M. Clerc, S. Residori, and G. Assanto, states rely on the existence of higher-order spatial dispersion Eds., pp. 187–211, Springer, Berlin Heidelberg, Germany, terms that can counteract the repulsive nonlinearity. These CS polaritons are moving objects, since the ﬁrst order [3] T. Ackemann, W. J. Firth, and G. L. Oppo, “Fundamental- dispersion is nonzero at the inﬂection point. In 2D, use of sand applications of spatial dissipative solitons in photonic a conﬁning potential in the perpendicular direction to the devices,” in Advances in Atomic Molecular and Optical Physics, inclined pump beam has been proposed to obtain 2D P. R. B. E. Arimondo and C. C. Lin, Eds., vol. 57 of AdvancesIn localized states. The authors claim that their theoretical pre- Atomic,Molecular,and OpticalPhysics, chapter 6, pp. 323– dictions are in good agreement with the almost simultaneous 421, Academic Press, 2009. experimental observation reported in [157]ofmoving [4] R. Kuszelewicza, S. Barbay, G. Tissoni, and G. Almuneau, “quasilocalized” polaritons. The latter authors have however “Editorial on dissipative optical solitons,” European Physical adiﬀerent interpretation in terms of the straightening of the Journal D, vol. 59, no. 1, pp. 1–2, 2010. [5] H.G.Solari,M.Natiello, andG.Mindlin, Nonlinear Dynam- Bogolyubov dispersion in superﬂuids. ics: A Two-Way Trip from Physics to Math, IOP Publishers, In spite of the opposite signs of dispersion in polaritons London, UK, 1996. excited close to the magic angle, truly 2D self-conﬁned [6] R. Gilmore and M. Lefranc, The Topology of Chaos, Alice in polaritons have nevertheless been obtained numerically in a Stretch and Squeeze land, Wiley, New York, NY, USA, 2002. recent work [170]. Starting from the 1D bright CS polariton [7] F. Moss, L. A. Lugiato, and W. Schleigh, Eds., Noise and Chaos conditions demonstrated in [172], the authors show that in Nonlinear Dynamical Systems, Cambridge University Press, there exists a range of excitation intensities for which New York, NY, USA, 1990. the width of the localized state remains constant in both [8] B. Belousov, “A periodic reaction and its mechanism,” in directions. While in the propagation direction the explana- Oscillationsand Traveling Waves in Chemical Systems,R.Field tion for self-localization remains the same as in the 1D case, and M. Burger, Eds., pp. 605–613, Wiley, New York, NY, USA, in the perpendicular direction self-localization is attributed to the parametric nonlinearity: the 2D CS polariton is thus [9] J. C. Roux, R. H. Simoyi, and H. L. Swinney, “Observation of a strange attractor,” Physica D, vol. 8, no. 1-2, pp. 257–266, stable in both directions thanks to diﬀerent physical mecha- nisms, each of them sustaining their family of 1D self-local- [10] F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, “Exper- ized states. imental evidence of subharmonic bifurcations, multistability, Other theoretical studies have focused on diﬀerent phys- and turbulence in a Q-switched gas laser,” Physical Review ical mechanism for CS polariton formation. In [173], taking Letters, vol. 49, no. 17, pp. 1217–1220, 1982. into account the polarization degree of freedom of exciton [11] N. B. Abraham, P. Mandel, and L. M. Narducci, “I dynamical polaritons, the authors show 1D vectorial bright and dark instabilities and pulsations in lasers,” Progress in Optics, vol. CS polaritons formation. Exploring in [174] the saturation 25, pp. 1–190, 1988. of exciton-photon coupling, the author shows that normal [12] F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, incidence, resting CS polaritons may exist. 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Cavity Solitons in VCSEL Devices

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Cavity Solitons in VCSEL Devices

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