Introduction

Spatial light modulators (SLMs)1,2,3,4 are devices that can spatially modulate the amplitude, phase or polarization of light, which makes them crucial components in a wide range of applications, from emerging holographic and AR/VR displays5 to bio-imaging, free-space optical communications or quantum computing, to name a few3. Among SLMs, phase-only devices typically employ liquid crystals6 (LCs) to control the phase retardation of light on individual pixels. Due to their anisotropic molecular morphology, collectively aligned LC molecules can create a birefringent medium with an anisotropic refractive index. In the case of a nematic LC, this anisotropy can reach values as large as ∆n = 0.2–0.4 in the visible spectral range (here, \(\Delta n = n_e - n_o\) is the difference between the extraordinary and ordinary refractive indices, ne and no, respectively). Importantly, the alignment of the LC molecules can be reoriented towards a particular direction by applying an external electric field and consequently the anisotropic refractive index can be dynamically controlled. By biasing individual pixels, the LC orientation can be locally modified, creating a refractive index landscape that translates into different local phase retardations experienced by an impinging light field. This simple, yet powerful approach imposes a certain thickness for the LC layer to be able to span the full 2π phase range. This turns into high driving voltages needed to rotate the LC molecules and ultimately limits the ability to reduce the pixel size without incurring significant cross talks that render the local phase unpredictable6. Currently the smallest pixel size for commercially available reflective one dimensional (1D) LCoS SLM is 1.6 μm7; and the smallest pixel size commercially available for two dimensional (2D) reflective LCoS1,2,8 devices is more than 3 μm, a figure that has been stagnant for almost the last decade. Large pixel sizes not only result in narrower field of view (FOV), but also limit the ability to properly map sharp variations of phase in a given profile, which is of critical importance in certain applications, such as quantum optics or microscopy.

Recently, a novel approach to realize SLM devices has emerged by using actively tunable metasurfaces9,10. These are planar arrays of nanostructures where the phase retardation comes from their resonant interaction with light11,12,13,14,15,16,17,18,19,20,21,22. Active tuning of amplitude, phase or polarization is achieved either by modifying the optical properties of these meta-atoms or those of their surroundings23,24. Recent studies have demonstrated the use of phase change materials25,26,27,28,29,30,31, transparent conducting oxides9,32,33,34, two-dimensional materials35,36,37,38,39, semiconductors40,41,42 and liquid crystals10,43,44,45,46,47 as tuning media, with very few examples achieving individual pixel control9,10,34. Moreover, using the concept of Huygens’ metasurfaces, it is possible to limit the coupling between amplitude and phase modulation10,48,49. Because of their large birefringence, mature fabrication technology and negligible losses in the visible range, LC are particularly interesting when aiming for display applications. As the phase retardation comes from the metasurface itself and the LC acts only as a tunable environment, its thickness can be significantly reduced, in turn helping to shrink the pixel size10. So far, however, these metasurface-based devices are monochromatic in nature and their extension to multi-spectral operation poses significant design challenges that are yet to be addressed.

Here, we introduce a novel SLM that employs LC-tunable Fabry-Perot (FP) nanocavities as pixels, to simultaneously address the limitations of conventional LC-SLMs, as well as those of metasurface-based ones. Previously, this type of structure, in the non-miniaturized version, has been used to realize tunable filters50,51,52,53. The device, in particular, (i) consists of a thin (sub-micron) LC cell, as to improve the response time and reduce the inter pixel cross talk, (ii) comprises small (~1 μm) pixels to achieve wide FOV (18°) and (iii) can operate simultaneously at multiple wavelengths, including red (R), green (G) and blue (B) wavelengths in the visible spectrum. This device, referred to as Fabry-Perot spatial light modulator (FP-SLM), enables high reflectance and large phase modulations of 2π at these multiple wavelengths simultaneously. As shown next, we experimentally realize the device and configure it to achieve efficient programmable wide-angle beam steering and tunable-focus lensing.

Results

Device design

Figure 1(a), shows a schematic of our FP-SLM device, which consists of an array of FP nanocavities, formed by sandwiching a thin layer of LC between two partially reflective mirrors. The device comprises two sets of conducting electrodes: a thin layer (23 nm) of indium-tin-oxide (ITO) on top, serving as a common electrode and a set of linear pixelated electrodes formed by patterning a 150 nm thick layer of Aluminum (Al) at the bottom (two of which are schematically shown in Fig. 1(a)). These bottom electrodes define the size of each FP nanocavity pixel and can be individually biased to electrically tune the LC orientation inside each nanocavity. The whole system is sandwiched between a glass substrate and a superstrate. Light is incident from the top, with its electric field polarized along the x-direction, coinciding with the initial orientation of the LC director when the device is unbiased, thus experiencing the LC extraordinary refractive index (ne). When the LC director is reoriented to an angle θLC by applying an electrical bias (Fig. 1(a)), the refractive index experienced by light is modified (ending in the ordinary one, n0, when the LC is fully vertically rotated, θLC = 0°), thus resulting into the modulation of the resonant frequency of the FP cavity. The LC in our device rotates in the x-z plane, determined by its initial alignment direction, and has a large birefringence \(\Delta n = n_e - n_0 = 0.291\) (ne = 1.813; n0 = 1.522).

Fig. 1: Concept of FP-SLM.
figure 1

a The schematic of the FP-SLM showing two pixels. The system comprises two partially reflecting mirrors, denoted as upper and lower DBR, a top ITO layer acting as a common electrode, a LC layer with thickness hLC and a set of Al electrodes forming pixels with a width wAl, periodicity P and inter-pixel gaps G, as specified in the main text. When bias is applied between an Al electrode and the top ITO electrode the orientation of the LC director on top of the pixel can be modified from its initial in-plane state (θLC = 90°) to a certain tilted angle θLC. b Simulated reflectance spectra for two different LC orientation angles, θLC = 90° and 0°, for the non-pixelated FP-SLM with hLC = 750 nm. The dashed vertical lines represent the operating wavelengths, while the color arrows are guides to the eye indicating the initial and final positions of the resonances. c–e Simulated reflectance and phase shifts at the operating RGB wavelengths versus the LC rotation angle

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The two partially reflective mirrors on top and bottom that form the cavity, as shown in Fig. 1(a), consist of alternating layers of high and low refractive index transparent dielectric materials TiO2/SiO2, forming distributed Bragg reflectors (DBR). The thickness (tlayer) of each dielectric layer in the DBR is optimized such that:

$$t_{layer} = \lambda /4n_{layer}$$
(1)

where nlayer is the refractive index of the layer and λ the optimization wavelength. In particular, the thicknesses in each DBR (upper & lower) are adjusted such that the DBRs exhibit high reflectance across the whole visible wavelength range (400 nm–800 nm). The detailed description of the optimization can be found in Methods, and the simulated reflectance in Supplementary Fig. S1. After the DBRs are optimized, we study the performance of FP-SLM device shown in Fig. 1(a).

For the proof of concept, we first simulate (see Methods) the device performance considering a continuous bottom Al electrode. The FP-SLM device is based on Fabry Perot nanocavities, in which the number of resonances and spectral positions across the visible wavelength range can be tuned by varying the thickness of the LC layer (hLC). The FP-SLM reflectance spectra as a function of hLC are shown as a color map in Supplementary Fig. S2. For our device, we choose an optimum value of hLC = 750 nm, which results in high reflectance resonances with large associated phase shifts at all the three RGB wavelengths. Figure 1(b) shows the simulated reflectance spectrum, which indeed displays the desired resonances at RGB wavelengths. As shown there, these resonances blue-shift when the LC is reoriented from θLC = 90° (in-plane, blue curve) to θLC = 0° (out-of-plane, purple curve). Based on this behavior, we chose the operating wavelengths of the device such that the resonance positions completely “cross” these wavelengths when the LC is switched. These are demarcated by dashed vertical lines in Fig. 1(c) and are λ = 460 nm (for blue, B), 532 nm (for green, G) and 649 nm (for red, R), with an additional wavelength λ = 600 nm for orange (O). Importantly, LC reorientation and FP resonance shift give rise to large phase modulations at these wavelengths with high associated reflectivity. This is demonstrated in Fig. 1d–f, where we plot the reflectance and phase shift at the three RGB wavelengths as a function of orientation of the LC molecules, indeed showing that the high reflectance (>60%) and ~2π phase shifts can be achieved for all of them.

Experimental demonstration

For the experimental demonstration of our FP-SLM, we fabricated a device consisting of 96 (linear) electrodes, which can be addressed individually. Each electrode has a width of wAl = 1 μm and is separated from the neighboring pixel by a gap G = 140 nm, resulting in a pixel pitch of P = 1.14 μm (Fig. 1a). Figure 2(a) shows a camera image of the final device mounted on and wire bonded to a printed circuit board (PCB). The wires are encapsulated with a glue to protect them from any short-circuit or physical tear. The device is fabricated (see Methods) using a combination of electron beam lithography and dry etching and photolithography and wet etching for the bottom electrodes and fan-outs, respectively. Ion-assisted deposition was used to achieve the precise thickness required for the DBRs (see Supplementary Fig. S1 for the experimentally measured reflectance spectra and comparison with the theoretical ones). A zoomed-in optical image on the active pixel area is shown in Fig. 2(b). Figure 2(c) shows the top view scanning electron microscopy image (SEM, Hitachi SU8220) of the Al linear electrodes before the deposition of the lower DBR (the inset displaying a tilted-view, magnified SEM image of the pixels). The desired height of the LC cell is achieved using polyimide as a spacer, which is then infiltrated with the LC using capillary forces. In the final device, an LC cell thickness of hLC = 530 nm was achieved, which is a bit lower than our designed LC height of 750 nm.

Fig. 2: Performance of the fabricated device.
figure 2

a Optical image of the device mounted on the PCB board and connected to the voltage supply. The group of wires provides voltage to the individual electrodes (scale bar: 10 mm). b Optical microscope image of the fabricated 96-electrodes FP-SLM device, showing the electrodes and the active area (scale bar: 100 μm). c Top view SEM image of the fabricated device (scale bar: 25 μm). The inset shows a magnified tilted view SEM images (scale bar: 500 nm). The measured thickness of the Al electrodes is 158 nm. d Reflectance spectra for the FP-SLM. In red, simulated reflection assuming hLC = 530 nm and θLC = 90°. In blue, the measured spectra when no bias is applied to the device. e Simulated and (f) measured reflectance spectra as a function, respectively, of θLC and bias applied (Vrms). In the experiment, all pixels are simultaneously biased

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To characterize our device, we first corroborate that all electrodes of the fabricated device can be individually controlled by biasing each of them (square waveform input, 10 Vrms at 1 kHz) and looking at the induced intensity modulation under white light illumination in a crossed polarizer-analyzer configuration, where the LC is aligned at 45 degrees with respect to the polarizer. In this situation, the electrodes should become dark after the LC is reoriented vertically upon biasing. We find that all the electrodes are working well, as shown in Supplementary Video S1. Then, we remove the analyzer and measure the reflectance spectrum (see Methods for the details on the characterization setup) when the LC director is parallel to the polarization direction and no voltage is applied to the device. Figure 2(d) shows the obtained results and, for comparison, the simulated ones when we consider hLC = 530 nm and θLC = 90°. As can be seen, a good agreement between both is found, displaying three distinct resonances at three different wavelengths (viz. blue, orange and red). Note that the resonance in the green range has been shifted to orange due to offset of LC thickness in the fabricated device compared to that in the optimized model. Upon biasing all the electrodes with an increasing AC voltage Vrms at 1 kHz, the observed resonances experience the expected blue-shift, as shown in the reflectance color map in Fig. 2(e). For comparison, Fig. 2(f) shows the simulated results when the rotation of LC is varied from 90° to 0° (the expected reflectance and phase modulations at the operating wavelengths of this device with hLC = 530 nm are shown in Supplementary Fig. S3). Next, we measure the phase modulation provided by this device upon biasing, using interferometric measurements (see Methods for details). Again, the same Vrms is applied to all electrodes, in this case from 0 V to 8 V. The results obtained near the blue, orange and red resonant wavelengths are shown, respectively, in Fig. 3a–c. The corresponding simulated phase tunability as a function of the LC rotation is shown in Fig. 3d–f, demonstrating good agreement with the experiment.

Fig. 3: Multi-spectral phase modulation of the FP-SLM.
figure 3

a–c Experimentally measured and (d–f) simulated phase shifts as a function of wavelength and, respectively, applied voltage to the FP-SLM device and LC director rotation angle (θLC) around the operational wavelengths (shown as vertical dashed lines) in the blue (a, d) orange (b, e) and red (c, f) spectral regions. g–i Simulated (solid blue curve) and measured (solid red curve with symbols) at the operational wavelength in (g) the blue (λ = 503 nm), (h) the orange (λ = 596 nm) and (i) the red (λ = 662 nm in simulation, λ = 640 nm in experiment) spectral regions

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The maximum phase retardations obtained experimentally for the operating wavelengths in the blue (503 nm), orange (596 nm) and red (662 nm) are plotted in Fig. 3g–i, together with the simulated results. Note that, in simulations, 640 nm is taken for the red wavelength instead, which is due to the slight spectral shift and smaller tuning range achieved in the experiment for this wavelength. As seen in the figures, we experimentally achieved phase shifts close to 2π for all the three wavelengths, namely >1.75π for blue and orange and ~1.5π for red.

To demonstrate the capability of wavefront control at the individual pixel level, we first program the FP-SLM as a tunable-angle beam steering device. To do so, different voltage profiles are applied to the 96 electrodes so as to create 0-2π linear phase gradients in periodically repeated super-cells. The size of these super-cells determines the diffraction angle (θD), which, for the first (±1) orders, follows the simple formula1 \(\theta _D = \pm \sin ^{ - 1}\left( {\lambda /{{{\mathrm{n}}}}P} \right)\), where n is the number of pixels comprising the super-cell. When a 0-2π linear phase profile is mapped in this super-cell, the energy channels into a single diffraction order (+1 or −1, depending on the sign of the slope of the gradient), resulting in beam steering. We first show in Fig. 4(a) that, when the device is unbiased, all the reflection goes into the zeroth order (simple specular reflection in the normal direction). We then bias the electrodes with periodic voltage profiles optimized to achieve the 0-2π linear phase mapping corresponding to the −1 diffraction order in super-cells with varying dimensions (see Methods). Figure 4b–d show three particular cases, in which the super-cells comprise 5, 8 and 12 electrodes, as schematically depicted on top of the figures (see Supplementary Fig. S4 for the optimized voltage profiles). The colormaps in the figure show the measured reflectance as a function of reflection angle and wavelength, in the regions near the FP-SLM resonances. As can be seen, at the selected operation wavelength the reflected intensity concentrates at a certain angle, which indeed corresponds to the −1 diffraction order. Also it can be readily seen, that reprogramming the FP-SLM with different super-cells enables tunable-angle beam steering (see Supplementary Fig. S5 for tuning using a wider range of super-cells). Importantly, this is possible at all selected operating wavelengths of the device (see Supplementary Figs. S6 and S7).

Fig. 4: Programmable beam steering with the FP-SLM.
figure 4

a–d Color maps showing the measured reflectance as a function of wavelength and the reflection angle: (a) when all electrodes are unbiased, and (b–d) when voltage patterns are applied to the electrodes creating linear phase profiles corresponding to a blazed grating with (b) 5-pixels, (c) 8-pixels and (d) 12-pixels supercells. The voltage patterns are schematically shown on top of the panels. e–g Extracted diffraction (reflectance) efficiencies for the main orders supported by the induced gratings (−1st and +1st). The top panels correspond to the cases depicted in (b–d), leading to power channeling into the −1st order, while the bottom ones correspond to the reversed angle configuration, channeling power into the +1st order

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An important feature of the FP-SLM is the fine, continuous control over the phase, while maintaining a high reflectivity, thus limiting simultaneous amplitude modulation. Loss of efficiency due to amplitude modulation is further reduced by numerical optimization of super-cell voltages (see Fig. S4). This is shown in the top panels in Fig. 4e–g. For the 5-pixel super-cell, we measure an efficiency ~20% (defined as the absolute reflectance into the −1 order) for all three operating wavelengths. In the other two cases (i.e,. 8-pixels and 12-pixels) the efficiency is higher, peaking at a maximum above 40% for the eight-pixel case when operating in the blue region. We note, moreover, the remarkable difference between reflectance into the desired (−1) diffraction order and the undesired (+1) one, as well as the fact that the beam steering angle can be switched from negative to positive angle with very similar efficiencies by reversing the linear phase gradient, as shown in the bottom panels in Fig. 4e–g. We also note that, for the 5-pixels super-cell operating in the red region, which corresponds to the largest steering angle (~7°), this asymmetry is reduced, which might follow from the limited phase modulation obtained for this wavelength (~1.5π) and the steep phase profile required to map the tilted wavefront. This asymmetry further reduces if 4-pixels super-cells are considered (see Supplementary Fig. S8, which also presents the reflection into the zeroth order for all cases, which is still dominating in some of them) and almost completely disappears for three-pixels (not shown here), which we take as the limit at which the device stops working. Ultimately, this translates into a maximum field of view ~18° (in the red region), corresponding to the 4-pixels case. For completeness, the simulated beam steering efficiencies are shown in Supplementary Fig. S9.

Finally, to demonstrate the versatility of the FP-SLM, we re-program it to act as a tunable cylindrical lens. For that, the electrodes are configured to impart a position-dependent phase profile following the formula:

$$\phi \left( x \right) = \frac{{2\pi }}{\lambda }\left[ {\left( {x^2 + f^2} \right)^{1/2} - f} \right]$$
(2)

where x is the distance to the center of the lens (i.e., the center of the device) and f is the lens focal distance. First, we show that by reconfiguring the device, it is possible to focus light at the same focal distance for all the three operating wavelengths (blue, orange and red). Following Eq. (2), the device needs to impart different phase profiles for each of the different wavelengths in order the keep the same f. Interestingly, these phase profiles can be readily seen when measuring the spatially resolved near-zone reflection spectra of the device at z = 0 μm (z being the distance to the device), as shown in Fig. 5a–c. There, the spectral position of the resonance as a function of x can be easily identified and, as seen, it follows closely the shape of the phase profile of the lens, with the different Fresnel zones being apparent. Note that, indeed, the optimized profile for each of the three wavelengths is slightly different, which is needed to focus all wavelengths at a same focal distance z = 525 μm from the device, corresponding to a numerical aperture (NA) of NA = 0.1. Figure 5d–f show the spatially resolved reflection spectra, with the resulting focusing for the three wavelength ranges measured at the same distance of z = 525 μm from the device. The highest focusing intensities are measured at 499 nm, 591 nm and 661 nm wavelengths, which are very similar to those where we achieved maximum beam steering efficiencies, as shown in Fig. 4. The corresponding line profiles are presented in Fig. 5g–i, displaying characteristic Airy profiles. By integrating the intensity contained within the first Airy ring and normalizing by the incident power, we estimate a total efficiency of ~21% for the blue wavelength, ~27% for the orange and ~16% for the red. These focusing efficiencies are achieved readily, without numerical optimization (see Methods), which could further improve these efficiencies and reduce influence of amplitude modulation and imperfect phase profiles. We stress again that, in order to keep the same focal distance for the different wavelengths, different phase profiles and therefore different voltages are needed. These are shown in Supplementary Fig. S10 for completeness. If, instead, a single voltage profile is used, the different wavelengths focus at different distances, as shown in Supplementary Video S2. Finally, in Fig. 5j–l, we show that, by reconfiguring the device, it is possible to continuously shift the focal distance to any desired value for any of the three operating wavelength ranges. We illustrate this by plotting the intensity distributions as the light propagates away from the lens when the device is reconfigured to achieve different focal distances for the orange wavelength of 591 nm, namely 350 μm (NA = 0.15), 500 μm (NA = 0.11) and 625 μm (NA = 0.09). Beyond this lensing demonstration, which seeks to underline versatility and readiness of our device, we note that it should be possible to further improve the device performance, e.g., the lens profiles, by utilizing machine learning methods, but this is however left for future work.

Fig. 5: Programmable lensing with the FP-SLM.
figure 5

a–c Measured spatially resolved near-zone (z = 0) reflectance spectra as a function of the transverse position in the device. The plots show tailored resonance positions, imparting phase profiles to achieve focusing to the same focal distance for the three operating wavelengths. d–f Measured spatially resolved reflectance spectra at z = 525 μm, showing the resulting focal spots with maximum efficiencies at 499 nm, 591 nm and 661 nm wavelengths. g–i Line profiles of the focal spots at the wavelengths indicated in (d–f). Focusing efficiencies corresponding to the shaded areas are 21%, 27% and 16%, respectively. j–l Measured intensity distributions as a function of the distance to the device (z) for the orange wavelength of 591 nm. Reconfigurable change of focal distance is demonstrated for three exemplary focus positions, i.e., 350 μm (j), 500 μm (k), and 625 μm (l)

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Discussion and conclusion

In summary, we have proposed an architecture to realize phase-only, multispectral reflective SLMs with reduced pixel size. The device consists of an array of FP nanocavities infiltrated with LCs, which can be individually biased to provide continuous 2π phase modulation with high associated reflectivity at RGB wavelengths, including, potentially, those of commercially available RGB diode lasers. By using the phase modulation associated with the FP resonance spectral shifts, we uncouple it from the physical thickness of the LC, which can be reduced down to 530 nm only. This allows us to dramatically reduce the inter-pixel cross-talk, enabling miniaturization of the pixel size down to ~1 μm. We demonstrate the concept by realizing a fully programmable device with 96 linear electrodes that can be individually addressed. First, we employ it to perform dynamic beam steering, achieving peak efficiencies >40% and a maximum FOV of ~18°. Then, we reconfigure our device to realize fixed focal distance lensing for the different operating wavelengths with efficiencies ranging from 16% to 27% for NA = 0.1. The same device is then used to tune the focal distance at a given wavelength, demonstrating NAs from 0.09 to 0.15. Our design could be readily extended to two dimensional SLM devices by using standard CMOS technology for integrated circuits and is amenable to other electro-optical tuning mechanisms. Moreover, we foresee that the voltage and crosstalk could be further reduced, and consequently also the pixel size, if the electrodes (or at least the top one) would be placed inside the cavity formed by the dielectric mirrors, or if one would require single wavelength operation. We believe that the proposed design methodology will have wide implications in the field of ultra-high resolution dynamic wavefront control, with numerous applications in diverse fields, ranging from solid-state LiDAR to AR/VR and holographic displays, optical communications or quantum computing, to mention some.

Materials and methods

Simulation methodology and optimization of distributed bragg reflectors

The device design was carried out by full wave numerical simulation based on Finite Difference Time Domain method (FDTD, Lumerical Solutions). First, we calculate the reflectance of the upper & lower DBRs separately and optimize them. For that, the thicknesses of the layers in each DBR (upper & lower) is adjusted such that it can give high reflectance across the visible wavelength range (400 nm–800 nm). To calculate the thickness of the layers we consider the refractive indices of TiO2 and SiO2 to be constant (\(n_{{TiO}_{2}}\) = 2.48 and \(n_{{SiO}_{2}}\) = 1.46, respectively). In subsequent simulations, the refractive index of all materials is considered to be dispersive. For TiO2, we use experimental data from ellipsometry measurements (see Supplementary Fig. S11) while for SiO2 we used SiO2-Palik as included in Lumerical´s material database). The upper DBR comprises the thin layer of ITO (23 nm) acting as a transparent electrode (see Supplementary Fig. S12 for the ITO refractive index data measure by ellipsometry and used in simulations), and three pairs of TiO2/SiO2 layers, optimized according to Eq. (1). In particular, the first pair is optimized considering the target wavelength λ2u = 580 nm and the next two pairs are optimized at λ1u = 500 nm. The lower DBR consists of six pairs of TiO2/SiO2, where the first three pairs are optimized at λ1d = 450 nm and the next three at λ2d = 530 nm. The last layer in the lower DBR is a 150 nm thick Al layer acting as a bottom electrode (in simulations, we used Al-Palik as included in Lumerical´s material database).

For the simulation of the full FP-SLM system, Periodic Boundary Conditions (PBC) are applied in x & y directions, mimicking a single unit cell, and two PML layers are then placed on the top and bottom in the z-direction. The incident light travels through the device along z-direction with the electric field polarized along the x-direction and is then reflected back through different layers. The reflected light is then collected using a plane monitor above the topmost layer of the device. The reflected phase is calculated by averaging over the electric fields recorded at the monitor. When comparing the diffraction angle as obtained from simulations to the one that is obtained in the experiment (measured in air), we apply Snell’s law such as to account for the refraction experienced by light when exiting the device.

Device fabrication

The device fabrication starts with sputtering a 150 nm thick Al on an 8 inch silicon wafer with a 1 μm thick thermal SiO2 layer using physical vapor deposition system (AMAT Endura). The wafer is then diced into 20 × 20 mm substrates. Next, the deposited Al is patterned to create the linear electrodes and fan-outs. The electrodes in the active region are fabricated using electron beam lithography (Elionix ELS-7000) using ZEP-520A-7 positive electron beam (EB) resist, followed by reactive ion etching (RIE, Oxford OIPT Plasma Lab) of Al using chlorine (Cl2) gas and boron trichloride (BCl3), and EB resist as a mask. The electrode fan-outs are fabricated using Photolithography (EVG 62008 Infinity) using positive photoresist S1811, followed by wet etching of Al using the photoresist as a mask. The bottom DBR consists of six pairs of TiO2/SiO2 among which the bottom most layer, i.e., SiO2, is first deposited using an ion assisted deposition tool (IAD, Oxford Optofab3000), and then followed by planarization by spin coating a 600 nm thick flowable oxide layer (FOX 24) and subsequent RIE using C4F8 gas to achieve the desired thickness (during the process, FOX 24 layer is completely etched). The rest of the 11 layers of the DBR stack are then deposited using the same deposition tool. The bottom substrate is then attached to a printed circuit board (PCB) and 96 electrodes are wire-bonded using 1 mil gold wires (where: 1 mil = 0.001 inch). A polymer adhesive is used to encapsulate the wires. The top DBR, which consists of six alternate layers of TiO2 and SiO2, is deposited using the same deposition tool on an ITO-glass with uniform ITO layer (23 nm). A layer of polyimide is then spin coated on the top substrate, followed by curing at 150 °C for 30 min on a hot plate. The cured slides are then rubbed unidirectionally with a piece of soft velvet clothes to define a preferred liquid crystal alignment direction. The rubbing strength is controlled by a commercially available rubbing machine (Holmarc Opto-Mechatronics - HO-IAD-BTR-03).

The LC cell is assembled by pressing the top (25 mm × 5 mm) against the bottom substrate (20 mm × 20 mm) using homemade press equipped with a multi-point optical profilometer. The resultant cell thickness is defined by a UV adhesive, a spacer and the pressure applied. The cell thickness is measured using a spectrometer. The nematic liquid crystal QYPDLC-001C is then encapsulated into the cell through capillary filling. The device is checked with a microscope under crossed polarizer-analyzer configuration, when the LC alignment is parallel to the polarizer to ensure the uniform extinction of LC in the gap and on the electrodes of the device.

Electro-optical characterization

Incident light from a halogen lamp is linearly polarized perpendicular to the 96 discrete Al electrodes. A pinhole having a diameter of 75 μm (Thorlabs P75D) is used to limit the angular spread of the incident light to less than 1° from the normal. The light passes through a bright field objective lens (Nikon 20×, NA = 0.45) and is collected by the same lens after it is reflected from the device. A commercial silver mirror (Thorlabs PF10-03-P01) is used to record the incident light intensity as a reference for reflective spectrum calculation and normalization. For beam bending measurements, the back focal plane (BFP) of the objective lens is imaged to the 100 μm entrance slit of a spectrograph (Andor Kymera 328i). Perpendicular to the slit, i.e., parallel to the electrodes, the light is dispersed by a blazed grating so that the back focal plane can be spectrally resolved in one direction. The image is collected by a Newton EMCCD-971 sensor array with an angular resolution of 0.16° and a spectral resolution of 0.31 nm. Diffraction (reflectance) efficiencies as shown in Fig. 4, are calculated by normalizing the diffracted (reflected) light from the device to the light reflected from a commercial silver mirror (after taking into account the photodetector noise effect i.e., dark current subtraction).

Similarly, in the lensing experiments the spectrally resolved real space is imaged at different distances from the device. The voltages at the 96 electrodes are set using a Texas Instruments (TI) 96-channel, 12-bit digital-to-analog converter (DAC) chip on an evaluation board (DAC60096EVM). The board is addressed by an ESP 32 microcontroller (MCU) via serial peripheral interface (SPI). The MCU, in turn, is connected to a CPU via “universal asynchronous receiver-transmitter” (UART), so that the voltage patterns can be ultimately set and optimized in a python program (see section “Device performance optimization” below for the optimization method).

Phase retardation measurements

The phase retardation φ of the device is measured at different applied voltages and at different wavelengths with a Michelson interferometer using a temporal phase-shift approach and five step phase retrieval algorithm54,55. A supercontinuum source (SuperK EXTREME, NKT Photonics) and multi-wavelength filter (SuperK SELECT, NKT Photonic) are used as the light source. The laser beam of a given wavelength is split into two beams using a beam splitter: one beam, shone on the sample and reflected back, is referred here as the signal beam; another beam shone on a mirror mounted on a piezo-driven stage, is referred here as the reference beam. The reflected signal and the reference beams interfere and form fringes in their overlap region, which are then imaged on a camera (Thorlabs, Quantalux 2.1 MP Monochrome sCMOS Camera). The temporal phase shift is introduced by moving the mirror in the reference arm to different positions using the piezo stage, which results in creating desired optical path differences (corresponding to 0, 0.5π, π, 1.5π and 2π phase shift). The corresponding fringes are captured with the camera as I1, I2, I3, I4 and I5 (where I denotes the intensity) and are used to calculate the wrapped phase map according to a five-step phase retrieval algorithm as shown in equation below.

$$\varphi = {\it{arctan}}\left[ {\frac{{2\left( {I_2 - I_4} \right)}}{{2I_3 - I_5 - I_1}}} \right]$$

For the five-step algorithm, the phase shift step between two adjacent frames should be 0.5 π, corresponding to the piezo stage moving a distance of quarter (1/4) of the wavelength. As it is a reflection geometry, the light path is doubled, therefore the moving step is one-eighth (1/8) of the wavelength. After the wrapped phase is obtained with the algorithm, it is filtered with a sin-cos filter and unwrapped to obtain the final phase map of the device. A local reference isolated from the electrodes (and hence providing a constant phase irrespective of the applied voltage), is used to calculate the relative phase-change in the area of interest.

Device performance optimization

Beam steering profiles

Properties of the fabricated devices can naturally differ slightly from the intended device design, especially in prototype development. Demonstrating the full potential of a new technology can become challenging if these differences reduce efficiency and are not compensated for. While our device is fairly close to its design, in Fig. 2(d) and Fig. 3 in the main text, differences between simulation and experiment in reflectance and phase spectra become apparent, especially in the red wavelength region. Furthermore, as already pointed out in the main text, we noticed a slight inter-pixel crosstalk. Therefore, manual voltage setting is challenging and by doing so, one is not able to exploit and demonstrate the device performance to its full extent. Therefore, we used the python Application Programming Interface (API) of the nonlinear optimization (NLopt) toolbox56 to optimize the voltage supercells in our bending experiments. Our setup allows a cycle time of a spectral measurement of around 0.47 s. The cycle time is composed of exposure time of 0.25 s, which is necessary to obtain a sufficient signal-to-noise ratio, and overhead time of 0.22 s, which includes CCD readout time and other spectrometer software processing. While the cycle time constitutes a lower limit to the cost function evaluation time of our real time optimization, we add a small buffer time so that a single evaluation is still performed in less than a second. During this time, a back focal plane (BFP) spectral measurement is performed, the data are evaluated and the voltages are updated. The cost function maximizes the integral of light intensity in the target wavelength and bending angle range normalized by the intensity in the same wavelength range but across all solid angles captured by the objective. While the parameter space in an optimization of phase values is a hypersphere, the parameter space formed by 96 voltage values, having a lower bound of 0 V and an upper bound of 10 V, is a perfect hypercube. In order to account for rapidly varying voltages, necessary to realize phase jumps from 0 to 2π at the supercell boundaries, we employ the “Locally biased DIviding RECTangles” (DIRECT-L) algorithm, which is a global, derivative free optimization algorithm57,58. The algorithm works best for low aspect ratio parameter spaces, which is the case of a hypercube. It initiates all voltages at the medium value of 5 V and by setting a large initial step size of 5 V the whole parameter space is spun with the first divisions. Having supercells sizes ranging from 5 electrodes to 12 electrodes, optimizations require 5 to 20 min of time, which relates to at least 300 to 1200 function evaluations, respectively. Subsequently, in order to refine the result of the global optimization, we run a purely local optimizer using the same cost function with the result of the global optimizer as input parameter. The local derivative free algorithm used for that purpose is the “Constrained Optimization BY Linear Appoximation” (COBYLA) algorithm, also provided by the NLopt package56,59,60. Representative results on the obtained optimized voltages are shown in Fig. S4.

Lensing profiles

The aforementioned slight inter-pixel crosstalk and natural fabrication imperfections can be even a bigger challenge for more complex functionalities than beam steering. While for beam steering, optimization parameters are reduced to the supercell size, a drastic reduction of parameters is not possible for e.g., optimizing a lens profile. Symmetry would allow to half the number of electrodes, but 48 optimization parameters is still too much for a real time optimization in our experiments. Therefore, we demonstrate the readiness of our device by realizing efficient lensing without numerical optimization, purely based on knowledge about the phase profile according to formula (2) in the main text and dependence of resonance position and resulting phase from the set voltages. The voltage patterns used for the lensing experiments are provided in Fig. S10. Again, we stress that applying machine learning methods will further improve device efficiency for complex functionalities.