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Subwavelength Grating Structures in Silicon-on-Insulator Waveguides

Subwavelength Grating Structures in Silicon-on-Insulator Waveguides Hindawi Publishing Corporation Advances in Optical Technologies Volume 2008, Article ID 685489, 8 pages doi:10.1155/2008/685489 Research Article Subwavelength Grating Structures in Silicon-on-Insulator Waveguides J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Delage, ˆ A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu Institute for Microstructural Sciences, National Research Council of Canada, Ottawa, ON, Canada K1A 0R6 Correspondence should be addressed to J. H. Schmid, jens.schmid@nrc-cnrc.gc.ca Received 20 December 2007; Revised 24 April 2008; Accepted 28 May 2008 Recommended by Graham Reed First implementations of subwavelength gratings (SWGs) in silicon-on-insulator (SOI) waveguides are discussed and demonstrated by experiment and simulations. The subwavelength effect is exploited for making antireflective and highly reflective waveguide facets as well as efficient fiber-chip coupling structures. We demonstrate experimentally that by etching triangular SWGs into SOI waveguide facets, the facet power reflectivity can be reduced from 31% to <2.5%. Similar structures using square gratings can also be used to achieve high facet reflectivity. Finite difference time-domain simulations show that >94% facet reflectivity can be achieved with square SWGs for 5 μm thick SOI waveguides. Finally, SWG fiber-chip couplers for SOI photonic wire waveguides are introduced, including design, simulation, and first experimental results. Copyright © 2008 J. H. Schmid 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. 1. INTRODUCTION SWG surface structures that exhibit very high reflectivity over a broad wavelength band have also been demonstrated [3, 4]. In this paper we discuss the first implementations Subwavelength gratings (SWGs) have been known and used for many years [1], most commonly as an alternative to of SWG structures in silicon-on-insulator (SOI) integrated antireflective (AR) coatings on bulk optical surfaces. The planar waveguide circuits. Integrated planar waveguide circuits are widely used in defining property of an SWG is a pitch that is sufficiently small to suppress all but the 0th order diffraction, the latter optical telecommunication systems, with arrayed waveguide grating (AWG) multiplexers being one of the most complex referring to the light that is reflected or transmitted according of such circuits [5]. Currently, these commercial waveguide to Snell’s law. According to the grating equation for normally incident light (sin θ = mλ/Λ,where θ is the angle of devices are typically made from doped silica glass with a low refractive index contrast. The high-index contrast (HIC) diffraction, λ is the wavelength of light, Λ is the grating SOI material system offers the potential of a significant pitch, and m is the diffraction order) diffraction is suppressed for Λ <λ, as the diffraction angle becomes imaginary for size and cost reduction of integrated planar waveguide devices, including AWGs [6, 7]. In addition, new applications all orders m. Conceptually, the light propagating through a SWG structure “senses” the average optical properties are emerging for miniaturized SOI waveguide devices. For of the SWGmedium. TheSWG canthusberepresented example, we have recently demonstrated a compact high resolution microspectrometer [8] and highly sensitive pho- as a locally homogeneous effective medium with optical properties determined by the grating geometry. The effect of tonic wire evanescent field sensors (PWEF) with a detection limit of ∼20 fg of organic molecules [9, 10]. However, there a specific optical coating can be mimicked by an SWG with are also fundamental challenges of the SOI material system an appropriate modulation depth and duty cycle. Effective multilayer and gradient-index (GRIN) structures can also be related to the fixed value of the refractive indices of the constituent materials (Si and SiO ). Since the SWG effect obtained with SWGs. Low reflectivities on optical surfaces 2 allows one to engineer artificial materials with intermediate have been demonstrated with SWGs both by a single-layer AR effect as well as by a GRIN effect [2]. More recently, effective indices simply by lithographic patterning, it has 2 Advances in Optical Technologies the potential to circumvent this limitation. We demonstrate SOI waveguides and compared the experimental results with this on two specific examples, namely, the control of the reflectivity calculations using effective medium theory and Fresnel reflectivity of the waveguide facets and the fiber-to- finite difference time-domain (FDTD) simulations. chip coupling, both relying on the SWG effect. The Fresnel reflectivity of a cleaved SOI waveguide 2. ANTIREFLECTIVE WAVEGUIDE FACETS facet is typically ∼30%, which is the reflectivity of the Si-air interface. This comparatively high facet reflectivity The AR effect of specific SWG structures on waveguide facets causes Fabry-Per ´ ot cavity effects in SOI planar waveguide is analogous to the same effectonbulkoptical surfaces.It devices and also increases the fiber-chip coupling loss. Thus can be described using the effective medium theory (EMT) antireflective facets are often desirable. For some devices, [21]. According to EMT, a composite medium comprising for example, optical cavities, a facet reflectivity larger than two different materials interleaved at the subwavelength scale 30% is required. Both AR and highly reflective (HR) facets can be approximated as a homogeneous medium with a can be achieved by the use of thin-film coatings; however, refractive index expressed as a power series in (Λ/λ), where the use of optical coatings on facets has various drawbacks. Λ is the pitch of the SWG and λ is the wavelength of the For example, film deposition has to be carried out at the light. For the case of a one-dimensional surface grating, the chip level after cleaving, requiring additional processing first-order expressions for the anisotropic refractive index are and precluding device testing at the wafer level. Thin film given by deposition processes can be complex, may reduce yield, and 1/2 2 2 may require the use of expensive deposition equipment. ,(1a) n = fn +(1 − f )n 1 2 Furthermore, optical coatings may become mechanically −1/2 f (1 − f ) unstable under thermal cycling, leading to restrictions on . (1b) n = + 2 2 device power and limitation of device lifetime. n n 1 2 A major problem in the design and fabrication of silicon Equations (1a)and (1b) refer to the case of the electric field microphotonic devices is the limited efficiency of optical of the incident light being parallel or perpendicular to the coupling to silicon waveguides at the input/output interfaces. grooves (see Figure 1), respectively. In these equations, n Due to the large mode size disparities, the light coupling 1 and n are the refractive indices of the two media comprising between an optical fiber and a silicon waveguide with a small cross section is largely inefficient. Various solutions the SWG, and f is the filling factor, defined as the fraction of material with index n in a thin slice parallel to the surface, as to this problem have been suggested, for example, three- 1 shown in Figure 1. The equations above are valid in the limit dimensional mode size transformers, edge [11]and off-plane (Λ/λ) → 0. Figure 1 shows the geometry of SWGs with square [12–15] grating couplers, inversely tapered waveguides [16] and triangular shapes at a silicon-air interface (n = 3.5, n = and GRIN planar waveguide lenses [17], each having some 1 2 1). For square gratings (top left), the filling factor profile advantages and drawbacks. A comparative review of various is a step function (left center panel). Using (1a)and (1b), coupling schemes is contained in [18]. For submicron silicon the refractive index profile, which is also a step function, wire waveguides, inverse tapers have emerged as a partic- is obtained (bottom left). The effective index in the grating ularly efficient coupling method. Demonstrated coupling region is polarization dependent, as per (1a)and (1b). The losses of inverse tapers with a minimum width of 0.1 μm TM mode has the electric field parallel to the grating grooves, reported in [16] are 6dB and 3.3dB for TE and TM polarized light, respectively. While this is a remarkable achievement, corresponding to (1a) whereas the electric field of the TE mode is perpendicular to the grooves, corresponding to (1b). a further improvement of the total coupling efficiency is For triangular gratings (top right in Figure 1), the filling desirable. Furthermore, the coupling efficiency of inverse factor profile is a linearly decreasing function along the depth tapers is strongly dependent on the minimum taper width, of the grating (center right). The corresponding effective a fact that results in tight fabrication tolerances for the taper index profiles are continuously decreasing functions across width. the grating region for both polarizations as shown in the We have recently proposed the use of the SWG effect as bottom right panel of Figure 1. a general tool for waveguide mode modifications, including light coupling between an optical fiber and high index Thestepfunctioneffective index profile of a square grating is equivalent to that of a single-layer coating on a contrast waveguides of submicrometer dimensions [19]and silicon surface. The thickness of this effective layer is given modification of facet reflectivity [20]. In this paper, we review our work but also provide new experimental and by the modulation depth of the grating and the effective refractive index can be adjusted between the values of silicon modeling results on the use of SWGs in SOI waveguides. and air by changing the duty cycle of the SWG. From thin All SWG patterns discussed here, both for facet reflectivity film theory, the requirements for a single-layer interference modification and for fiber-to-chip coupling enhancement, AR coating for light crossing the boundary between two can be fabricated by standard lithography and vertical materials of reflective indices n and n at normal incidence etching processes. This has two obvious advantages. First, 1 2 AR AR AR are n = n n and t = mλ/(4n )where n is the film devices can be processed at the wafer level before dicing; 1 2 f f f and second, shape control of the SWG is limited only by refractive index, t is the film thickness, and m = 1, 3, 5,... the resolution of the lithography and pattern transfer. To is an odd integer. Thus an AR surface with a square SWG demonstrate the effects, we have carried out experiments on can be designed by choosing the effective refractive index for J. H. Schmid et al. 3 Square SWG Triangular SWG TM Si Air Si Air TE 1 μm f f 1 1 (a) (b) 0.5 0.5 Figure 2: Scanning electron micrographs of SOI waveguide facets patterned with (a) square and (b) triangular SWGs. 0 0 n n eff xx eff 4 Eq.(1) 4 Eq.(1) Deep Deep 3 3 TM TM etch etch Shallow etch 2 2 Ridge waveguide SWG Adiabatic taper 1 TE 1 TE facet x x Figure 3: Schematic top view of a SOI ridge waveguide terminated at both ends with a SWG (not to scale), as used for waveguide Figure 1: Effective medium theory applied to square and triangular SWGs on a Si-air interface. Top: schematic of the grating geometry. transmission measurements described in the text. Center: filling factor corresponding to the square and triangular SWGs. Bottom: resulting effective refractive index profiles for light with the electric field along the grating grooves (TM, dashed curves) loss was determined from the reference waveguides with and perpendicular to the grating grooves (TE, solid curves). flat facets to be 1.7 dB/cm for TE and 5.2 dB/cm for TM polarized light, using the Fabry-Per ´ ot method. The Fresnel reflectivity of a material with the mode effective index was a specific polarization in (1a)and (1b) equal to the required used as an approximation for the reference waveguide facet AR n . This determines the filling factor and thus the duty cycle reflectivity. This value differs from the reflectivity of a Si- of the grating. The modulation depth is then determined air interface by less than 0.5% for either polarization. The by the condition above for the AR coating thickness t.In polarization dependence of the propagation loss is believed contrast to the square gratings, the antireflective properties to be due to scattering loss from the etched sidewalls of the of triangular gratings arise from the GRIN effect, as the waveguides. The reproducibility of the loss measurement was effective refractive index varies continuously between the found to be good with waveguide-to-waveguide fluctuations bulk values of the two media that comprise the grating, of the loss less than 0.5 dB/cm. A comparison of transmission namely, Si and air. spectra of waveguides with flat facets and with triangular Figure 2 shows the scanning electron microscope images and square SWG patterned facets is shown in Figure 4 for of SOI ridge waveguide facets patterned with square and TE polarized light. The peak-to-peak grating modulation triangular SWGs. These structures were fabricated with a depth is 720 nm for the triangular SWG pattern and 270 nm two-step patterning process on SOI substrates with a Si layer for the square pattern which has a duty ratio of 61%. The thickness of 1.5 μm and a buried oxide (BOX) layer thickness amplitude of the FP fringes is reduced from 4.5 dB for of 1 μm, as described in [20]. Square and triangular facet pat- the flat facets to approximately 0.3 dB and 0.5 dB for the terns with various dimensions as well as flat reference facets triangular and square SWGs, respectively. Assuming the same were produced by electron beam lithography and reactive propagation loss for all waveguides as obtained from the ion etching (RIE). The facet reflectivity was inferred from reference measurement on waveguides with flat facets, the Fabry-Per ´ ot (FP) transmission measurements on waveguides power reflectivities of the triangular and square SWG facets terminated with SWG facets, as shown schematically in are calculated to be 2.1% and 3.6%, respectively, from the Figure 3. The ridge waveguides have a width of 1.5 μm, amplitude of the observed FP fringes shown in Figure 4. adiabatically tapered to a width of 4 μm near the facets. This For triangular gratings, the facet reflectivity was mea- increased waveguide width at the facet makes is possible sured as a function of the modulation depth of the SWG to include 10 periods of the SWG with a pitch of 0.4 μm. for both polarizations and compared with EMT theory for The etch depth for the shallow etch (defining the ridge the equivalent grating on a bulk silicon surface. The results waveguide) is 0.7 μm, while the deep facet etch is terminated are shown in Figure 5. The EMT calculation was carried out at the bottom oxide. by discretizing the continuous effective index profiles shown Transmittance of fabricated waveguides was measured as in Figure 1 (bottom right) in steps of 1 nm. The resulting a function of wavelength near λ = 1.55 μm. Propagation discrete index profile for each polarization is the same as 4 Advances in Optical Technologies surface emitting laser (VCSEL) [23]. In order to obtain the −14 SWG effect, these gratings need to be separated from the Square SWG substrate by a layer of low index material. This was achieved −16 in a VCSEL device by fabricating a grating freely suspended above the substrate with an air gap of ∼1 μm. A similar Triangular SWG SWG structure can be envisioned for planar waveguide −18 facets consisting of a row of vertical posts in front of a flat Flat facet waveguide facet at a specific distance (equivalent to the air −20 gap of the VCSEL structure). However, in such a structure there is no vertical mode confinement in the air gap, resulting −22 in out-of-plane radiative loss as the light propagates in the air gap. For a SOI waveguide thickness of ∼1 μm or less, these radiative losses are prohibitive for practical devices, as we −24 have found with three-dimensional FDTD simulations. 1550.1 1550.2 Interestingly though, FDTD simulations show that if a Wavelength (nm) square grating is etched directly into the facet without a Figure 4: Fabry-Per ´ ot fringes for the reference waveguide with separating air gap, high reflectivities can also be obtained. flat facets and for the waveguides terminated with antireflective The modeled structure is shown in Figure 6(a).Itisa triangular or square SWG structures. The curves are offset for 7 μmwideSislabwaveguide (n = 3.476) with SiO Si 2 clarity. lateral claddings (n = 1.44), terminated at the facet SiO with a square grating. The grating period is 0.7 μm, the duty cycle is 54% and the grating modulation depth is that of a stack of 1 nm thick films. The reflectivity of the 485 nm. The external medium is air (n = 1). A continuous- SWG is then calculated as the reflectivity of this equivalent wave field excitation of a TE (electric field in the plane of thin film stack using standard thin film theory. There is the drawing) waveguide fundamental mode of free space good quantitative agreement of experiment and theory (see wavelength λ = 1550 nm propagating in the waveguide Figure 5). The reflectivity decreases substantially with the towards the facet was assumed. The mesh size used was grating modulation depth, as the gradient-index section 10 nm and the simulation was run for a total of 10 000 time −17 becomes more adiabatic. The minimum measured reflectiv- steps of Δt = 2.2 × 10 seconds. The calculated TE electric ity of 2.0% for TE and 2.4% for TM polarization is obtained field map is shown in Figure 6(b). The excitation plane for for a modulation depth of 720 nm, which is the maximum the waveguide mode source is indicated in the figure by a grating depth used in our experiments. The quoted values blue line, including the mode propagation direction (arrow). are an average over 4 measured samples. According to the It can be seen that the transmittance through the grating EMT calculations, reflectivities below 1% can be achieved for structure is efficiently suppressed, hence the mirror effect. SWG modulation depths of approximately 1 μmand 2.5 μm Between the excitation plane and the facet, the forward for TE and TM polarized light, respectively. Since the SWG propagating and the reflected light form a standing wave profiles are defined lithographically, their shape and thus the interference pattern. To the left of the excitation plane, the effective index profile can be readily engineered for specific reflected mode propagates unperturbed in the waveguide. requirements (e.g., polarization properties), in a similar way The facet reflectivity is calculated as an overlap integral of as for bulk SWG surfaces [22]. the reflected intensity profile in the waveguide region to For square SWGs (Figure 2, left), the lowest measured the left of the excitation plane with the fundamental TE facet reflectivity was 3.6% for TE polarized light whereas the mode. A reflectivity value of 97% was obtained for this 2D TM reflectivity of the same sample was 23%. Such a large structure. Figure 6(c) shows the simulation of light coupling polarization dependence is expected for square gratings. As from an external optical fiber to the Si waveguide. In this discussed above, according to EMT, the square AR SWGs can case, a light source with Gaussian intensity profile with a be represented as a single-layer AR coating, the efficiency of 1/e width of 10.4 μm (SMF-28 fiber mode), is located at the which is known to be rather sensitive to the index of the excitation plane (white line in Figure 6(c)). The calculated layer. Since the effective index of the SWG is polarization field in the waveguide reveals a strong transverse modulation dependent (Figure 1, bottom left), optimal AR performance with a period half of the grating pitch. This modulation can only be achieved for one polarization state for a partic- persists almost unperturbed for several micrometers as the ular SWG duty cycle. The strong polarization dependence of light propagates in the waveguide. Since the overlap integral square SWG facets can potentially be exploited for making of this modulated field with the fundamental mode of the polarization selective waveguide elements. waveguide is comparatively small, coupling from an external fiber to the waveguide is inefficient. These markedly different grating properties for light 3. WAVEGUIDE FACETS WITH HIGH REFLECTIVITY propagating in opposite directions may seem surprising, but Subwavelength gratings with high reflectivity have recently have a straightforward explanation. Obviously, diffraction is suppressed on the air side of the grating, since Λ <λ . been demonstrated on optical surfaces as a replacement air for the top distributed Bragg reflector in a vertical-cavity However, the grating is not subwavelength for light coupled Waveguide transmittance (dB) J. H. Schmid et al. 5 0 0 10 10 TE TM −1 −1 −2 0 500 1000 0 500 1000 Length of gradient-index section (nm) Length of gradient-index section (nm) Exp Exp EMT EMT (a) (b) Figure 5: Experimental and theoretical results from effective medium theory for the reflectivity of facets with triangular SWGs as a function of the length of the gradient-index section (i.e., the grating modulation depth). grating from the air to Si, the power diffracted into the +1 and −1diffracted orders is approximately 98%, with <2% of light reflected or transmitted in 0th order. The intensity pattern in Figure 6(c) is thus a superposition of the −1and +1 diffraction orders, while the 0th order is suppressed. This zero-order suppression effect is commonly employed in phase masks used in the fabrication of fiber-Bragg gratings [24]. The reflectance of HR gratings on waveguide facets can be estimated from measured FP fringes similar to the AR measurements discussed in the previous section. The most (a) (b) (c) notable difference is that fiber-waveguide coupling is now Figure 6: FDTD simulations of HR SOI facets. (a) Layout used largely inefficient due to the diffraction effect explained for a typical simulation. The light and dark blue regions are the above. In fact, waveguides terminated with HR facets on silicon waveguide core and SiO lateral cladding, respectively. (b) both sides were found experimentally to have no measurable Simulated TE field map for a waveguide mode launched at the plane transmittance (T < −60 dB). To circumvent this problem indicated in the figure. (c) TE field map for an external optical fiber and measure the internal (Si-air) facet reflectivity, we have mode coupling into the waveguide. used waveguides that are terminated with an HR grating on the output facet but with a regular flat facet having a Fresnel reflectivity of 31% on the input side. This way an asymmetric FP cavity is formed. As in the case of the AR into the Si waveguide, where the first diffraction order is not evanescent, since Λ >λ .Inour case Λ = 700 nm, λ = facets, FP fringes can be observed in the transmission spectra Si air 1.55 μm, and λ = λ /n = 446 nm. This is a fundamental of these waveguides. In Figure 7, the spectrum of such an Si air Si asymmetric cavity waveguide is compared to that of a refer- difference between the HR gratings and the square AR gratings discussed in the previous section, which have a pitch ence waveguide terminated on both ends with flat facets. The of Λ = 400 nm and are thus subwavelength both in the measured peak-to-peak fringe modulations are 6.4 dB and Si and in air. It can be shown with rigorous coupled wave 4.2 dB for the respective waveguides. Using a simple Fabry- analysis (RCWA) that for a plane wave normally incident Per ´ ot model for the asymmetric cavity, this corresponds to an HR facet reflectivity of 75%, clearly demonstrating from inside the bulk Si on a surface grating with the same pitch and duty cycle as our HR facet gratings, both the the validity of the HR grating concept. However, since this diffraction efficiency and the transmittance are extremely reflectivity is significantly lower than the best results of our 2D FDTD simulations, full 3D FDTD simulations of small, while the specular (0th order) reflectivity is >99.9%. Conversely, when the plane wave is incident on such a bulk the HR facet structures were carried out. These simulations Facet reflectivity Facet reflectivity 6 Advances in Optical Technologies Facet Flat facet Cladding −20 a Λ Si ··· From optical fiber BOX −25 HR grating Figure 8: Schematic of an SWG fiber-to-waveguide coupler, side view. −30 end, near the chip facet, it matches that of the optical fiber. We have demonstrated the proposed principle on various 1549.9 1550 1550.1 SWG coupling structures [19], using two-dimensional FDTD Wavelength (nm) calculations for an SOI waveguide with Si core thickness Figure 7: Measured Fabry-Per ´ ot fringes in the transmission of 0.3 μm with SiO cladding. Efficiencies as large as 76% spectrum of a waveguide with an HR grating on the output facet. (1.35 dB loss) and a negligible return loss (−35 dB, or 0.03%) A reference waveguide with flat facets is also shown. The curves are were calculated for coupling from a standard optical fiber offset for clarity. (SMF-28, mode field diameter 10.4 μm) using a 50-μm-long SWG coupler. Further loss reduction can be expected by advanced design, including parabolic width tapering and reveal a strong dependence of the expected reflectivity on chirping the SWG pitch. The coupling efficiency tolerance mode confinement. For the 1.5 μm thick SOI waveguides to misalignment is high. Transverse misalignment of ±2 μm with the 0.7 μm pitch gratings used in our experiments, the results in an excess coupling loss of only 0.5 dB. The angular highest reflectivity obtained in the 3D FDTD simulations is misalignment tolerance is also large, with only 0.24 dB loss 80%, in good agreement with the measurement. For thicker penalty for angular misalignment of ±2degrees.Wehave waveguides with the same facet grating dimensions the also demonstrated the reduction of the coupler length down achievable reflectivity increases significantly. For example, to 10 μmand foundanexcesslossof0.6 dB compared to 94% reflectivity is expected for 5 μm thickness according the 50 μm long coupler discussed above. Unlike waveguide to the 3D FDTD simulations. Physically, the reason for the grating couplers based on diffraction, the SWG mechanism is mode size effect is the dependence of the grating reflectivity nonresonant, and hence intrinsically wavelength insensitive. on the incident angle. With RCWA we find that the grating First SWG waveguide couplers for SOI photonic wires reflectivity for plane waves drops from >99.9% to 81% when (PWs) have recently been fabricated in our lab. The dimen- ◦ ◦ the angle of incidence is increased from 0 to 10 . Therefore, sions of the PWs are 0.45 μm (width) × 0.26 μm (height). the larger range of incident angles contained in a smaller, Such thin PW waveguides have been shown to provide the more localized mode, results in a lower reflectivity. maximum sensitivity for evanescent field waveguide-based biosensors [9]. The coupler structures were fabricated on SOI substrates from SOITEC with an Si layer and BOX 4. FIBER-TO-CHIP COUPLERS thickness of 0.26 μmand 2 μm, respectively. Electron beam An original application of SWGs for fiber-to-waveguide cou- lithography with a chemically amplified negative resist (NEB pling and mitigating losses due to the mode size mismatch 22 A3) was used to define both waveguides and SWG of optical fibers and submicron SOI waveguides has been couplers in a single step. The pattern was then etched proposed recently [19]. The principle of this fiber-chip through the Si layer to the BOX with inductively coupled coupler is based on a gradual modification of the waveguide plasma RIE. After the resist mask was stripped, a 2 μm thick mode effective index by the SWG effect. Theideaisillustrated upper cladding layer of SU-8 resist with a refractive index in a schematic side view of a coupler structure in Figure 8. of n = 1.58 was deposited on the sample using a standard The waveguide mode effective index is altered by chirping the spin and bake procedure. The samples were then cleaved and SWG duty ratio r (z) = a(z)/Λ,where a(z) is the length of the polished as necessary to obtain good facet quality. The ideal waveguide core segment. Unlike in the case of the AR and HR SWG coupler structure described above requires a specific SWG structures discussed above, where the direction of light duty cycle at the facet; however, for cleaving and polishing propagation is orthogonal to the grating vector, here they the facet some tolerance in the exact position of the facet are colinear, that is, the light propagates along the grating. with respect to the pattern is required. Therefore, the SWG Nevertheless, EMT applies to these structures in a similar was extended with constant grating parameters for 400 μm way. The effective index of the mode in the SWG coupling beyond the ideal position of the facet. This allows the final structure increases with the grating duty ratio. The duty ratio position of the fabricated facet to be within this distance from and hence the volume fraction of the Si waveguide core is the end of the coupler structure. SEM images of a fabricated modified such that at one end of the coupler the effective coupler structure are shown in Figure 9. On the left side, index is matched to the SOI waveguide while at the other the part of the SWG joining the PW waveguide is shown. Waveguide transmittance (dB) J. H. Schmid et al. 7 fluctuations. We expect the loss can be reduced by further 1 μm improvements in our design and fabrication, using a thicker box and/or a wider taper width. Our experiments provide a first verification of the proposed SWG coupler concept. Also, the SWG principle experimentally demonstrated in this paper can be generalized to other types of waveguide (a) (b) modifications including effective index changes and mode transformations, opening new possibilities for engineering of Figure 9: SEM micrographs of a fabricated SOI photonic wire waveguide properties at the subwavelength scale. waveguide with an SWG coupler (top view). (a) The SWG coupler joining the photonic wire waveguide. (b) Mid-section of the SWG 5. SUMMARY AND CONCLUSIONS coupler. We have reviewed our work in implementing first SWG structures in SOI waveguides. Three types of structures have been discussed, namely, AR and HR waveguide facets and The pitch of the grating is 0.2 μm and the smallest gaps fiber-chip couplers, all fabricated using standard fabrication are nominally 50 nm. Due to the proximity effect in the e- techniques. The AR facets were demonstrated exploiting beam lithography, the grating gaps become successively more either a GRIN effect from triangular SWGs or a single- closed as the waveguide, which is written with a higher e- beam dose, is approached. Within a distance of a few periods layer AR effect from square SWGs. The GRIN AR structures were found to be particularly efficient, with measured of the SWG from the waveguide, the grating is essentially a facet reflectivities below 2.5% for both polarizations. These subwavelength sidewall grating. This gradual closing of the gaps may in fact be beneficial to the performance of the experimental results are in good agreement with EMT calculations. A minimum reflectivity of 3.6% for the TE coupler, as it reduces the small discontinuity in the effective mode is reported for square SWGs, including highly polar- mode index as the waveguide transforms into an SWG, ization selective properties. HR facets employ a very similar making the transition more adiabatic. Figure 9(b) shows the structure to that of square AR SWG waveguide facets but same coupler at a position closer to the facet. Here the with different grating parameters. The 0.7 μm pitch of the fabricated structure shows little deviation from the design HR grating is large enough that the ±1ordersofdiffraction except for some corner rounding. To increase the effective are allowed in the Si, but are evanescent in air. For light index gradient along the SWG coupler, the width of the SWG segments is tapered from 0.45 μm at the waveguide to 0.2 μm incident from the air, such gratings act as a zero-order suppressed phase mask. In the opposite direction (light at the facet. incident from the waveguide), high specular reflectivity is Samples with SWG couplers of varying lengths and taper widths have been fabricated. Two identical couplers are observed. We have measured up to 75% reflectivity for facets in 1.5 μm thick SOI waveguides, in good agreement connected via S-shaped PW waveguides for transmission with 3D FDTD simulations. The FDTD simulations predict measurements. The S-shape helps to reduce the amount that reflectivities in excess of 95% can be achieved for SOI of scattered light reaching the photodetector, as the latter waveguides with a thickness of 5 μm or more. Finally, the is laterally offset from the light source. The SWG couplers principle, design and first experimental results on SWG fiber- are compared with inverse tapers of similar dimensions, as chip couplers were reviewed. Coupling losses on the order well as untapered waveguides. The inverse taper couplers of ∼1 dB can be achieved with these structures according to are adiabatically tapered waveguides that reach a specific minimum width at the facet [16]. Coupling loss was inferred FDTD simulations and losses of 6.5 dB and 4 dB for TE and TM polarized light, respectively, have been demonstrated from measurements of the waveguide transmittance at a experimentally. The first results suggest that the SWG wavelength λ = 1.55 μm using an erbium doped fiber amplified spontaneous emission (ASE) source with 50 mW couplers may outperform inverse taper fiber-chip couplers in terms of fabrication robustness, compactness, and tolerance output power. An indium gallium arsenide photo diode was to misalignment. used as a detector. 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Subwavelength Grating Structures in Silicon-on-Insulator Waveguides

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Copyright © 2008 J. H. Schmid 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.
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Hindawi Publishing Corporation Advances in Optical Technologies Volume 2008, Article ID 685489, 8 pages doi:10.1155/2008/685489 Research Article Subwavelength Grating Structures in Silicon-on-Insulator Waveguides J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Delage, ˆ A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu Institute for Microstructural Sciences, National Research Council of Canada, Ottawa, ON, Canada K1A 0R6 Correspondence should be addressed to J. H. Schmid, jens.schmid@nrc-cnrc.gc.ca Received 20 December 2007; Revised 24 April 2008; Accepted 28 May 2008 Recommended by Graham Reed First implementations of subwavelength gratings (SWGs) in silicon-on-insulator (SOI) waveguides are discussed and demonstrated by experiment and simulations. The subwavelength effect is exploited for making antireflective and highly reflective waveguide facets as well as efficient fiber-chip coupling structures. We demonstrate experimentally that by etching triangular SWGs into SOI waveguide facets, the facet power reflectivity can be reduced from 31% to <2.5%. Similar structures using square gratings can also be used to achieve high facet reflectivity. Finite difference time-domain simulations show that >94% facet reflectivity can be achieved with square SWGs for 5 μm thick SOI waveguides. Finally, SWG fiber-chip couplers for SOI photonic wire waveguides are introduced, including design, simulation, and first experimental results. Copyright © 2008 J. H. Schmid 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. 1. INTRODUCTION SWG surface structures that exhibit very high reflectivity over a broad wavelength band have also been demonstrated [3, 4]. In this paper we discuss the first implementations Subwavelength gratings (SWGs) have been known and used for many years [1], most commonly as an alternative to of SWG structures in silicon-on-insulator (SOI) integrated antireflective (AR) coatings on bulk optical surfaces. The planar waveguide circuits. Integrated planar waveguide circuits are widely used in defining property of an SWG is a pitch that is sufficiently small to suppress all but the 0th order diffraction, the latter optical telecommunication systems, with arrayed waveguide grating (AWG) multiplexers being one of the most complex referring to the light that is reflected or transmitted according of such circuits [5]. Currently, these commercial waveguide to Snell’s law. According to the grating equation for normally incident light (sin θ = mλ/Λ,where θ is the angle of devices are typically made from doped silica glass with a low refractive index contrast. The high-index contrast (HIC) diffraction, λ is the wavelength of light, Λ is the grating SOI material system offers the potential of a significant pitch, and m is the diffraction order) diffraction is suppressed for Λ <λ, as the diffraction angle becomes imaginary for size and cost reduction of integrated planar waveguide devices, including AWGs [6, 7]. In addition, new applications all orders m. Conceptually, the light propagating through a SWG structure “senses” the average optical properties are emerging for miniaturized SOI waveguide devices. For of the SWGmedium. TheSWG canthusberepresented example, we have recently demonstrated a compact high resolution microspectrometer [8] and highly sensitive pho- as a locally homogeneous effective medium with optical properties determined by the grating geometry. The effect of tonic wire evanescent field sensors (PWEF) with a detection limit of ∼20 fg of organic molecules [9, 10]. However, there a specific optical coating can be mimicked by an SWG with are also fundamental challenges of the SOI material system an appropriate modulation depth and duty cycle. Effective multilayer and gradient-index (GRIN) structures can also be related to the fixed value of the refractive indices of the constituent materials (Si and SiO ). Since the SWG effect obtained with SWGs. Low reflectivities on optical surfaces 2 allows one to engineer artificial materials with intermediate have been demonstrated with SWGs both by a single-layer AR effect as well as by a GRIN effect [2]. More recently, effective indices simply by lithographic patterning, it has 2 Advances in Optical Technologies the potential to circumvent this limitation. We demonstrate SOI waveguides and compared the experimental results with this on two specific examples, namely, the control of the reflectivity calculations using effective medium theory and Fresnel reflectivity of the waveguide facets and the fiber-to- finite difference time-domain (FDTD) simulations. chip coupling, both relying on the SWG effect. The Fresnel reflectivity of a cleaved SOI waveguide 2. ANTIREFLECTIVE WAVEGUIDE FACETS facet is typically ∼30%, which is the reflectivity of the Si-air interface. This comparatively high facet reflectivity The AR effect of specific SWG structures on waveguide facets causes Fabry-Per ´ ot cavity effects in SOI planar waveguide is analogous to the same effectonbulkoptical surfaces.It devices and also increases the fiber-chip coupling loss. Thus can be described using the effective medium theory (EMT) antireflective facets are often desirable. For some devices, [21]. According to EMT, a composite medium comprising for example, optical cavities, a facet reflectivity larger than two different materials interleaved at the subwavelength scale 30% is required. Both AR and highly reflective (HR) facets can be approximated as a homogeneous medium with a can be achieved by the use of thin-film coatings; however, refractive index expressed as a power series in (Λ/λ), where the use of optical coatings on facets has various drawbacks. Λ is the pitch of the SWG and λ is the wavelength of the For example, film deposition has to be carried out at the light. For the case of a one-dimensional surface grating, the chip level after cleaving, requiring additional processing first-order expressions for the anisotropic refractive index are and precluding device testing at the wafer level. Thin film given by deposition processes can be complex, may reduce yield, and 1/2 2 2 may require the use of expensive deposition equipment. ,(1a) n = fn +(1 − f )n 1 2 Furthermore, optical coatings may become mechanically −1/2 f (1 − f ) unstable under thermal cycling, leading to restrictions on . (1b) n = + 2 2 device power and limitation of device lifetime. n n 1 2 A major problem in the design and fabrication of silicon Equations (1a)and (1b) refer to the case of the electric field microphotonic devices is the limited efficiency of optical of the incident light being parallel or perpendicular to the coupling to silicon waveguides at the input/output interfaces. grooves (see Figure 1), respectively. In these equations, n Due to the large mode size disparities, the light coupling 1 and n are the refractive indices of the two media comprising between an optical fiber and a silicon waveguide with a small cross section is largely inefficient. Various solutions the SWG, and f is the filling factor, defined as the fraction of material with index n in a thin slice parallel to the surface, as to this problem have been suggested, for example, three- 1 shown in Figure 1. The equations above are valid in the limit dimensional mode size transformers, edge [11]and off-plane (Λ/λ) → 0. Figure 1 shows the geometry of SWGs with square [12–15] grating couplers, inversely tapered waveguides [16] and triangular shapes at a silicon-air interface (n = 3.5, n = and GRIN planar waveguide lenses [17], each having some 1 2 1). For square gratings (top left), the filling factor profile advantages and drawbacks. A comparative review of various is a step function (left center panel). Using (1a)and (1b), coupling schemes is contained in [18]. For submicron silicon the refractive index profile, which is also a step function, wire waveguides, inverse tapers have emerged as a partic- is obtained (bottom left). The effective index in the grating ularly efficient coupling method. Demonstrated coupling region is polarization dependent, as per (1a)and (1b). The losses of inverse tapers with a minimum width of 0.1 μm TM mode has the electric field parallel to the grating grooves, reported in [16] are 6dB and 3.3dB for TE and TM polarized light, respectively. While this is a remarkable achievement, corresponding to (1a) whereas the electric field of the TE mode is perpendicular to the grooves, corresponding to (1b). a further improvement of the total coupling efficiency is For triangular gratings (top right in Figure 1), the filling desirable. Furthermore, the coupling efficiency of inverse factor profile is a linearly decreasing function along the depth tapers is strongly dependent on the minimum taper width, of the grating (center right). The corresponding effective a fact that results in tight fabrication tolerances for the taper index profiles are continuously decreasing functions across width. the grating region for both polarizations as shown in the We have recently proposed the use of the SWG effect as bottom right panel of Figure 1. a general tool for waveguide mode modifications, including light coupling between an optical fiber and high index Thestepfunctioneffective index profile of a square grating is equivalent to that of a single-layer coating on a contrast waveguides of submicrometer dimensions [19]and silicon surface. The thickness of this effective layer is given modification of facet reflectivity [20]. In this paper, we review our work but also provide new experimental and by the modulation depth of the grating and the effective refractive index can be adjusted between the values of silicon modeling results on the use of SWGs in SOI waveguides. and air by changing the duty cycle of the SWG. From thin All SWG patterns discussed here, both for facet reflectivity film theory, the requirements for a single-layer interference modification and for fiber-to-chip coupling enhancement, AR coating for light crossing the boundary between two can be fabricated by standard lithography and vertical materials of reflective indices n and n at normal incidence etching processes. This has two obvious advantages. First, 1 2 AR AR AR are n = n n and t = mλ/(4n )where n is the film devices can be processed at the wafer level before dicing; 1 2 f f f and second, shape control of the SWG is limited only by refractive index, t is the film thickness, and m = 1, 3, 5,... the resolution of the lithography and pattern transfer. To is an odd integer. Thus an AR surface with a square SWG demonstrate the effects, we have carried out experiments on can be designed by choosing the effective refractive index for J. H. Schmid et al. 3 Square SWG Triangular SWG TM Si Air Si Air TE 1 μm f f 1 1 (a) (b) 0.5 0.5 Figure 2: Scanning electron micrographs of SOI waveguide facets patterned with (a) square and (b) triangular SWGs. 0 0 n n eff xx eff 4 Eq.(1) 4 Eq.(1) Deep Deep 3 3 TM TM etch etch Shallow etch 2 2 Ridge waveguide SWG Adiabatic taper 1 TE 1 TE facet x x Figure 3: Schematic top view of a SOI ridge waveguide terminated at both ends with a SWG (not to scale), as used for waveguide Figure 1: Effective medium theory applied to square and triangular SWGs on a Si-air interface. Top: schematic of the grating geometry. transmission measurements described in the text. Center: filling factor corresponding to the square and triangular SWGs. Bottom: resulting effective refractive index profiles for light with the electric field along the grating grooves (TM, dashed curves) loss was determined from the reference waveguides with and perpendicular to the grating grooves (TE, solid curves). flat facets to be 1.7 dB/cm for TE and 5.2 dB/cm for TM polarized light, using the Fabry-Per ´ ot method. The Fresnel reflectivity of a material with the mode effective index was a specific polarization in (1a)and (1b) equal to the required used as an approximation for the reference waveguide facet AR n . This determines the filling factor and thus the duty cycle reflectivity. This value differs from the reflectivity of a Si- of the grating. The modulation depth is then determined air interface by less than 0.5% for either polarization. The by the condition above for the AR coating thickness t.In polarization dependence of the propagation loss is believed contrast to the square gratings, the antireflective properties to be due to scattering loss from the etched sidewalls of the of triangular gratings arise from the GRIN effect, as the waveguides. The reproducibility of the loss measurement was effective refractive index varies continuously between the found to be good with waveguide-to-waveguide fluctuations bulk values of the two media that comprise the grating, of the loss less than 0.5 dB/cm. A comparison of transmission namely, Si and air. spectra of waveguides with flat facets and with triangular Figure 2 shows the scanning electron microscope images and square SWG patterned facets is shown in Figure 4 for of SOI ridge waveguide facets patterned with square and TE polarized light. The peak-to-peak grating modulation triangular SWGs. These structures were fabricated with a depth is 720 nm for the triangular SWG pattern and 270 nm two-step patterning process on SOI substrates with a Si layer for the square pattern which has a duty ratio of 61%. The thickness of 1.5 μm and a buried oxide (BOX) layer thickness amplitude of the FP fringes is reduced from 4.5 dB for of 1 μm, as described in [20]. Square and triangular facet pat- the flat facets to approximately 0.3 dB and 0.5 dB for the terns with various dimensions as well as flat reference facets triangular and square SWGs, respectively. Assuming the same were produced by electron beam lithography and reactive propagation loss for all waveguides as obtained from the ion etching (RIE). The facet reflectivity was inferred from reference measurement on waveguides with flat facets, the Fabry-Per ´ ot (FP) transmission measurements on waveguides power reflectivities of the triangular and square SWG facets terminated with SWG facets, as shown schematically in are calculated to be 2.1% and 3.6%, respectively, from the Figure 3. The ridge waveguides have a width of 1.5 μm, amplitude of the observed FP fringes shown in Figure 4. adiabatically tapered to a width of 4 μm near the facets. This For triangular gratings, the facet reflectivity was mea- increased waveguide width at the facet makes is possible sured as a function of the modulation depth of the SWG to include 10 periods of the SWG with a pitch of 0.4 μm. for both polarizations and compared with EMT theory for The etch depth for the shallow etch (defining the ridge the equivalent grating on a bulk silicon surface. The results waveguide) is 0.7 μm, while the deep facet etch is terminated are shown in Figure 5. The EMT calculation was carried out at the bottom oxide. by discretizing the continuous effective index profiles shown Transmittance of fabricated waveguides was measured as in Figure 1 (bottom right) in steps of 1 nm. The resulting a function of wavelength near λ = 1.55 μm. Propagation discrete index profile for each polarization is the same as 4 Advances in Optical Technologies surface emitting laser (VCSEL) [23]. In order to obtain the −14 SWG effect, these gratings need to be separated from the Square SWG substrate by a layer of low index material. This was achieved −16 in a VCSEL device by fabricating a grating freely suspended above the substrate with an air gap of ∼1 μm. A similar Triangular SWG SWG structure can be envisioned for planar waveguide −18 facets consisting of a row of vertical posts in front of a flat Flat facet waveguide facet at a specific distance (equivalent to the air −20 gap of the VCSEL structure). However, in such a structure there is no vertical mode confinement in the air gap, resulting −22 in out-of-plane radiative loss as the light propagates in the air gap. For a SOI waveguide thickness of ∼1 μm or less, these radiative losses are prohibitive for practical devices, as we −24 have found with three-dimensional FDTD simulations. 1550.1 1550.2 Interestingly though, FDTD simulations show that if a Wavelength (nm) square grating is etched directly into the facet without a Figure 4: Fabry-Per ´ ot fringes for the reference waveguide with separating air gap, high reflectivities can also be obtained. flat facets and for the waveguides terminated with antireflective The modeled structure is shown in Figure 6(a).Itisa triangular or square SWG structures. The curves are offset for 7 μmwideSislabwaveguide (n = 3.476) with SiO Si 2 clarity. lateral claddings (n = 1.44), terminated at the facet SiO with a square grating. The grating period is 0.7 μm, the duty cycle is 54% and the grating modulation depth is that of a stack of 1 nm thick films. The reflectivity of the 485 nm. The external medium is air (n = 1). A continuous- SWG is then calculated as the reflectivity of this equivalent wave field excitation of a TE (electric field in the plane of thin film stack using standard thin film theory. There is the drawing) waveguide fundamental mode of free space good quantitative agreement of experiment and theory (see wavelength λ = 1550 nm propagating in the waveguide Figure 5). The reflectivity decreases substantially with the towards the facet was assumed. The mesh size used was grating modulation depth, as the gradient-index section 10 nm and the simulation was run for a total of 10 000 time −17 becomes more adiabatic. The minimum measured reflectiv- steps of Δt = 2.2 × 10 seconds. The calculated TE electric ity of 2.0% for TE and 2.4% for TM polarization is obtained field map is shown in Figure 6(b). The excitation plane for for a modulation depth of 720 nm, which is the maximum the waveguide mode source is indicated in the figure by a grating depth used in our experiments. The quoted values blue line, including the mode propagation direction (arrow). are an average over 4 measured samples. According to the It can be seen that the transmittance through the grating EMT calculations, reflectivities below 1% can be achieved for structure is efficiently suppressed, hence the mirror effect. SWG modulation depths of approximately 1 μmand 2.5 μm Between the excitation plane and the facet, the forward for TE and TM polarized light, respectively. Since the SWG propagating and the reflected light form a standing wave profiles are defined lithographically, their shape and thus the interference pattern. To the left of the excitation plane, the effective index profile can be readily engineered for specific reflected mode propagates unperturbed in the waveguide. requirements (e.g., polarization properties), in a similar way The facet reflectivity is calculated as an overlap integral of as for bulk SWG surfaces [22]. the reflected intensity profile in the waveguide region to For square SWGs (Figure 2, left), the lowest measured the left of the excitation plane with the fundamental TE facet reflectivity was 3.6% for TE polarized light whereas the mode. A reflectivity value of 97% was obtained for this 2D TM reflectivity of the same sample was 23%. Such a large structure. Figure 6(c) shows the simulation of light coupling polarization dependence is expected for square gratings. As from an external optical fiber to the Si waveguide. In this discussed above, according to EMT, the square AR SWGs can case, a light source with Gaussian intensity profile with a be represented as a single-layer AR coating, the efficiency of 1/e width of 10.4 μm (SMF-28 fiber mode), is located at the which is known to be rather sensitive to the index of the excitation plane (white line in Figure 6(c)). The calculated layer. Since the effective index of the SWG is polarization field in the waveguide reveals a strong transverse modulation dependent (Figure 1, bottom left), optimal AR performance with a period half of the grating pitch. This modulation can only be achieved for one polarization state for a partic- persists almost unperturbed for several micrometers as the ular SWG duty cycle. The strong polarization dependence of light propagates in the waveguide. Since the overlap integral square SWG facets can potentially be exploited for making of this modulated field with the fundamental mode of the polarization selective waveguide elements. waveguide is comparatively small, coupling from an external fiber to the waveguide is inefficient. These markedly different grating properties for light 3. WAVEGUIDE FACETS WITH HIGH REFLECTIVITY propagating in opposite directions may seem surprising, but Subwavelength gratings with high reflectivity have recently have a straightforward explanation. Obviously, diffraction is suppressed on the air side of the grating, since Λ <λ . been demonstrated on optical surfaces as a replacement air for the top distributed Bragg reflector in a vertical-cavity However, the grating is not subwavelength for light coupled Waveguide transmittance (dB) J. H. Schmid et al. 5 0 0 10 10 TE TM −1 −1 −2 0 500 1000 0 500 1000 Length of gradient-index section (nm) Length of gradient-index section (nm) Exp Exp EMT EMT (a) (b) Figure 5: Experimental and theoretical results from effective medium theory for the reflectivity of facets with triangular SWGs as a function of the length of the gradient-index section (i.e., the grating modulation depth). grating from the air to Si, the power diffracted into the +1 and −1diffracted orders is approximately 98%, with <2% of light reflected or transmitted in 0th order. The intensity pattern in Figure 6(c) is thus a superposition of the −1and +1 diffraction orders, while the 0th order is suppressed. This zero-order suppression effect is commonly employed in phase masks used in the fabrication of fiber-Bragg gratings [24]. The reflectance of HR gratings on waveguide facets can be estimated from measured FP fringes similar to the AR measurements discussed in the previous section. The most (a) (b) (c) notable difference is that fiber-waveguide coupling is now Figure 6: FDTD simulations of HR SOI facets. (a) Layout used largely inefficient due to the diffraction effect explained for a typical simulation. The light and dark blue regions are the above. In fact, waveguides terminated with HR facets on silicon waveguide core and SiO lateral cladding, respectively. (b) both sides were found experimentally to have no measurable Simulated TE field map for a waveguide mode launched at the plane transmittance (T < −60 dB). To circumvent this problem indicated in the figure. (c) TE field map for an external optical fiber and measure the internal (Si-air) facet reflectivity, we have mode coupling into the waveguide. used waveguides that are terminated with an HR grating on the output facet but with a regular flat facet having a Fresnel reflectivity of 31% on the input side. This way an asymmetric FP cavity is formed. As in the case of the AR into the Si waveguide, where the first diffraction order is not evanescent, since Λ >λ .Inour case Λ = 700 nm, λ = facets, FP fringes can be observed in the transmission spectra Si air 1.55 μm, and λ = λ /n = 446 nm. This is a fundamental of these waveguides. In Figure 7, the spectrum of such an Si air Si asymmetric cavity waveguide is compared to that of a refer- difference between the HR gratings and the square AR gratings discussed in the previous section, which have a pitch ence waveguide terminated on both ends with flat facets. The of Λ = 400 nm and are thus subwavelength both in the measured peak-to-peak fringe modulations are 6.4 dB and Si and in air. It can be shown with rigorous coupled wave 4.2 dB for the respective waveguides. Using a simple Fabry- analysis (RCWA) that for a plane wave normally incident Per ´ ot model for the asymmetric cavity, this corresponds to an HR facet reflectivity of 75%, clearly demonstrating from inside the bulk Si on a surface grating with the same pitch and duty cycle as our HR facet gratings, both the the validity of the HR grating concept. However, since this diffraction efficiency and the transmittance are extremely reflectivity is significantly lower than the best results of our 2D FDTD simulations, full 3D FDTD simulations of small, while the specular (0th order) reflectivity is >99.9%. Conversely, when the plane wave is incident on such a bulk the HR facet structures were carried out. These simulations Facet reflectivity Facet reflectivity 6 Advances in Optical Technologies Facet Flat facet Cladding −20 a Λ Si ··· From optical fiber BOX −25 HR grating Figure 8: Schematic of an SWG fiber-to-waveguide coupler, side view. −30 end, near the chip facet, it matches that of the optical fiber. We have demonstrated the proposed principle on various 1549.9 1550 1550.1 SWG coupling structures [19], using two-dimensional FDTD Wavelength (nm) calculations for an SOI waveguide with Si core thickness Figure 7: Measured Fabry-Per ´ ot fringes in the transmission of 0.3 μm with SiO cladding. Efficiencies as large as 76% spectrum of a waveguide with an HR grating on the output facet. (1.35 dB loss) and a negligible return loss (−35 dB, or 0.03%) A reference waveguide with flat facets is also shown. The curves are were calculated for coupling from a standard optical fiber offset for clarity. (SMF-28, mode field diameter 10.4 μm) using a 50-μm-long SWG coupler. Further loss reduction can be expected by advanced design, including parabolic width tapering and reveal a strong dependence of the expected reflectivity on chirping the SWG pitch. The coupling efficiency tolerance mode confinement. For the 1.5 μm thick SOI waveguides to misalignment is high. Transverse misalignment of ±2 μm with the 0.7 μm pitch gratings used in our experiments, the results in an excess coupling loss of only 0.5 dB. The angular highest reflectivity obtained in the 3D FDTD simulations is misalignment tolerance is also large, with only 0.24 dB loss 80%, in good agreement with the measurement. For thicker penalty for angular misalignment of ±2degrees.Wehave waveguides with the same facet grating dimensions the also demonstrated the reduction of the coupler length down achievable reflectivity increases significantly. For example, to 10 μmand foundanexcesslossof0.6 dB compared to 94% reflectivity is expected for 5 μm thickness according the 50 μm long coupler discussed above. Unlike waveguide to the 3D FDTD simulations. Physically, the reason for the grating couplers based on diffraction, the SWG mechanism is mode size effect is the dependence of the grating reflectivity nonresonant, and hence intrinsically wavelength insensitive. on the incident angle. With RCWA we find that the grating First SWG waveguide couplers for SOI photonic wires reflectivity for plane waves drops from >99.9% to 81% when (PWs) have recently been fabricated in our lab. The dimen- ◦ ◦ the angle of incidence is increased from 0 to 10 . Therefore, sions of the PWs are 0.45 μm (width) × 0.26 μm (height). the larger range of incident angles contained in a smaller, Such thin PW waveguides have been shown to provide the more localized mode, results in a lower reflectivity. maximum sensitivity for evanescent field waveguide-based biosensors [9]. The coupler structures were fabricated on SOI substrates from SOITEC with an Si layer and BOX 4. FIBER-TO-CHIP COUPLERS thickness of 0.26 μmand 2 μm, respectively. Electron beam An original application of SWGs for fiber-to-waveguide cou- lithography with a chemically amplified negative resist (NEB pling and mitigating losses due to the mode size mismatch 22 A3) was used to define both waveguides and SWG of optical fibers and submicron SOI waveguides has been couplers in a single step. The pattern was then etched proposed recently [19]. The principle of this fiber-chip through the Si layer to the BOX with inductively coupled coupler is based on a gradual modification of the waveguide plasma RIE. After the resist mask was stripped, a 2 μm thick mode effective index by the SWG effect. Theideaisillustrated upper cladding layer of SU-8 resist with a refractive index in a schematic side view of a coupler structure in Figure 8. of n = 1.58 was deposited on the sample using a standard The waveguide mode effective index is altered by chirping the spin and bake procedure. The samples were then cleaved and SWG duty ratio r (z) = a(z)/Λ,where a(z) is the length of the polished as necessary to obtain good facet quality. The ideal waveguide core segment. Unlike in the case of the AR and HR SWG coupler structure described above requires a specific SWG structures discussed above, where the direction of light duty cycle at the facet; however, for cleaving and polishing propagation is orthogonal to the grating vector, here they the facet some tolerance in the exact position of the facet are colinear, that is, the light propagates along the grating. with respect to the pattern is required. Therefore, the SWG Nevertheless, EMT applies to these structures in a similar was extended with constant grating parameters for 400 μm way. The effective index of the mode in the SWG coupling beyond the ideal position of the facet. This allows the final structure increases with the grating duty ratio. The duty ratio position of the fabricated facet to be within this distance from and hence the volume fraction of the Si waveguide core is the end of the coupler structure. SEM images of a fabricated modified such that at one end of the coupler the effective coupler structure are shown in Figure 9. On the left side, index is matched to the SOI waveguide while at the other the part of the SWG joining the PW waveguide is shown. Waveguide transmittance (dB) J. H. Schmid et al. 7 fluctuations. We expect the loss can be reduced by further 1 μm improvements in our design and fabrication, using a thicker box and/or a wider taper width. Our experiments provide a first verification of the proposed SWG coupler concept. Also, the SWG principle experimentally demonstrated in this paper can be generalized to other types of waveguide (a) (b) modifications including effective index changes and mode transformations, opening new possibilities for engineering of Figure 9: SEM micrographs of a fabricated SOI photonic wire waveguide properties at the subwavelength scale. waveguide with an SWG coupler (top view). (a) The SWG coupler joining the photonic wire waveguide. (b) Mid-section of the SWG 5. SUMMARY AND CONCLUSIONS coupler. We have reviewed our work in implementing first SWG structures in SOI waveguides. Three types of structures have been discussed, namely, AR and HR waveguide facets and The pitch of the grating is 0.2 μm and the smallest gaps fiber-chip couplers, all fabricated using standard fabrication are nominally 50 nm. Due to the proximity effect in the e- techniques. The AR facets were demonstrated exploiting beam lithography, the grating gaps become successively more either a GRIN effect from triangular SWGs or a single- closed as the waveguide, which is written with a higher e- beam dose, is approached. Within a distance of a few periods layer AR effect from square SWGs. The GRIN AR structures were found to be particularly efficient, with measured of the SWG from the waveguide, the grating is essentially a facet reflectivities below 2.5% for both polarizations. These subwavelength sidewall grating. This gradual closing of the gaps may in fact be beneficial to the performance of the experimental results are in good agreement with EMT calculations. A minimum reflectivity of 3.6% for the TE coupler, as it reduces the small discontinuity in the effective mode is reported for square SWGs, including highly polar- mode index as the waveguide transforms into an SWG, ization selective properties. HR facets employ a very similar making the transition more adiabatic. Figure 9(b) shows the structure to that of square AR SWG waveguide facets but same coupler at a position closer to the facet. Here the with different grating parameters. The 0.7 μm pitch of the fabricated structure shows little deviation from the design HR grating is large enough that the ±1ordersofdiffraction except for some corner rounding. To increase the effective are allowed in the Si, but are evanescent in air. For light index gradient along the SWG coupler, the width of the SWG segments is tapered from 0.45 μm at the waveguide to 0.2 μm incident from the air, such gratings act as a zero-order suppressed phase mask. In the opposite direction (light at the facet. incident from the waveguide), high specular reflectivity is Samples with SWG couplers of varying lengths and taper widths have been fabricated. Two identical couplers are observed. We have measured up to 75% reflectivity for facets in 1.5 μm thick SOI waveguides, in good agreement connected via S-shaped PW waveguides for transmission with 3D FDTD simulations. The FDTD simulations predict measurements. The S-shape helps to reduce the amount that reflectivities in excess of 95% can be achieved for SOI of scattered light reaching the photodetector, as the latter waveguides with a thickness of 5 μm or more. Finally, the is laterally offset from the light source. The SWG couplers principle, design and first experimental results on SWG fiber- are compared with inverse tapers of similar dimensions, as chip couplers were reviewed. Coupling losses on the order well as untapered waveguides. The inverse taper couplers of ∼1 dB can be achieved with these structures according to are adiabatically tapered waveguides that reach a specific minimum width at the facet [16]. Coupling loss was inferred FDTD simulations and losses of 6.5 dB and 4 dB for TE and TM polarized light, respectively, have been demonstrated from measurements of the waveguide transmittance at a experimentally. The first results suggest that the SWG wavelength λ = 1.55 μm using an erbium doped fiber amplified spontaneous emission (ASE) source with 50 mW couplers may outperform inverse taper fiber-chip couplers in terms of fabrication robustness, compactness, and tolerance output power. An indium gallium arsenide photo diode was to misalignment. used as a detector. 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