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hv photonics Communication High-Flexibility Control of Structured Light with Combined Adaptive Optical Systems 1 , 1 1 1 , 2 3 Ruediger Grunwald * , Mathias Jurke , Martin Bock , Max Liebmann , Binal Poyyathuruthy Bruno , 3 3 Hitesh Gowda and Ulrike Wallrabe Max-Born-Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Strasse 2a, 12489 Berlin, Germany; jurke@mbi-berlin.de (M.J.); mbock@mbi-berlin.de (M.B.); max.liebmann@holoeye.com (M.L.) HOLOEYE Photonics AG, Volmerstrasse 1, 12489 Berlin, Germany Laboratory for Microactuators, IMTEK-Department of Microsystems Engineering, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany; binal.bruno@imtek.uni-freiburg.de (B.P.B.); hitesh.gowda@imtek.uni-freiburg.de (H.G.); wallrabe@imtek.uni-freiburg.de (U.W.) * Correspondence: grunwald@mbi-berlin.de Abstract: Combining the specific advantages of high-resolution liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs) and reflective or refractive micro-electro-mechanical systems (MEMS) presents new prospects for the generation of structured light fields. In particular, adaptive self- apodization schemes can significantly reduce diffraction by low-loss spatial filtering. The concept enables one to realize low-dispersion shaping of nondiffracting femtosecond wavepackets and to temporally switch, modulate or deflect spatially structured beams. Adaptive diffraction management by structured illumination is demonstrated for piezo-based and thermally actuated axicons, spiral phase plates (SPPs) and Fresnel bi-mirrors. Improved non-collinear autocorrelation with angular- tunable Fresnel-bi-mirrors via self-apodized illumination and phase contrast of an SLM is proposed. An extension of the recently introduced nondiffractive Talbot effect to a tunable configuration by combining an SLM and a fluid lens is reported. Experimental results for hexagonal as well as Citation: Grunwald, R.; Jurke, M.; orthogonal array beams are presented. Bock, M.; Liebmann, M.; Bruno, B.P.; Gowda, H.; Wallrabe, U. High- Keywords: structured light; combined systems; beam shaping; spatial light modulators; adaptive Flexibility Control of Structured optics; MEMS; nondiffracting beams; self-apodization; Talbot effect; fluid lens Light with Combined Adaptive Optical Systems. Photonics 2022, 9, 42. https://doi.org/10.3390/ photonics9010042 1. Introduction Received: 30 November 2021 The generation of structured light fields is currently a hot and fast-growing topic in Accepted: 12 January 2022 optical physics [1–5]. Reconfigurable structured light fields with programmable spatio- Published: 13 January 2022 temporal parameters are of increasing interest for numerous advanced applications such Publisher’s Note: MDPI stays neutral as ultrafast materials processing, plasma filament generation, optical communication, with regard to jurisdictional claims in metrology, microscopy, information processing, particle tweezing, pulse characterization, published maps and institutional affil- or nonlinear spectroscopy. Recently, successful efforts were reported on beam shaping with iations. digital mirror devices [6–11]. It is known that the imaging or shaping quality can be improved by implementing cascaded adaptive optical (AO) devices, e.g., as double-deformable-mirror systems for phase compensation in high-resolution microscopy, ophthalmoscopy, astronomy and other Copyright: © 2022 by the authors. modern imaging techniques [12–15]. To overcome the limitations concerning the critical Licensee MDPI, Basel, Switzerland. energy fluence on spatial light modulators (SLMs), which causes phase distortions or This article is an open access article even material damage, power splitting by using multiple devices was demonstrated [16]. distributed under the terms and Recently, it was shown that the combination of multi-aperture diffractive-optical elements conditions of the Creative Commons and acousto-optic deflectors enables one to reach high temporal flexibility with repetition Attribution (CC BY) license (https:// rates up to 330 kHz for conventional beam profiles and shaping on nanosecond scale [17]. creativecommons.org/licenses/by/ Such systems are of particular interest for high-speed and high-power micromachining. 4.0/). Photonics 2022, 9, 42. https://doi.org/10.3390/photonics9010042 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 42 2 of 13 To shape laser pulses at ultrashort pulse durations, however, efficient control of dispersion and diffraction is necessary. For appropriate diffraction management and beam smoothing, so-called apodization techniques can be applied [18–20]. The essential mechanism of apodization consists of implementing soft apertures instead of apertures with hard edges in the optical systems. The term “apodization” is related to the resulting suppression of edge diffraction by appropriate window functions and stems from the Latin “apodisatio” meaning “eliminating foots” and goes even further back to a corresponding ancient Greek expression. In imaging optical systems, apodization by graded absorption or reflection layers [21] or structured edges is often used to improve spatial resolution, e.g., for microscopes, telescopes [22] or camera lenses. Diffraction limited imaging can be obtained by optimized diffractive lenses with apodization [23]. Graded reflectance mirrors play an important role as spatially variable outcoupling mirrors and mode selectors in unstable laser resonators with large mode volumes [24,25]. Thus, the implementation of flexible, robust, and fast apodization techniques is a very attractive goal in modern optics, which profits from recent progress in the development of high-resolution pixelated commercial spatial light modulators. DMDs are purely reflective devices that in most cases solve the problems of amplitude and phase steering by temporal accumulation of switching cycles and exploiting angu- lar spectra of encoded diffractive gratings, respectively. The obtainable efficiencies are relatively low (typically between 1% and 20%). Although spectrally stable performance has been demonstrated with DMDs over a range of about 200 nm [26], the angular shap- ing principle causes unwanted spatio-temporal coupling phenomena at extremely short pulse durations. An alternative approach consists in the direct small-angle phase shaping with new types of fast steerable, highly reflective micro-electro-mechanical systems (MEMS) that enable large phase elongations and high-power structured beam generation at pulse dura- tions down to the few-cycle range. Both the well-established beam shaper concepts based on DMDs or low-dispersion phase-only liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs) [27–32] and the shape-variant MEMS with piezo- or thermal actuation [33–39] exhibit specific advantages and drawbacks. Their combination, however, can be used to significantly improve system performance at ultrashort pulse durations and even to obtain new functionality. In the following, explorative studies of selected configurations on the basis of liquid crystal devices working at small deflecting angles are reported. These systems integrate (i) the structural flexibility and adaptive capability of high-resolution, pixelated LCoS-SLMs with (ii) the high obtainable phase-stroke, faster possible switching speed and the low dispersion of reflective MEMS or electrically tunable fluid lenses. Specific advantages and disadvantages of this particular type of combined system will be discussed, and applications for low-distortion shaping and characterization of ultrashort wavepackets will be proposed. Tunable nondiffracting self-imaging will be presented here for the first time, to the best of our knowledge. 2. Self-Apodization and “Doubly Nondiffracting” Beams The approach of combined systems enables one to realize specific unconventional scenarios of nondiffracting beam shaping and apodization. The intensity profile of the beam shaped by a first active component (e.g., LCoS-SLM) illuminating the second active component (e.g., MEMS) acts as a spatial filter function. In comparison to other approaches, this one is relatively simple and highly flexible at the same time. Depending on the application, different design criteria can be considered. In particular, this can be (a) the beam diameter (e.g., to completely illuminate the active area of a spatial light modulator for simultaneously shaping a maximum number of partial beams as an array with maximum possible sampling resolution), (b) the smoothness of the illuminating beam (to minimize diffraction and to avoid hot spots), and (c) the final beam divergence. Photonics 2022, 9, x FOR PEER REVIEW 3 of 13 as an array with maximum possible sampling resolution), (b) the smoothness of the illu- Photonics 2022, 9, 42 3 of 13 minating beam (to minimize diffraction and to avoid hot spots), and (c) the final beam divergence. This approach enables the generation of nondiffracting (ND) Bessel-like beams [40] This approach enables the generation of nondiffracting (ND) Bessel-like beams [40] or light bullets [41,42]; light slices; or even more complex structured wavepackets [41,43] or light bullets [41,42]; light slices; or even more complex structured wavepackets [41,43] under the conditions of so-called “self-apodization” [44,45], i.e., with apodization at an under the conditions of so-called “self-apodization” [44,45], i.e., with apodization at an optimum coincidence of spatial intensity zeros (or minima) and the position of hard edges. optimum coincidence of spatial intensity zeros (or minima) and the position of hard edges. The principle of self-apodization is illustrated in Figure 1 for the truncation of a Bessel The principle of self-apodization is illustrated in Figure 1 for the truncation of a Bessel beam. beam. Figure 1. Principle of self-apodization with a truncated Bessel beam. Diffraction at hard edges of Figure 1. Principle of self-apodization with a truncated Bessel beam. Diffraction at hard edges of an an aperture is minimized by adaptive beam pre-shaping. The light profile acts as the filter function aperture is minimized by adaptive beam pre-shaping. The light profile acts as the filter function (schematically). (a) unfiltered Bessel beam, (b) truncated Bessel beam. For a thin circular aperture at (schematically). (a) unfiltered Bessel beam, (b) truncated Bessel beam. For a thin circular aperture at monochromatic illumination, a special self-apodization condition is well-approximated by a truncated monochromatic illumination, a special self-apodization condition is well-approximated by a trun- cated Bessel fu Bessel function nction with f with first zer irst zero radi o radius equal us eto qual to the the apertur ape e r radius ture radius [4 [44,45].4,45]. The field profile of a perfect Bessel beam follows the first-kind zero-order Bessel The field profile of a perfect Bessel beam follows the first-kind zero-order Bessel func- function J . The intensity of the truncated Bessel beam I which fulfills the special 0 TB, tion J0. The intensity of the truncated Bessel beam ITB, which fulfills the special boundary boundary condition (coincidence with the aperture), can be written as condition (coincidence with the aperture), can be written as 𝐼 (𝑟) 𝐽 for r < a (1) I (r)µ J for r < a (1) TB 𝐼 (𝑟) ∝ 0 for r > a (2) I (r)µ 0 for r a (2) TB (J0 = first-kind zero-order Bessel function, r = radial coordinate and a = aperture ra- (J = first-kind zero-order Bessel function, r = radial coordinate and a = aperture radius). dius). In this way, diffraction at apertures can be efficiently minimized so that there may be In this way, diffraction at apertures can be efficiently minimized so that there may be some legitimacy to classify the particular operational conditions as “doubly nondiffracting some legitimacy to classify the particular operational conditions as “doubly nondiffract- (ND ) mode” corresponding to spatially, angularly and/or temporally “highly localized ing (ND2) mode” corresponding to spatially, angularly and/or temporally “highly local- wavepackets” at ultrashort pulse duration [43]. This idea was naturally a strong motivation ized wavepackets” at ultrashort pulse duration [43]. This idea was naturally a strong mo- for current activities on nondiffracting beam shaping. The illuminating amplitude distri- tivation for current activities on nondiffracting beam shaping. The illuminating amplitude bution function in case of self-apodization is designed to concentrate the light completely distribution function in case of self-apodization is designed to concentrate the light com- within a finite aperture. Compared to Bessel–Gauss-type illuminating beams [46], this pletely within a finite aperture. Compared to Bessel–Gauss-type illuminating beams [46], should enable, under optimized conditions, enhanced transfer efficiency with, at the same this should enable, under optimized conditions, enhanced transfer efficiency with, at the time, significantly reduced spatial and temporal beam distortions. same time, significantly reduced spatial and temporal beam distortions. In the case of multiple beam-shaping components, e.g., for spatially resolved charac- In the case of multiple beam-shaping components, e.g., for spatially resolved charac- terization or processing, diffraction leads typically to additional array-specific interference terization or processing, diffraction leads typically to additional array-specific interfer- phenomena such as the Talbot self-imaging effect [47–49]. For a diffraction-less array beam ence phenomena such as the Talbot self-imaging effect [47–49]. For a diffraction-less array shaping in the proper sense, the basic idea of self-apodization has to be extended, and beam shaping in the proper sense, the basic idea of self-apodization has to be extended, one has to distinguish between near- and far-field, i.e., between separated and coupled and sub-beams one has t (or o d , ifist you ingu like, ish pur betw e een ne and mixed ar- and optical far-field, information). i.e., betwee Inn sep modified arated Young-type and cou- pled sub-beams (or, if you like, pure and mixed optical information). In modified Young- double-slit experiments with near-field needle beams propagated through hard-edged ty diaphragms, pe double-sit litwas experime foundnt that s wit difh fraction near-fiel can d nee be avoi dle beams ded to a prop largeag extent ated t by hro fulfilling ugh hard- the edged d self-apodization iaphragmconditions s, it was found t [50]. h On at di the ffrother action c hand, an bthe e avsuperposition oided to a largof e ext needle ent bbeams y ful- can be exploited to generate arrays of undistorted wavepackets by purely geometrical filling the self-apodization conditions [50]. On the other hand, the superposition of needle (nondiffracting) self-imaging [51]. Theoretical estimations show that at sufficiently small beams can be exploited to generate arrays of undistorted wavepackets by purely geomet- Fresnel numbers, self-imaging should be feasible even with sub-femtosecond accuracy [42]. rical (nondiffracting) self-imaging [51]. Theoretical estimations show that at sufficiently For highly precise shaping and diagnostic of extremely short pulses with multichannel techniques such as spatially resolved autocorrelation or frequency resolved optical gating, the separation of spatial channels is of eminent significance. Therefore, one has to find a Photonics 2022, 9, x FOR PEER REVIEW 4 of 13 Photonics 2022, 9, 42 4 of 13 small Fresnel numbers, self-imaging should be feasible even with sub-femtosecond accu- racy [42]. For highly precise shaping and diagnostic of extremely short pulses with multi- channel techniques such as spatially resolved autocorrelation or frequency resolved opti- reasonable compromise between the counteracting requirements of self-apodization, spatial cal gating, the separation of spatial channels is of eminent significance. Therefore, one has separation, spatial resolution and temporal resolution. to find a reasonable compromise between the counteracting requirements of self-apodi- zation, spatial separation, spatial resolution and temporal resolution. 3. Experimental Techniques Beam-shaping experiments with dual-stage adaptive optical systems were performed 3. Experimental Techniques with cw and ultrashort-pulsed near-infrared laser sources, diode lasers and Ti:sapphire Beam-shaping experiments with dual-stage adaptive optical systems were per- lasers, at center wavelengths about of 800 nm. The following combinations were investi- formed with cw and ultrashort-pulsed near-infrared laser sources, diode lasers and gated, which all exploit the SLM as primary illuminating beam generator and an MEMS Ti:sapphire lasers, at center wavelengths about of 800 nm. The following combinations mirror as secondary steering and switching components (Table 1). were investigated, which all exploit the SLM as primary illuminating beam generator and an MEMS mirror as secondary steering and switching components (Table 1). Table 1. Overview of different types of combined systems tested in beam shaping experiments. All arrangements consisted of a high-spatial-resolution, pixelated, phase-only liquid-crystal-on-silicon Table 1. Overview of different types of combined systems tested in beam shaping experiments. All spatial light modulator (LCoS-SLM, HOLOEYE) and a particular type of actuated optical component arrangements consisted of a high-spatial-resolution, pixelated, phase-only liquid-crystal-on-silicon (MEMS, IMTEK). spatial light modulator (LCoS-SLM, HOLOEYE) and a particular type of actuated optical compo- nent (MEMS, IMTEK). SLM MEMS SLM MEMS Com1 LCoS, 10 Megapixels Piezo-actuated Fresnel bi-mirror Com1 LCoS, 10 Megapixels Piezo-actuated Fresnel bi-mirror Com2 LCoS, 10 Megapixels Thermally actuated spiral phase plate (SPP) Com2 LCoS, 10 Megapixels Thermally actuated spiral phase plate (SPP) Com3 LCoS, 10 Megapixels Piezo-actuated Axicon mirror array (2 2) Com3 LCoS, 10 Megapixels Piezo-actuated Axicon mirror array (2 × 2) Com4 LCoS, 10 Megapixels Piezo-actuated Fresnel mirror array (2 2) Com4 LCoS, 10 Megapixels Piezo-actuated Fresnel mirror array (2 × 2) Com5 LCoS, 10 Megapixels Piezo-actuated fluid lens Com5 LCoS, 10 Megapixels Piezo-actuated fluid lens Figure 2 shows schematically the basic setup for structured beam shaping, with two Figure 2 shows schematically the basic setup for structured beam shaping, with two adaptive components corresponding to configuration Com 1. adaptive components corresponding to configuration Com 1. Figure 2. Combined system containing a high-resolution LCoS-SLM and a shape-variable MEMS Figure 2. Combined system containing a high-resolution LCoS-SLM and a shape-variable MEMS corresponding to configuration Com 1 (schematically). As an example, the drawn MEMS represents corresponding to configuration Com 1 (schematically). As an example, the drawn MEMS represents a a Fresnel bi-mirror. Beam shaping is evaluated with a CCD camera. The nonlinear crystal symbol- Fresnel bi-mirror. Beam shaping is evaluated with a CCD camera. The nonlinear crystal symbolizes izes the options for additional nonlinear processing—here, the extraction of SHG autocorrelation the options for additional nonlinear processing—here, the extraction of SHG autocorrelation signal. signal. In general, the MEMS can be a single or multiple reflective or transmissive structure. In general, the MEMS can be a single or multiple reflective or transmissive structure. To illuminate extended areas on the SLM, the diameters of the illuminating, linearly To illuminate extended areas on the SLM, the diameters of the illuminating, linearly polarized laser beams could also be enlarged by a 4× beam expander, attenuated by grey polarized laser beams could also be enlarged by a 4 beam expander, attenuated by grey glass filters or a broadband polarizer (not shown in the figure), or frequency-converted glass filters or a broadband polarizer (not shown in the figure), or frequency-converted by by nonlinear crystals. In our experiments, the SLM was a GAEA-2-type phase-only liquid- nonlinear crystals. In our experiments, the SLM was a GAEA-2-type phase-only liquid- crystal-on-silicon (LCoS) device with 10 megapixels operated at tilted geometry in crystal-on-silicon (LCoS) device with 10 megapixels operated at tilted geometry in pseudo- pseudo-reflection, i.e., with double light pass through the liquid crystal layer. The pixel reflection, i.e., with double light pass through the liquid crystal layer. The pixel size was size was 3.74 × 3.74 µm and the maximum phase stroke was calibrated for 2π at 800 nm. 3.74 3.74 m and the maximum phase stroke was calibrated for 2 at 800 nm. Because of the high spatial resolution, the large number of pixels and the phase stroke, quasi countinuous relief structures can directly be written in the phase map. Two different lasers Photonics 2022, 9, x FOR PEER REVIEW 5 of 13 Because of the high spatial resolution, the large number of pixels and the phase stroke, quasi countinuous relief structures can directly be written in the phase map. Two different Photonics 2022, 9, 42 5 of 13 lasers were used as light sources: (1) a fiber-coupled cw diode laser (wavelength 790 nm), and (2) a few-cycle Ti:sapphire oscillator (Laser Quantum, minimum pulse duration 6 fs, central wavelength about 800 nm). A third laser source (120-fs Ti:sapphire laser, Spectra Physics) was used for investigating thermal response and damage resistance of the SLM were used as light sources: (1) a fiber-coupled cw diode laser (wavelength 790 nm), and at high fluences (to be published elsewhere). (2) a few-cycle Ti:sapphire oscillator (Laser Quantum, minimum pulse duration 6 fs, central Because of the high spatial resolution of the SLM, structured illumination can be well- wavelength about 800 nm). A third laser source (120-fs Ti:sapphire laser, Spectra Physics) ad was apted to used for arbitrary investigating MEMS geometr thermal response ies. Thus and , diffraction damage c resistance an be red of uced the SLM and ener at high gy tra fluences nsfer ca (to n b be e ma published ximized elsewher by optimiz e). ing the phase map of the SLM, which can act with variable funct Becauseiona of the lity (e.g high., lens, spir spatial resolution al grating, of axi the con, SLM, etc.). The re structursu edltillumination ing intensity dist canri- be but well-adapted ion on the MEM to arbitrary S is monit MEMS ored b geometries. y a highly Thus, sensit difive fraction CCD near can be-in reduced frared camer and en- a ergy transfer can be maximized by optimizing the phase map of the SLM, which can act (Thorlabs, DCC3240N, 1280 × 1024 pixels). With additional nonlinear crystals (BBO) and with variable functionality (e.g., lens, spiral grating, axicon, etc.). The resulting intensity spectral filters, second harmonic generation (SHG) and detection were enabled. Nonlinear distribution on the MEMS is monitored by a highly sensitive CCD near-infrared camera processing has particular potential not only for temporal shaping and diagnosing ultra- (Thorlabs, DCC3240N, 1280 1024 pixels). With additional nonlinear crystals (BBO) and short pulses but also for enhancing the spatial resolution, e.g., in microscopy or photoli- spectral filters, second harmonic generation (SHG) and detection were enabled. Nonlinear thography. processing has particular potential not only for temporal shaping and diagnosing ultrashort In the following, we report on exploring experiments on combined systems, in par- pulses but also for enhancing the spatial resolution, e.g., in microscopy or photolithography. ticular on the optimization of self-apodization by spatially filtered illumination, temporal In the following, we report on exploring experiments on combined systems, in par- switching experiments, the improvement of interference contrast in non-collinear auto- ticular on the optimization of self-apodization by spatially filtered illumination, temporal correlation and the realization of tunable nondiffracting self-imaging (geometrical Talbot switching experiments, the improvement of interference contrast in non-collinear auto- effect) with arrays of nondiffracting needle beams. correlation and the realization of tunable nondiffracting self-imaging (geometrical Talbot effect) with arrays of nondiffracting needle beams. 4. Results and Discussion 4.1. Self-Apodization by Spatially Filtered Illumination 4. Results and Discussion Mathematically, self-apodization can be described by the convolution con(x, y) of 4.1. Self-Apodization by Spatially Filtered Illumination input beam intensity profile function f(x, y) and the beam-shaping pupil function g(x, Mathematically, self-apodization can be described by the convolution con(x, y) of y): con = f(x, y) * g(x, y). The boundary condition for minimum diffraction requires a input beam intensity profile function f (x, y) and the beam-shaping pupil function g(x, y): coincidence of an edge and a zero of g(x, y) [44,45]. Figure 3 shows the light concentra- con = f (x, y) * g(x, y). The boundary condition for minimum diffraction requires a coinci- tion for Com1 in two separated lines in the far field profile by illuminating a Fresnel dence of an edge and a zero of g(x, y) [44,45]. Figure 3 shows the light concentration for mirror with a pair of elliptical axicon profiles programmed in the phase map of the Com1 in two separated lines in the far field profile by illuminating a Fresnel mirror with a LCoS-SLM. pair of elliptical axicon profiles programmed in the phase map of the LCoS-SLM. Figure 3. Structured illumination in configuration Com 1: a pair of elliptical cylinder axicons was Figure 3. Structured illumination in configuration Com 1: a pair of elliptical cylinder axicons was programmed i programmed into nto the the SLM SLM phase phase map map (center (cente , r, b)b to ) to illuminate illuminate both both parts parts of of a MEMS a ME Fr MS esnel Fresnel bi- bi-mirror 2 2 mirror (area of partia (area of partial mirrors: l mi 2.5 rro rs:5 2. mm 5 × 5 mm ). The comparison ). The compariso of the n of distorted the distort intensity ed intensity profile profile at a distance at a distance close to the overlapping zone without (left, a) and with pre-shaping (right, c) shows a sig- close to the overlapping zone without (left, a) and with pre-shaping (right, c) shows a significant nificant improvement of the beam quality and the effect of self-apodization, i.e., a reduced diffrac- improvement of the beam quality and the effect of self-apodization, i.e., a reduced diffraction by tion by generating minimum intensity at the mirror edges (distance 5 cm, diode laser emitting at generating minimum intensity at the mirror edges (distance 5 cm, diode laser emitting at 790 nm 790 nm central wavelength, and field of view 4.4 × 4.4 mm ). central wavelength, and field of view 4.4 4.4 mm ). A fast-axis cut through a simulated distribution corresponding to the experimental A fast-axis cut through a simulated distribution corresponding to the experimental conditions for Figure 3c as well as cuts through the related phase profiles of the ellipti- conditions for Figure 3c as well as cuts through the related phase profiles of the ellipti- cal axicons (corresponding to Figure 3b) are plotted in Figure 4a,b, respectively. Phase cal axicons (corresponding to Figure 3b) are plotted in Figure 4a,b, respectively. Phase as a function of grey values was calibrated from LUT (grey value 255 causes 2 phase stroke at 800 nm). The simulation was performed with virtual lab wave propagation software (LightTrans). Photonics 2022, 9, x FOR PEER REVIEW 6 of 13 as a function of grey values was calibrated from LUT (grey value 255 causes 2π phase stroke at 800 nm). The simulation was performed with virtual lab wave propagation software (LightTrans). Photonics 2022, 9, x FOR PEER REVIEW 6 of 13 as a function of grey values was calibrated from LUT (grey value 255 causes 2π phase Photonics 2022, 9, 42 6 of 13 stroke at 800 nm). The simulation was performed with virtual lab wave propagation software (LightTrans). Figure 4. Simulation of the beam propagation for configuration Com 1. (a) Distribution approxi- mately corresponding to the experimental conditions for Figure 3c; (b) cuts through the fast axis (FA) and slow axis (SA) phase profiles of the elliptical axicons. Figure 4. Simulation of the beam propagation for configuration Com 1. (a) Distribution approximately Figure 4. Simulation of the beam propagation for configuration Com 1. (a) Distribution approxi- corresponding to the experimental conditions for Figure 3c; (b) cuts through the fast axis (FA) and mately corresponding to the experimental conditions for Figure 3c; (b) cuts through the fast axis Both the measured and simulated time-integrated intensity profiles already show slow axis (SA) phase profiles of the elliptical axicons. (FA) and slow axis (SA) phase profiles of the elliptical axicons. a significant improvement compared to the unfiltered illumination but still minimal Both the measured and simulated time-integrated intensity profiles already show a Both the measured and simulated time-integrated intensity profiles already show residual side wings of Bessel distributions. The axicons generate quasi-nondiffracting significant improvement compared to the unfiltered illumination but still minimal residual a significant improvement compared to the unfiltered illumination but still minimal side wings of Bessel distributions. The axicons generate quasi-nondiffracting light slices, light slices, which interfere in the region of crossing and propagate to the far field that residual side wings of Bessel distributions. The axicons generate quasi-nondiffracting which interfere in the region of crossing and propagate to the far field that is well separated, light slices, which interfere in the region of crossing and propagate to the far field that is well separated, if diffraction is sufficiently suppressed (Figure 5). if diffraction is sufficiently suppressed (Figure 5). is well separated, if diffraction is sufficiently suppressed (Figure 5). Figure 5. Measured far field distribution at a distance of 5.5 cm behind the SLM after optimizing the axicon parameters for configuration Com 1 (field of view: 7.03 × 5.62 mm ). The distance between the maxima is 953 µm. To compensate the 45° angle of incidence and to exactly adapt the linear foci to the Figure 5. Measured far field distribution at a distance of 5.5 cm behind the SLM after optimizing the Figure 5. Measured far field distribution at a distance of 5.5 cm behind the SLM after optimizing the target pupil function, size, shape and distance of the axicon lenses were optimized with axicon parameters for configuration Com 1 (field of view: 7.03 5.62 mm ). The distance between modified graphics software via gray value distributions and a calibrated look up table axicon parameters for configuration Com 1 (field of view: 7.03 × 5.62 mm ). The distance between the maxima is 953 m. (LUT). The directional adaptation by variation of the rotation angle is demonstrated the maxima is 953 µm. with multiple focal lines in Figure 6. With the SLM, it was easily possible to adjust ar- To compensate the 45 angle of incidence and to exactly adapt the linear foci to the rays of light slices parallel to the edges of rectangular sections of a Fresnel bi-micrror target pupil function, size, shape and distance of the axicon lenses were optimized with (linear axicon). For a self-apodized illumination of MEMS acting as spiral phase plates modified graphics software via gray value distributions and a calibrated look up table To compensate the 45° angle of incidence and to exactly adapt the linear foci to the (SPPs) in configuration Com 2, circular or elliptical foci have to be shaped by toroidal (LUT). The directional adaptation by variation of the rotation angle is demonstrated with phase profiles. target pupil function, size, shape and distance of the axicon lenses were optimized with multiple focal lines in Figure 6. With the SLM, it was easily possible to adjust arrays of light slices parallel to the edges of rectangular sections of a Fresnel bi-micrror (linear axicon). For modified graphics software via gray value distributions and a calibrated look up table a self-apodized illumination of MEMS acting as spiral phase plates (SPPs) in configuration (LUT). The directional adaptation by variation of the rotation angle is demonstrated Com 2, circular or elliptical foci have to be shaped by toroidal phase profiles. Figure 7 shows the variation of the diameter (a–d), a radial translation of the ring with multiple focal lines in Figure 6. With the SLM, it was easily possible to adjust ar- focus (e,g) and a typical torus lens profile (f). The thermally tunable spiral phase plate was rays of light slices parallel to the edges of rectangular sections of a Fresnel bi-micrror designed for the generation of orbital angular momentum beams with tunable topologi- cal charge. (linear axicon). For a self-apodized illumination of MEMS acting as spiral phase plates (SPPs) in configuration Com 2, circular or elliptical foci have to be shaped by toroidal phase profiles. Photonics 2022, 9, x FOR PEER REVIEW 7 of 13 Photonics 2022, 9, x FOR PEER REVIEW 7 of 13 Photonics 2022, 9, 42 7 of 13 Photonics 2022, 9, x FOR PEER REVIEW 7 of 13 Figure 6. Rotation of the structured illumination for configuration Com 1: three selected orientations of focal lines on the Fresnel-mirror shaped by SLM graphics software: (a) diagonal, (b) perpendicu- Figure 6. Rotation of the structured illumination for configuration Com 1: three selected orientations lar and (c) parallel to the contact line of the partial mirrors of the Fresnel bi-mirror. of focal lines on the Fresnel-mirror shaped by SLM graphics software: (a) diagonal, (b) perpendicu- lar and (c) parallel to the contact line of the partial mirrors of the Fresnel bi-mirror. Figure 7 shows the variation of the diameter (a–d), a radial translation of the ring focus (e,g) and a typical torus lens profile (f). The thermally tunable spiral phase plate Figure 7 shows the variation of the diameter (a–d), a radial translation of the ring Figure 6. Rotation of the structured illumination for configuration Com 1: three selected orientations Figure 6. Rotation of the structured illumination for configuration Com 1: three selected orientations was designed for the generation of orbital angular momentum beams with tunable top- focus (e,g) and a typical torus lens profile (f). The thermally tunable spiral phase plate of focal lines on the Fresnel-mirror shaped by SLM graphics software: (a) diagonal, (b) perpendicular of focal lines on the Fresnel-mirror shaped by SLM graphics software: (a) diagonal, (b) perpendicu- ologic was de al c signe harge. d for t he generation of orbital angular momentum beams with tunable top- lar and (c) parallel to the contact line of the partial mirrors of the Fresnel bi-mirror. and (c) parallel to the contact line of the partial mirrors of the Fresnel bi-mirror. ological charge. Figure 7 shows the variation of the diameter (a–d), a radial translation of the ring focus (e,g) and a typical torus lens profile (f). The thermally tunable spiral phase plate was designed for the generation of orbital angular momentum beams with tunable top- ological charge. Figure 7. Configuration Com 2: a torus-like phase map (SLM, f) was used to generate a flexible ring Figure 7. Configuration Com 2: a torus-like phase map (SLM, f) was used to generate a flexible ring Figure 7. Configuration Com 2: a torus-like phase map (SLM, f) was used to generate a flexible ring focus on a spiral phase plate (SPP, diameter 2.9 mm, distance SLM-SPP: 15.5 cm, angle of incidence: focus on a spiral phase plate (SPP, diameter 2.9 mm, distance SLM-SPP: 15.5 cm, angle of incidence: focus on a spiral phase plate (SPP, diameter 2.9 mm, distance SLM-SPP: 15.5 cm, angle of incidence: 21 , distance between SPP and detector plane: 5 cm). By varying radius (a–d) and decenter (e,g), the 21°, distance between SPP and detector plane: 5 cm). By varying radius (a–d) and decenter (e,g), the 21°, distance between SPP and detector plane: 5 cm). By varying radius (a–d) and decenter (e,g), the optimum performance was approximated (c). optimum performance was approximated (c). optimum performance was approximated (c). Figure 7. Configuration Com 2: a torus-like phase map (SLM, f) was used to generate a flexible ring In Figure 8, three different cases of illumination of a 4 4 MEMS axicon array are In Figure 8, three different cases of illumination of a 4 × 4 MEMS axicon array are focus on a spiral phase plate (SPP, diameter 2.9 mm, distance SLM-SPP: 15.5 cm, angle of incidence: drawn In Figur corresponding e 8, three todiffer Com e3.nt c With ases quasi-uniform of illuminati illumination on of a 4 × 4 (Figur MEMS a e 8a), x no icon back- array are drawn corresponding to Com 3. With quasi-uniform illumination (Figure 8a), no back- 21°, distance between SPP and detector plane: 5 cm). By varying radius (a–d) and decenter (e,g), the ground suppression is obtained. The other pictures demonstrate the capability to individ- drawn corresponding to Com 3. With quasi-uniform illumination (Figure 8a), no back- ground suppression is obtained. The other pictures demonstrate the capability to individ- optimum performance was approximated (c). ually address array elements with programmable needle beams for the cases of arbitrary ground suppression is obtained. The other pictures demonstrate the capability to individ- ually address array elements with programmable needle beams for the cases of arbitrary beam positions (Figure 8b) and centered beam localization (Figure 8c). ually beam addre In Figur positio ss arr n e s ( 8,F ta ig hy ree ure elemen differ 8b) and e ts with progr nt c cent ases ered of b illu eam ami mmabl loca natili on of z e nee ation a 4 d (Fi le be × 4 gurMEMS a ams e 8c).for the cases o xicon array are f arbitrary drawn corresponding to Com 3. With quasi-uniform illumination (Figure 8a), no back- beam positions (Figure 8b) and centered beam localization (Figure 8c). ground suppression is obtained. The other pictures demonstrate the capability to individ- ually address array elements with programmable needle beams for the cases of arbitrary beam positions (Figure 8b) and centered beam localization (Figure 8c). Figure 8. Configuration Com 3: individually addressable configurations were realized by flexibly Figure 8. Configuration Com 3: individually addressable configurations were realized by flexibly positioning SLM-generated needle beams (i.e., single-maximum Bessel beams) on the elements of a positioning SLM-generated needle beams (i.e., single-maximum Bessel beams) on the elements of a 4 × 4 MEMS axicon array (pitch: 1 mm). The axicons were illuminated by an approximated plane 4 4 MEMS axicon array (pitch: 1 mm). The axicons were illuminated by an approximated plane Figure 8. Configuration Com 3: individually addressable configurations were realized by flexibly wave (a), two arbitrarily displaced needle beams of different intensity (b), and the same two sub- wave (a), two arbitrarily displaced needle beams of different intensity (b), and the same two sub- positioning SLM-generated needle beams (i.e., single-maximum Bessel beams) on the elements of a beams centered at two selected axicons (c). beams centered at two selected axicons (c). Figure 8. Configuration Com 3: individually addressable configurations were realized by flexibly 4 × 4 MEMS axicon array (pitch: 1 mm). The axicons were illuminated by an approximated plane positioning SLM-generated needle beams (i.e., single-maximum Bessel beams) on the elements of a wave (a), two arbitrarily displaced needle beams of different intensity (b), and the same two sub- 4.2. Temporal Switching 4 × 4 MEMS axicon array (pitch: 1 mm). The axicons were illuminated by an approximated plane beams centered at two selected axicons (c). wave ( In a), Figur two e arbitrarily 9, the fr disp equency laced needle response beam of s of d a single, iffere piezo-actuated nt intensity (b), and the Fresnel-mirr same two sub- or is de- beams centered at two selected axicons (c). picted (Com 4). Photonics 2022, 9, x FOR PEER REVIEW 8 of 13 Photonics 2022, 9, x FOR PEER REVIEW 8 of 13 4.2. Temporal Switching 4.2. Temporal Switching In Figure 9, the frequency response of a single, piezo-actuated Fresnel-mirror is de- Photonics 2022, 9, 42 8 of 13 In Figure 9, the frequency response of a single, piezo-actuated Fresnel-mirror is de- picted (Com 4). picted (Com 4). Figure 9. Dynamic behavior. Configuration Com 4 combines the high-resolution spatial shaping of Figure 9. Dynamic behavior. Configuration Com 4 combines the high-resolution spatial shaping of Figure 9. Dynamic behavior. Configuration Com 4 combines the high-resolution spatial shaping the SLM and the fast-switching capability of the MEMS. The frequency response of combined SLM the SLM and the fast-switching capability of the MEMS. The frequency response of combined SLM of and F therSLM esnel-m and irror is the fast-switching shown as oscillo capability scope trof aces the for two MEMS. seThe lectefr dequency frequencies resp : ( onse a) 200 ofHz combined and (b) and Fresnel-mirror is shown as oscilloscope traces for two selected frequencies: (a) 200 Hz and (b) 450 Hz (time interval 75 ms in both cases). Far field oscillation was detected by a fast photodiode. SLM and Fresnel-mirror is shown as oscilloscope traces for two selected frequencies: (a) 200 Hz and 450 Hz (time interval 75 ms in both cases). Far field oscillation was detected by a fast photodiode. At higher frequencies, the signal of the unscreened detector was slightly distorted by electromag- (b) 450 Hz (time interval 75 ms in both cases). Far field oscillation was detected by a fast photodiode. At higher frequencies, the signal of the unscreened detector was slightly distorted by electromag- netic interference (laser source: diode laser, 790 nm). At higher frequencies, the signal of the unscreened detector was slightly distorted by electromagnetic netic interference (laser source: diode laser, 790 nm). interference (laser source: diode laser, 790 nm). The MEMS was illuminated by a laser diode, and the angular deflection was moni- The MEMS was illuminated by a laser diode, and the angular deflection was moni- tored by a photodiode in the far field. The combination of the slow switching SLM (flick- The MEMS was illuminated by a laser diode, and the angular deflection was monitored tored by a photodiode in the far field. The combination of the slow switching SLM (flick- ering at about 60 Hz video frequency) and a faster switching MEMS requires one to care- by a photodiode in the far field. The combination of the slow switching SLM (flickering ering at about 60 Hz video frequency) and a faster switching MEMS requires one to care- fully synchronize the frequency combs to avoid beating effects. Best performance was at about 60 Hz video frequency) and a faster switching MEMS requires one to carefully fully synchronize the frequency combs to avoid beating effects. Best performance was found in a MEMS frequency range between 100 Hz and 350 Hz, thus demonstrating the synchronize the frequency combs to avoid beating effects. Best performance was found in found in a MEMS frequency range between 100 Hz and 350 Hz, thus demonstrating the capabilities of combining specific advantages of SLM and MEMS in spatial and temporal a MEMS frequency range between 100 Hz and 350 Hz, thus demonstrating the capabilities capabilities of combining specific advantages of SLM and MEMS in spatial and temporal domains. of combining specific advantages of SLM and MEMS in spatial and temporal domains. domains. 4.3. Contrast Management for Non-Collinear Autocorrelation 4.3. Contrast Management for Non-Collinear Autocorrelation 4.3. Contrast Management for Non-Collinear Autocorrelation Combined systems offer the opportunity to circumvent the diffractive distortion of Combined systems offer the opportunity to circumvent the diffractive distortion Combined systems offer the opportunity to circumvent the diffractive distortion ultrashort pulses by self-apodization. As an application of combined SLM and Fresnel of ultrashort pulses by self-apodization. As an application of combined SLM and Fres- of ultrashort pulses by self-apodization. As an application of combined SLM and Fres- bi-mirror (configuration Com 1), we studied the possibility to improve the quality of non- nel bi-mirror (configuration Com 1), we studied the possibility to improve the quality nel bi-mirror (configuration Com 1), we studied the possibility to improve the quality collinear autocorrelation of few-cycle pulses. The principle of adaptive non-collinear of non-collinear autocorrelation of few-cycle pulses. The principle of adaptive non-col- of non-collinear autocorrelation of few-cycle pulses. The principle of adaptive non-col- autocorrelation with flexible Fresnel bi-mirrors was previously published by some of the linear autocorrelation with flexible Fresnel bi-mirrors was previously published by linear autocorrelation with flexible Fresnel bi-mirrors was previously published by authors [52]. Arrangement and signal analysis are described in this reference. To demon- some of the authors [52]. Arrangement and signal analysis are described in this refer- some of the authors [52]. Arrangement and signal analysis are described in this refer- strate the potential of pre-structuring the illuminating beam, we compare unoptimized and ence. To demonstrate the potential of pre-structuring the illuminating beam, we com- ence. To demonstrate the potential of pre-structuring the illuminating beam, we com- optimized second harmonic interference patterns generated with pulses of a Ti:sapphire pare unoptimized and optimized second harmonic interference patterns generated pare unoptimized and optimized second harmonic interference patterns generated oscillator (Figure 10). with pulses of a Ti:sapphire oscillator (Figure 10). with pulses of a Ti:sapphire oscillator (Figure 10). Figure 10. Improvement of interference contrast generated with configuration Com 1 at pulsed Figure 10. Improvement of interference contrast generated with configuration Com 1 at pulsed Figure 10. Improvement of interference contrast generated with configuration Com 1 at pulsed illumination illuminationby by adap adapting ting gr gre ey y level level maps map and s an backgr d back ound groun levels d level onsSLM on SL (aM ( ,c) unoptimized a,c) unoptimized and and (b,d) illumination by adapting grey level maps and background levels on SLM (a,c) unoptimized and (b,d) optimized intensity maps as 2D and 3D plots (laser source: Ti: sapphire laser oscillator; 7 fs optimized intensity maps as 2D and 3D plots (laser source: Ti: sapphire laser oscillator; 7 fs pulses; (b,d) optimized intensity maps as 2D and 3D plots (laser source: Ti: sapphire laser oscillator; 7 fs pulses; distance from mirror: 15 cm; frequency conversion: BBO; voltage at Fresnel bi-mirror: distance from mirror: 15 cm; frequency conversion: BBO; voltage at Fresnel bi-mirror: 104.5 V; and pulses; distance from mirror: 15 cm; frequency conversion: BBO; voltage at Fresnel bi-mirror: 104.5 V; and FOV: 1.375 × 0.8 2 25 mm ). FOV: 1.375 0.825 mm ). 104.5 V; and FOV: 1.375 × 0.825 mm ). Diffraction at the edges can mostly be eliminated. Information about second-order field autocorrelation can be derived from averaged horizontal cuts through the intensity profiles [52]. Photonics 2022, 9, x FOR PEER REVIEW 9 of 13 Diffraction at the edges can mostly be eliminated. Information about second-order Photonics 2022, 9, 42 9 of 13 field autocorrelation can be derived from averaged horizontal cuts through the inten- sity profiles [52]. 4.4. 4.4. T Tunable unable Nondiffracting NondiffractingT Talbot Ef albot Effect fect Contrary Contraryto to th the well-known e well-known dif fractive diffractive s self-imaging elf-imaging or or Talbot Ta ef lbot effect [4 fect [47–49], 7–49 the coher ], the - ent cohe geometrical rent geomsuperposition etrical superpof ositi conical on ofBessel-l conical Be ike needle ssel-like ne beams edl also e bea results ms alin so r periodical esults in revivals of periodical phase and/or amplitude patterns, which appear at particular dis- periodical revivals of periodical phase and/or amplitude patterns, which appear at par- tances ticular[ 51 di]. sta These nces [distances 51]. These di depend stance on s d the epen conical d on t beam he coangle nical be (which am anis gle ( determined which is de- by the phase profile of the axicons programmed into the SLM) and the divergence of the termined by the phase profile of the axicons programmed into the SLM) and the diver- illuminating laser beam. Because of its non-diffracting nature, the phenomenon can be gence of the illuminating laser beam. Because of its non-diffracting nature, the phenom- used to transfer temporal information of ultrashort pulses from near-field to far-field dis- enon can be used to transfer temporal information of ultrashort pulses from near-field tances, or to realize laser-matter interactions at ultrashort pulse duration far from the beam to far-field distances, or to realize laser-matter interactions at ultrashort pulse duration shaper. By changing the illumination divergence or convergence, the nondiffracting Talbot far from the beam shaper. By changing the illumination divergence or convergence, the distances can be shifted. This adaptive approach makes the technique more attractive for nondiffracting Talbot distances can be shifted. This adaptive approach makes the tech- applications such as optical tweezing, filamentation, coupling or wavefront diagnosis. In nique more attractive for applications such as optical tweezing, filamentation, coupling the experiments, arrays with central holes were programmed to enable for easier centering or wavefront diagnosis. In the experiments, arrays with central holes were pro- and identifying the order of self-imaging. The geometry of parts of a hexagonal and an grammed to enable for easier centering and identifying the order of self-imaging. The orthogonal array is shown in Figure 11. geometry of parts of a hexagonal and an orthogonal array is shown in Figure 11. Figure 11. Hexagonal (a) and orthogonal (b) arrays of elliptical axicons programmed into the SLM Figure 11. Hexagonal (a) and orthogonal (b) arrays of elliptical axicons programmed into the SLM phase map for the generation of nondiffracting needle beams (parts of larger arrays, optimized for phase map for the generation of nondiffracting needle beams (parts of larger arrays, optimized 45° illumination, and 790 nm diode laser). In the central regions, a few elements (7 and 9, respec- for 45 illumination, and 790 nm diode laser). In the central regions, a few elements (7 and 9, tively) were eliminated to enable for centering the system, identifying the order of self-imaging and respectively) were eliminated to enable for centering the system, identifying the order of self-imaging visualizing residual diffraction effects (FOV on the SLM: 3.3 × 3.3 mm ). and visualizing residual diffraction effects (FOV on the SLM: 3.3 3.3 mm ). A tunable, piezo-actuated fluid lens (SLM04, IMTEK) was positioned 5 cm in front of A tunable, piezo-actuated fluid lens (SLM04, IMTEK) was positioned 5 cm in front the SLM. By changing the voltage at the piezo-actuator, the angular distribution of the of the SLM. By changing the voltage at the piezo-actuator, the angular distribution of the input beam at the SLM was tuned up to a maximum value of 75 V (at higher voltages, the input beam at the SLM was tuned up to a maximum value of 75 V (at higher voltages, the beam quality was found to be significantly reduced by aberrations). The beam propaga- beam quality was found to be significantly reduced by aberrations). The beam propagation tion was analyzed by detecting the distance-dependent intensity patterns on the CCD was analyzed by detecting the distance-dependent intensity patterns on the CCD camera camera (5 cm behind the SLM). The laser intensity was adjusted with a polarizer. Figure (5 cm behind the SLM). The laser intensity was adjusted with a polarizer. Figure 12 for the 12 for the hexagonal array shows how the nondiffracting self-imaging planes are shifted hexagonal array shows how the nondiffracting self-imaging planes are shifted to smaller to smaller distances to the SLM with increasing voltage. In Figure 13, the distances are distances to the SLM with increasing voltage. In Figure 13, the distances are kept constant kept constant and the patterns change with increasing voltage. One has to note equivalent and the patterns change with increasing voltage. One has to note equivalent patterns in patterns in both cases, which indicate that self-imaging appears at different distances de- both cases, which indicate that self-imaging appears at different distances depending on pending on the lens voltage. the lens voltage. Additionally, a number of specific problems were identified that have to be taken into account for further improvements: (i) the background generated by diffraction at the pixels of the SLM; (ii) reflection at interspaces between MEMS elements in arrays; (iii) temporal phase flickering of pulsed SLM because of liquid crystal viscosity; and (iv) strong angular dependence of programmed DOE, e.g., astigmatic spiral phase gratings. With the SLM, a background suppression was obtained by programming check-patterns as 2D gratings into structure-less areas or gaps and by appropriately modifying the phase con- trast between pixels and structures. Flickering of liquid crystal devices could be influenced by temperature control. Photonics 2022, 9, x FOR PEER REVIEW 10 of 13 Photonics 2022, 9, 42 10 of 13 Photonics 2022, 9, x FOR PEER REVIEW 10 of 13 Figure 12. Configuration Com 5: Experimental demonstration of tunable nondiffracting self-imaging Figure 12. Configuration Com 5: Experimental demonstration of tunable nondiffracting self-imaging Figure 12. Configuration Com 5: Experimental demonstration of tunable nondiffracting self-imaging with with a hex a hexagonal agonal ax axicon icon array array prog programmed rammed into th into the e SLM SLM and an illu and an illumination mination by by a flu a fluid id lens of lens of with a hexagonal axicon array programmed into the SLM and an illumination by a fluid lens of electrically steerable focal length. The pictures show the voltage-dependent axial shift of the integer electrically steerable focal length. The pictures show the voltage-dependent axial shift of the integer electrically steerable focal length. The pictures show the voltage-dependent axial shift of the integer self-imaging planes and an intermediate fractal plane corresponding to alternating phases (FOV self-imaging planes and an intermediate fractal plane corresponding to alternating phases (FOV about self-imaging planes and an intermediate fractal plane corresponding to alternating phases (FOV about 3.3 × 3.3 mm on CCD detector, spatial scales slightly adapted to show the geometrical simi- 3.3 3.3 mm on CCD detector, spatial scales slightly adapted to show the geometrical similarity). about 3.3 × 3.3 mm on CCD detector, spatial scales slightly adapted to show the geometrical simi- larity). The different distances for two voltages 24 V (a–c) and 50 V (d–f) indicate the axial tuning The different distances for two voltages 24 V (a–c) and 50 V (d–f) indicate the axial tuning (laser larity). The different distances for two voltages 24 V (a–c) and 50 V (d–f) indicate the axial tuning (laser source: diode laser, 790 nm). source: diode laser, 790 nm). (laser source: diode laser, 790 nm). Figure 13. Configuration Com 5: Experimental demonstration of tunable nondiffracting self-imaging Figure 13. Configuration Com 5: Experimental demonstration of tunable nondiffracting self-imaging Figure 13. Configuration Com 5: Experimental demonstration of tunable nondiffracting self-imaging with an orthogonal axicon array: interference patterns at three different distances for two different with an orthogonal axicon array: interference patterns at three different distances for two different with an orthogonal axicon array: interference patterns at three different distances for two different voltages at the tunable lens (FOV: 3.3 × 3.3 mm on CCD detector, laser source: diode laser, 790 nm). voltages voltages at at the the tunable tunable lens (F lens (FOV OV: 3.3 × : 3.3 3.3 3.3 mm on mm on CCD detector, CCD detector, laser laser sour source: ce: diode diode la laser ser,, 790 nm). 790 nm). Contrary to Figure 12, different patterns appear at different voltages for equal distances (compare Contrary to Figure 12, different patterns appear at different voltages for equal distances (compare Contrary to Figure 12, different patterns appear at different voltages for equal distances (compare a–c a–c and d–f). a–c and d–f). and d–f). Additionally, a number of specific problems were identified that have to be taken 5. Conclusions Additionally, a number of specific problems were identified that have to be taken into account for further improvements: (i) the background generated by diffraction at the into account for further improvements: (i) the background generated by diffraction at the To conclude, the highly flexible generation of structured light fields with tandem pixels of the SLM; (ii) reflection at interspaces between MEMS elements in arrays; (iii) pixels of the SLM; (ii) reflection at interspaces between MEMS elements in arrays; (iii) arrangements of adaptive phase-shaping components was demonstrated. The particular temporal phase flickering of pulsed SLM because of liquid crystal viscosity; and (iv) temporal phase flickering of pulsed SLM because of liquid crystal viscosity; and (iv) goal of the experiments was to achieve synergetic effects by combining specific advantages strong angular dependence of programmed DOE, e.g., astigmatic spiral phase gratings. strong angular dependence of programmed DOE, e.g., astigmatic spiral phase gratings. Photonics 2022, 9, 42 11 of 13 of high-resolution phase-only spatial light modulators and different types of piezo-actuated or thermally driven MEMS mirrors and lenses. The capability to efficiently reduce diffrac- tion by self-apodization and to control propagation properties by tuning angular profiles were experimentally verified. Self-apodization enables the generation of high-quality non- diffracting beams or wavepackets, which we refer to as “doubly non-diffracting beams”. The prize one has to pay for reduced losses and improved pulse transfer is the enhancement of the angular divergence of the shaped beams. Therefore, the concept is of particular interest for applications that tolerate wavefront transformation or preferentially utilize the near field. At extremely short pulse durations, space-time coupling effects have to be additionally compensated for. In our opinion, the beam quality factor M can only be applied to simple types of beams such as the Gaussian beam or the Bessel beam. In practice, the statistical description neglects important features of the shaped beams such as rippled substructure and temporal or spectral effects. For a confined analysis of the beam quality, the space-bandwidth-product could also be involved, which is known from signal theory [53]. By combining programmable axicon arrays with a fluid lens of tunable focal length, nondiffracting self-imaging was extended towards variable Talbot distances. This approach could find applications in micromanipulation, filamentation or adaptive wavefront sensing. Involving the control of amplitude or polarization maps will further enhance the number of free parameters. We would like to mention that, in recently reported studies of other groups, amplitude- and phase-shaping were simultaneously realized by two SLMs [16] or by using a DMD for programmable laser heating of a thermally deformable mirror [54]. Considering the specific properties of the diverse types of beam shapers, the combination of DMDs with SLMs and/or MEMS promises to be another fruitful concept for the future. To sum up, on the basis of first exploring studies, it has to be expected that combined and integrated adaptive optical systems will essentially contribute to advanced applications of ultrashort and intense pulsed lasers. Author Contributions: Conceptualization, R.G., M.B., M.L. and U.W.; methodology, R.G., M.B. and M.L.; software, M.B., M.J.; electronics, B.P.B. and M.J.; design, test and fabrication of MEMS, B.P.B., H.G. and U.W.; experiments and data analysis, R.G., M.L., M.J. and H.G.; writing—original draft preparation, R.G.; writing—review and editing, R.G. and U.W.; visualization, R.G. and M.J.; supervision, project administration and funding acquisition, R.G. and U.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by German Research Foundation (DFG), project MAXWELL III, grant numbers GR1782/16-1, WA 1657/6-2 and WA1657/11-1. Data Availability Statement: Data underlying the simulation results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. Acknowledgments: Experimental resources including lab space and laser systems were kindly provided by Elsaesser and Erik Nibbering (MBI). We thank Alexander Treffer for technical support and helpful discussions. The authors acknowledge support for microscopic characterization of components by Dieter Engel and Sandy Schwirzke-Schaaf (MBI). Furthermore, we thank Peter Scholze (MBI) for designing and manufacturing sophisticated mechanical mounts. Conflicts of Interest: The authors declare no conflict of interest. References 1. Forbes, A.; de Oliveira, M.; Dennis, M. Structured Light. Nat. Photon. 2021, 15, 253–262. [CrossRef] 2. Rubinsztein-Dunlop, H.; Forbes, A.; Berry, M.V.; Dennis, M.R.; Andrews, D.L.; Mansuripur, M.; Danz, C.; Alpmann, C.; Banzer, P.; Bauer, T. Roadmap on structured light. J. Opt. 2017, 19, 013001. [CrossRef] 3. Scholes, S.; Sroor, H.; Ait-Ameur, K.; Zhan, Q.; Forbes, A. General design principle for structured light lasers. Opt. Express 2020, 28, 35006–35017. 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Photonics – Multidisciplinary Digital Publishing Institute
Published: Jan 13, 2022
Keywords: structured light; combined systems; beam shaping; spatial light modulators; adaptive optics; MEMS; nondiffracting beams; self-apodization; Talbot effect; fluid lens
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