A full degree-of-freedom photonic crystal spatial light modulator

Programmable optical transformations are of fundamental importance across science and engineering, from adaptive optics in astronomy [1] and neuroscience [2, 3, 4], to dynamic matrix operations in machine learning accelerators [5] and quantum computing [6, 7, 8]. Despite this importance, fast, energy-efficient, and compact manipulation of multimode optical systems — the core objective of spatial light modulators (SLMs) — remains an open challenge [9, 10]. Specifically, the limited modulation bandwidth and/or pixel density of liquid crystal (LC) SLMs, digital micromirror displays, and other two-dimensional (2D) modulator arrays prevents complete control over the optical fields they tune.

Figure 1a illustrates these limitations for a typical SLM comprised of a two-dimensional (2D), $\Lambda$-pitch array of tunable pixels (subscript $p$) emitting at wavelength $\lambda$ into the solid angle $\Omega_{p}$ with a system (subscript $s$) modulation bandwidth $\omega_{s}$. Given these parameters, each “spatiotemporal” degree-of-freedom (DoF) simultaneously satisfying the minimum-uncertainty space- and time-bandwidth relations ($\delta A/\lambda^{2}\cdot\delta\Omega=1$ and $\delta t\cdot\delta\omega=1$, respectively) can be illustrated as a real-space voxel with area $\lambda^{2}/\Omega_{p}$ and time duration $1/\omega_{p}$ for pixel bandwidth $\omega_{p}$. The optical-delay-limited pixel bandwidth $\omega_{p}\approx(\Delta\epsilon_{p}/\epsilon)ck$ can be approximated as a function of the achievable permittivity swing $\Delta\epsilon_{p}$ (for the speed of light $c$) using first-order perturbation theory [11] or similarly derived from linear scattering theorems [12].

Integrating over the switching interval $T=1/\omega_{s}$ and aperture area $A$ then gives the total DoF count [27] ¹¹1Note that the exact coefficient of proportionality in Eqn. 1 depends on the number of polarizations, the complex amplitude and phase controllability of each mode, and the exact definition of distinguishability when defining the Fourier uncertainty relations. For simplicity, we have omitted these $\mathcal{O}(1)$ coefficients.

By comparison, the same switching period contains $N=A/\Lambda^{2}\leq F$ controllable modes, each confined to the pixel area $\Lambda^{2}$ and time window $T$ (shaded box in Fig. 1a). Complete spatiotemporal control with $N=F$ is only achieved under the following criteria: (C1) emitters fully “fill” the near-field aperture such that $\Omega_{p}$ matches the field-of-view $\Omega_{s}=(\lambda/\Lambda)^{2}$ of a single array diffraction order; and (C2) $\omega_{s}=\omega_{p}$. In the Fourier domain, the system’s “spatiotemporal bandwidth” $\nu=\Omega_{s}\omega_{s}$ counts the controllable DoF per unit area and time within a single far-field diffraction order. As illustrated by the shaded pillbox in Fig. 1a, (C1) and (C2) are both satisfied when $\nu$ matches the accessible pixel bandwidth $\Omega_{p}\omega_{p}$.

Practical constraints have prevented present-day SLM technology from achieving this bound. In general, commercial devices approximate (C1) without achieving (C2). Specifically, they offer excellent near-field fill-factor across megapixel-scale apertures but use large $\mathcal{O}(\epsilon)$, slow index perturbations. Liquid crystal SLMs, for example, are limited to $\omega_{s}\sim 2\pi\times 10^{3}\text{ Hz}\ll\omega_{p}$ by the slow rotation of viscous, anisotropic molecules that modulate the medium’s phase delay [29, 30]. Digital micromirror-based SLMs offer moderately faster ($\mathord{\sim}10^{5}$ Hz) binary amplitude modulation by displacing a mechanical reflector, but at the expense of diffraction efficiency [31]. Mechanical phase shifters [32, 33, 19, 20, 34] improve this efficiency but still require design trade-offs between pixel size and response time.

Recent research has focused on surmounting the speed limitations of commercial SLMs with integrated photonic phased arrays [16, 35, 36, 37] and active metasurfaces comprised of thermally [38, 39, 40], mechanically [41, 20], or electrically [25, 42, 43, 44, 26] actuated elements. These devices, however, do not satisfy (C1) (Table A2). Silicon photonics in particular has attracted significant interest due to its fabrication scalability; however, the combination of standard routing waveguides, high-power ($\mathord{\sim}$ mW/$\pi$ phase shift) thermal phase shifters, and vertical grating couplers in each pixel reduces the fill-factor of emitters, yielding $\Omega_{p}\gg\Omega_{s}$ [16]. Scattering into the numerous diffraction orders within $\Omega_{p}$ then reduces the achievable zero-order and overall diffraction efficiencies ($\eta_{0}$ and $\eta$, respectively). For this reason, $\eta_{0}$ is a useful measure of near-field fill.

Various workarounds, including 1D phased arrays with transverse wavelength tunability [35, 45, 46], sparse antenna arrays [15], and switched arrays [47, 22] improve steering performance but restrict the spatiotemporal basis (i.e. limit $F$). Alternative nanophotonics-based approaches, often limited to 1D modulation, have their drawbacks as well: phase change materials [38, 39, 40] have slow crystallization rates and large switching energies, while electro-optic devices [48, 23, 25, 43, 44, 26, 49], to date, have primarily relied on large-area grating-based resonators to achieve appreciable modulation.

Figure 1b compares the performance of these and other experimentally-demonstrated, active, 2D SLMs as a function spatiotemporal bandwidth’s two components: modulation bandwidth $\omega_{s}$ and field-of-view $\Omega_{s}$. Controllability aside, the evident trade-off between these parameters illustrates the difficulty of creating fast, compact modulator arrays with high $\nu$. Thus, in addition to satisfying the complete control criteria (C1) and (C2), an “ideal” SLM would (Fig. 2c): (C3) maximize $\nu$ by combining wavelength-scale pitches (for full-field $\Omega_{s}\rightarrow 2\pi$ beamforming) with gigahertz (GHz)-order bandwidths $\omega_{s}$ competitive with electronic processors; (C4) support femtojoule (fJ)-order switching energies as desired for information processing applications [51]; and (C5) have scalability to state-of-the-art megapixel-scale apertures.

These criteria motivate the resonant architecture in Fig. 1c. Here, (C3) and (C4) are achieved by switching a fully-filled array of wavelength-scale resonant optical antennas with fast, fJ-order perturbations $\Delta\epsilon_{p}/\epsilon\ll 1$. Each resonator’s far-field scattering and quality factor $Q$ can then be tuned to achieve (C1) and (C2), respectively. Combined, this resonant SLM architecture enables complete, efficient control of the large spatiotemporal bandwidth supported by its constituent pixels.

Figure 2 illustrates our specific implementation of this full-DoF resonant SLM: the photonic crystal spatial light modulator (PhC-SLM) [52]. Coherent signal light is reflected off a semiconductor slab (permittivity $\epsilon$) hosting a 2D array of semiconductor PhC cavities with instantaneous resonant frequency $\omega_{0}+\Delta_{mn}(t)$. A short-wavelength incoherent control plane imaged onto the cavity array controls each resonator’s detuning $\Delta_{mn}(t)\approx-\Delta\epsilon(t)/2\epsilon$ via the permittivity change $\Delta\epsilon_{p}(t)$ induced by photo-excited free carriers [53, 54]. We optimize the resonator bandwidth $\Gamma\approx\omega_{s}\approx 2\pi\times\mathrm{GHz}$ (corresponding to a quality factor $Q=\omega_{0}/\Gamma\sim 10^{5}$) to maximize the linewidth-normalized detuning $\Delta/\Gamma$ without significantly attenuating the cavity’s response at the carrier lifetime ($\tau$)-limited modulation rate $\omega_{s}=1/\tau$. Under these conditions, free carrier dispersion efficiently modulates the complex cavity reflectivity $r(\Delta)$ to enable fast ($>100$ MHz given a $\mathord{\sim}$ns free carrier lifetime [55]), low-energy (fJ-order) conversion of incoherent control light into a dense array of coherent, modulated signal modes (Appendix A).

This out-of-plane, all-optical switching approach is motivated by the recent development of high-speed, high-brightness $\upmu$LED arrays [56, 57] integrated with complementary metal-oxide-semiconductor (CMOS) drive electronics for consumer displays [58, 59] and high-speed visible light communication [60, 61]. In particular, gallium nitride $\upmu$LED arrays with GHz-order modulation bandwidths [61, 62], sub-micron pixel pitches [63], and large pixel counts [64] have been demonstrated within the past few years. Applying these arrays for reconfigurable, “wireless” all-optical cavity control eliminates electronic tuning elements at each pixel to avoid optical loss, pixel pitch limitations, and interconnect bottlenecks for planar architectures (as aperture area $A$ grows, $\mathcal{O}(A)$ pixel controls eventually cannot be routed through the $\mathcal{O}(\sqrt{A})$ perimeter) [65].

Free of these constraints, we designed high-finesse, vertically-coupled microcavities offering coupling efficiencies $>90\%$, phase-dominant reflection spectra [17, 66], and directional emission $\Omega_{p}\approx\Omega_{s}$ for high-efficiency beamforming (Section II). Bespoke, wafer-scale processing allows us to fabricate these “resonant antennas” in arrays with mean quality factors $\langle Q\rangle>10^{6}$ and sub-nm resonant wavelength standard deviation (Section III). For fine tuning, we developed a parallel laser-assisted thermal oxidation [67, 68] protocol to then trim $8\times 8$ cavity arrays to picometer-order uniformity [67, 68] (Section IV), enabling high-speed spatial light modulation with fJ-order switching energies and $\omega_{s}>2\pi\times 100$ MHz (Section V). Compared to the previous devices surveyed in Fig. 1b, our PhC-SLM offers near-complete control over an order-of-magnitude larger spatiotemporal bandwidth.

The sub-wavelength (i.e. normalized volume $\tilde{V}=V/(\lambda/n)^{3}<1$ relative to a cubic wavelength in the confining dielectric of refractive index $n$), high-$Q$ (up to $\mathord{\sim}10^{7}$) [69, 70] modes of 2D PhC cavities enable (C4) [71], but at the expense of (C1) since $Q$ optimization (via hole displacements as in Fig. 3a [72]) cancels radiative leakage. The exact displacement parameters are typically numerically optimized in computationally expensive finite-difference time-domain (FDTD) simulations, which ultimately limits the number of free parameters. Compared to the ideal apertures in Fig. 1c, the optimized cavity unit cell confines a spatially complex mode with $\Omega_{p}\gg\Omega_{s}$ (Fig. 4b, background), violating (C1) and limiting the zero-order diffraction efficiency to $\eta_{0}\approx 0.04$. The result is poor beamforming performance as exemplified by the distorted, low-efficiency far-field pattern emitted by a $64\times 64$ cavity array with optimized detunings (derived with the algorithm in Appendix F) to match a target far-field image (MIT logo).

Fortunately, these limitations are not fundamental: the effective scattering aperture $A_{0}=\lambda^{2}/\Omega_{p}$ of a resonant mode can extend beyond its $1/e$ decay area $A_{e}$. This apparent space-bandwidth violation $(A_{e}/\lambda^{2})\cdot\Omega_{p}=A_{e}/A_{0}<1$ is enabled by resonant scattering from the mode’s evanescent field, which raises the basic question: how should scatterers be arranged to produce a desired far-field emission pattern?

One established approach is a harmonic $2a$-period grating perturbation (Fig. 4a) that “folds” energy concentrated at the band-edge $k_{x}=\pi/a$ back to $k_{||}=0$, yielding vertical radiation at the expense of reduced $Q$ [73, 74, 75, 76]. In the perturbative regime, the far-field scattering profile is an image of the broad band-edge mode. Thus, once the grating-induced loss becomes dominant, further magnifying the perturbation reduces $Q$ without significantly improving directivity. Fig. 4b shows the narrowed far-field profile produced by a $\delta r_{i}/r\approx 0.02$ grating perturbation, which balances the reduced $Q\approx 8\times 10^{5}$ and a modest diffraction efficiency improvement ($\eta_{0}=0.18$).

By contrast, our design strategy (Fig. 3b) combines semi-analytic guided mode expansion (GME) simulations with automatic differentiation to maximize $\eta_{0}$ (and thereby the effective near-field fill factor) for a given target $Q$ using all of the hole parameters. In each iteration, GME approximates the cavity eigenmode and radiative loss rates $c_{mn}^{(i)}$ at each of the array’s reciprocal lattice vectors (i.e. diffraction orders) offset by the Bloch periodic boundary conditions $\vec{k}_{i}$ [77]. These coupling coefficients coarsely sample the cavity’s approximate far-field emission (Appendix C). Scanning $\vec{k}_{i}$ over the irreducible Brillouin zone of the rectangular cavity array improves the sampling resolution, and an overall $Q$ can be estimated by averaging the total loss rates $\Gamma^{(i)}=\sum_{mn}c_{mn}^{(i)}$ in each simulation. Reverse-mode automatic differentiation then allows us to efficiently optimize an objective function

targeting three main goals: 1) increase $Q$ to a design value $Q_{0}$; 2) force the associated radiative loss into the array’s zeroth diffraction order for efficient vertical coupling; and 3) minimize $V$ by maximizing $|E_{0}|$, the electric-field magnitude at the center of the unit cell. The resulting designs support tunable-$Q$ resonances with near-diffraction-limited ($\Omega_{p}\approx\Omega_{p}$) vertical beaming comparable to the ideal planar apertures of Fig. 1c. The example design of Fig. 4d, for instance, maintains $Q\approx 8\times 10^{5}$ with $\eta_{0}=0.86$ based on the simulated far-field profile in Fig. 4e.

We prototyped each design at a commercial electron beam lithography (EBL) foundry ²²2Applied Nanotools, Inc. https://www.appliednt.com/ before transitioning to the wafer-scale foundry process described in Sec. III. The near- and far-field reflection characteristics of the fabricated devices were measured with the cross-polarized microscopy setup detailed in Appendix D. Fig. 4b-c and Fig. 4e-f show the results for the grating coupled and inverse-designed cavities, respectively. The optimal grating-coupled cavities offer $Q\sim 4\times 10^{5}$ at $\lambda\approx 1553\text{ nm}$ with a near-field resonant scattering profile well-centered on the cavity defect (Fig. 4c, inset). The mode mismatch between this wavelength-scale PhC mode and the wide-field input beam (Gaussian beam with $\mathord{\sim}150~\upmu\text{m}$ waist diameter for array-level excitation) is further evidenced by the small normalized reflection amplitude (relative to that of the inverse designed cavities) on resonance as well as the broad far-field profile (Fig. 4b) with $\eta_{0}=0.24$.

By comparison, inverse design non-perturbatively modifies the cavity mode (Fig. 4d) to produce the near-ideal measured far-field profile in Fig. 4e satisfying (C1) with $\eta_{0}=0.98$ while simultaneously increasing $Q$ to $5.7\times 10^{5}$. We attribute the slight increase in zero-order diffraction efficiency over the simulated value $\eta_{0}=0.86$ to the substrate-dependent effects described in Appendix G. The fully-filled near-field resonant scattering image in Fig. 4f explains the close resemblance between this measured $S(\vec{k})$ and that of an ideal uniform aperture [79]. In addition, the narrowed emission profile $S(\vec{k})$ yields a $\mathord{\sim}5\times$ increase in cross-polarized reflection and the phase-dominant simulated direct reflection spectrum in Fig. 4f. The latter is achieved by 94% one-sided coupling to a Gaussian beam with optimized waist diameter (Appendix E).

Combined, these results break the traditional coupling–$Q$ tradeoff (offering an order-of-magnitude improvement in the figure-of-merit $\eta_{0}\cdot Q$ for the prototype devices in Fig. 4) to enable high-performance beamforming at the space-bandwidth limit (C1). These results are supported by the simulated hologram in Fig. 3d: an array of optimally detuned, inverse-designed cavities forms a clear far-field image with a several order-of-magnitude improvement in overall diffraction efficiency ($\eta=0.83$) over existing designs.

While EBL enables fabrication of few-pixel prototypes with state-of-the-art resolution and accuracy, serial direct-write techniques do not satisfy (C5). Field stitching issues and sample preparation aside, a single cm², megapixel-scale sample would require a full day of EBL write time alone. We therefore developed a full-wafer deep-ultraviolet photolithography process specifically optimized for wavelength-pitch arrays of high-$Q/V$ PhC microcavities in a commercial foundry [80].

A central goal was to create vertical etch side-walls. The transmission electron microscope (TEM) cross-section in Fig. 5i shows that the default fabrication process (optimized for isolated waveguides) yielded an oblique ($100^{\circ}$), incomplete etch through the silicon device layer for the target PhC lattice parameters. Both nonidealities erase the membrane’s vertical reflection symmetry, leading to coupling between even- and odd- symmetry (about the slab midplane) modes that ultimately limits the achievable $Q$ of bandgap-confined resonances [81]. By contrast, our revised fabrication process achieves near-vertical $91^{\circ}$ sidewall angles (Fig. 5ii), yielding high-quality PhC lattices for a range of hole diameters between the $\mathord{\sim}100$ nm critical-dimension and $2r\approx a$ (Fig. 5c). Using TEM cross-sectioning and automated optical metrology as feedback over multiple 300 mm wafer runs in the AIM Photonics foundry’s 193 nm DUV water-immersion lithography line, this new process relies on a combination of dose-optimized reverse (positive) tone lithography, high-accuracy laser written masks, and optimized etch termination. Following fabrication and dicing, we post-processed individual die with a backside silicon nitride anti-reflection coating and, as required, suspend the PhC membranes with a timed wet etch.

The resulting die contain isolated and arrayed PhC cavities with swept dimensions to offset systematic fabrication biases. We chose $Lm$-type cavity designs — formed by removing $m$ holes from the PhC lattice as demonstrated by the $L3$ unit cells in Fig. 4 — to host tunable-volume (via variable $m$), high-$Q$ resonant modes with even reflection symmetry (about the unit cell axes) as required for vertical emission [82]. The highest-performance isolated devices feature $Q>10^{6}$ with normalized volumes $\tilde{V}\approx 0.3$. With a joint spectral- and spatial-confinement (quantified by the figure-of-merit $Q/\tilde{V})\approx 4\times 10^{6}$, these devices are among the highest-finesse optical cavities ever fabricated in a foundry process.

Our optimized foundry processing extends this exceptional single-device performance (rivaling record EBL-fabricated devices) to large-scale cavity arrays. We developed a fully-automated measurement system (Appendix D) to locate and characterize hundreds of cavities per second via parallel camera readout. The resulting data, extracted from over $10^{5}$ devices measured across the wafer, allow us to statistically analyze resonator performance and fabrication variability at the die, reticle, and wafer level. Fig. 5d, for example, shows resonant wavelength and $Q$ variations within $8\times 8$ arrays of four different cavity designs. Using camera readout of the reflected wide-field excitation, each data set is extracted from a single wavelength scan of a tunable laser. Besides the expected correlation between uniformity and mode volume [83], the data demonstrates — for the first time, to our knowledge — the ability to fabricate sub-wavelength ($\tilde{V}<1$) microcavity arrays with $\langle Q\rangle>10^{6}$ and sub-nanometer resonant wavelength standard deviation ($\sigma_{\lambda}\approx 0.6$ nm). Critically for beamforming, this uniformity also extends to the far-field: Appendix H shows that each cavity in an $8\times 8$ array emits vertically with $\eta_{0}=0.86\pm 0.07$, in quantitative agreement with the simulated result in Fig. 4.

In addition to these overlapping far-field emission profiles, programmable multimode interference requires each cavity to operate near a common resonant wavelength $\lambda_{0}$. For sufficiently high-$Q$ resonators, this tolerance cannot be solely achieved through optimized fabrication since $\mathcal{O}(\text{nm})$ fabrication fluctuations translate to $\mathcal{O}(\text{nm})$ resonant wavelength variations [84, 85]. Our prototype $8\times 8$ arrays of $L3$ cavities (chosen to optimally balance requirements on $Q$, $V$, directive emission, and fabrication tolerance) typically span a $\mathord{\sim}3~\text{nm}$ peak-to-peak wavelength variation (given $\sigma_{\lambda}\approx 0.6$ nm), corresponding to hundreds of linewidths for the target $Q\sim 10^{5}$.

To correct this nonuniformity, we developed an automated, low-loss, and picometer-precision trimming procedure based on laser-assisted thermal oxidation (Fig. 6). Two features of our approach resolve the speed and controllability limitations of prior single-device implementations [67, 68]: 1) accelerated oxidation in a high-pressure chamber with in-situ characterization; and 2) holographic fanout of the trimming laser to simultaneously address multiple devices. In each iteration of the automated trimming loop (Fig. 6a), the resonant wavelengths $\{\lambda_{i}\}$ are measured and a subset $T$ containing $N$ devices is selected to maximize the total trimming distance $N(\min_{T}\{\lambda_{i}\}-\lambda_{t})$ to a target wavelength $\lambda_{t}$. Each cavity in $T$ is then targeted by a visible laser distributed by the liquid crystal SLM setup described in Appendix D. To generate the required phase masks, we developed an open-source, GPU-accelerated experimental holography software package that implements fixed-phase, weighted Gerchberg-Saxton (GS) phase retrieval algorithms ³³3slm-suite. https://github.mit.edu/cpanuski/qp-slm. Using camera feedback, the algorithm can generate thousands of near-diffraction-limited foci with $\mathord{\sim}1\%$ peak-to-peak power uniformity and single-camera-pixel-order location accuracy within a few iterations (Appendix I).

The holographically-targeted pixels are then laser-heated with a computed exposure power and duration (based on the current trimming rates, resonance locations, and other array characteristics) to grow thermal oxide at the membrane surface. For thin oxide layers, the consumption of silicon during the reaction with ambient oxygen permanently blueshifts the cavity resonance in proportion to the oxide thickness $t_{\text{SiO}_{2}}$ (Fig. 6b) [68]. Per the Deal-Grove model, the rate-limiting diffusion of oxygen through the grown oxide accelerates with increasing oxygen pressure — a well-known technique in microelectronics fabrication [87]. We therefore oxidize our samples in pure oxygen with partial pressure $P_{\text{O}_{2}}=5~\text{bar}$, enabling ${\rm d}\lambda_{0}/{\rm d}t\approx 0.1~\text{nm/s}$ resonance trimming rates over $\Delta\lambda_{0}>20~\text{nm}$ wavelength ranges. After each trimming exposure, we remeasure the resonance statistics and recycle the loop until all devices are aligned within a set tolerance about $\lambda_{t}$. The trimming algorithm also accounts for long-term moisture adsorption to the membrane surface, thermal cross-talk, and trimming rate variations (Appendix J).

Fig. 6 demonstrates the results of this trimming procedure applied to our prototype $8\times 8$ pixel PhC-SLM. Prior to trimming, the hyperspectral near-field reflection image in Fig. 6c shows the large ($>200$ linewidths for the mean quality factor $\langle Q\rangle=1.6\times 10^{5}$) resonant wavelength variation between the otherwise spatially uniform and high-fill resonant modes. Holographic trimming reduces the wavelength standard deviation and peak-to-peak spread by $>100\times$ to $\sigma_{\lambda}=2.5~\text{pm}$ and $\Delta\lambda_{0}^{\text{p-p}}=1.3\Gamma=13~\text{pm}$, respectively, enabling all 64 devices (imaged in Fig. 6d) to be resonantly excited at a common operating wavelength (Fig. 6e). Since $\sigma_{\lambda}$ is directly related to the corresponding hole radius and placement variability ($\sigma_{r}$ and $\sigma_{h}$, respectively) with an $\mathcal{O}(1)$ design-dependent constant of proportionality, the thermal oxide homogenizes the effective dimensions of each microcavity to the picometer scale. The mean quality factor and near-field reflection profile of the array remain largely unmodified throughout the process as evidenced by Fig. 6c and Fig. 6e.

To our knowledge, these results are the first demonstration of parallel, in situ, non-volatile microcavity trimming. The achievable scale is currently limited by environmental factors that could be overcome with stricter process control (Appendix J). Even without these improvements, the current uniformity, scale, and induced loss outperform the corresponding metrics of the previous techniques reviewed in Appendix J, paving the way towards scalable integrated photonics with high-$Q$ resonators.

Once trimmed to within a linewidth, each resonator reflects an incident coherent field $E_{\text{i}}(\vec{r},t)$, producing a far-field output [88]

that can be dynamically controlled within $S(\vec{k})$ by setting the detuning $\Delta_{mn}(t)$ (and therefore the near-field reflection coefficient $r$) of each resonator. Experimentally, we measure the intensity pattern $|E_{r}(\vec{k})|^{2}$ on the back focal plane of a microscope objective above the PhC-SLM (as with the single-device characterization in Sec. II) and optically program $\Delta_{mn}(t)$ via photo-excited free carriers. The corresponding setups are detailed in Appendix D.

Absent a control input ($\Delta_{mn}\approx 0$), Fig. 7d shows the static far-field intensity pattern $|E_{r}(\vec{k})|^{2}$ of a wide-field-illuminated (i.e. $E_{i}(\vec{r})\approx E_{i}$) $8\times 8$ trimmed array with $\{Q\}=1.85\times 10^{5}$ and $\sigma_{\lambda}=5$ pm at $\lambda=1562$ nm. The inverse-designed cavity unit cells minimize scattering into undesired diffraction orders, producing a high-efficiency ($\eta_{0}=0.66$) zero-order beam with the expected $1.3^{\circ}$ and $1.6^{\circ}$ horizontal and vertical beamwidths given the $42.0\lambda\times 36.4\lambda$ aperture size. The cross-sectional beam profiles are well matched to the simulated emission profile of uniform apertures with width $w=0.8\lambda$, suggesting an 80% effective linear fill of the array. This extracted value agrees with the observed zero-order efficiency and the array’s physical design (each $16a\times 16a$ cavity offering near-unity fill was padded to $20a\times 20a$ to limit coupling to adjacent cells).

After confirming the static performance of the array, we conducted optical switching experiments with two sources: an incoherent $\upmu$LED array and a pulsed visible laser. The $\upmu$LED array contains $16\times 16$ individually-addressable gallium nitride $\upmu$LEDs with $>$150 MHz small-signal bandwidth and $\mathord{\sim}10^{6}$ cd/m² peak luminances (at 450 nm) flip-chip bonded to high-efficiency CMOS drivers [89, 60]. Using the setup in Appendix D, we imaged the 100 $\upmu$m-pitch array with variable demagnification and rotation onto the PhC cavity array. Digitally triggering the CMOS drivers then enables reconfigurable, binary optical addressing as illustrated by the imaged projections of three letters on the PhC-SLM (Fig. 7a). We measured the resulting pixel reflection amplitude and phase using locked, shot-noise-limited balanced homodyne detection (Appendix D). Fig. 7a depicts the maximum phase shift $\Delta\phi$ as a function of CMOS trigger duration $T_{\text{CMOS}}$ and imaged pump energy density $E_{\upmu\text{LED}}$. Single-cavity switching is possible with energy densities below $10$ fJ/$\upmu$m² (corresponding to $\mathord{\sim}100$ fJ total energy for our chosen demagnification) and a minimum trigger duration $T_{\text{CMOS}}\approx 5$ ns. Shorter trigger pulses produce relatively constant-width pulses (due to the $\upmu$LED fall time) with insufficient energy for high-contrast switching.

Confining visible pump pulses in space and time to the silicon free-carrier diffusion length ($\sim 1~\upmu$m) and lifetime ($\tau\approx 1$ ns), respectively, would reduce the required switching energy and maximize bandwidth bandwidth. While either metric is achievable with existing $\upmu$LED arrays [90, 63] and optimization to achieve both simultaneously is ongoing [91], we demonstrated the expected performance enhancement with a pulsed visible ($\lambda=515$ nm) laser. Fig. 7b shows that 3 dB power reflectivity changes and high-contrast phase modulation are feasible for 5 fJ pump pulses over a switching interval $T_{\text{switch}}\approx 1$ ns, thereby satisfying (C4). Free-carrier dispersion is the dominant switching mechanism for these isolated, ns-order switching events (Appendix A). While repeated switching over $\upmu$s-order timescales leads to a slowly-varying thermo-optic detuning [92], various optical communications techniques (constant-duty line codes, for example [93]) can maintain average device temperature during high-speed free carrier modulation. To demonstrate this decoupling of switching mechanisms, we measured the normalized small-signal transfer function $T(\omega)$ between a harmonic pump power (produced by a network analyzer-driven amplitude electro-optic modulator) and the phase-locked homodyne response. When aligned to the thermally-detuned resonance, the results (Fig. 7c) match the expected second-order response $T(\omega)=1/\{\left[1+(\omega\tau)^{2}\right]\left[1+(\omega/\pi\Gamma)^{2}\right]\}$ set by carrier- and cavity-lifetime-limited bandwidths ($1/\tau$ for a fitted carrier lifetime $\tau=1.1$ ns and the measured $\Gamma=1.0$ GHz, respectively). While satisfying (C2) therefore requires higher-$Q$ resonators, the current regime of operation enables near-complete control over a larger bandwidth $\omega_{s}=2\pi\times 135~\text{MHz}\approx 1/\tau$, i.e. without significantly degrading the carrier-lifetime-limited modulation bandwidth.

Combining this optimized switching with the space-bandwidth-limited vertical beaming of each resonator enables multimode programmable optics approaching the fundamental limits of spatiotemporal control. We currently probe the PhC-SLM in a wide-field, cross-polarized setup that produces amplitude-dominant Lorentzian reflection profiles $r(\Delta)\propto 1/(1+j\Delta)$ regardless of the resonator coupling regime (cavity emission is isolated from specular reflection). For simplicity, we therefore conducted proof-of-concept demonstrations using the PhC-SLM as an array of high-speed binary amplitude modulators. In this modality, a nanosecond-class pulsed visible laser is passively fanned out to the desired devices. Devices targeted by pump light are detuned far from resonance ($\Delta\gg\Gamma$) and effectively extinguished, whereas unactuated cavities retain their high $\Delta\approx 0$ reflectivity.

We used pump-probe spectroscopy for wide-field imaging of these few-nanosecond switching events (Appendix D). Short infrared probe pulses were carved with a electro-optic amplitude modulator (DC biased to an intensity null) and variably delayed to coincide with the arrival of visible pump light at the PhC membrane, gating probe field transmission to the IR camera. We then measured the near- and far-field reflection as a function of the probe delay to reconstruct switching events with sub-nanosecond resolution. Fig. 7e-f plots the resulting far-field intensity profiles $|E_{r}|^{2}$ for horizontal and vertical on-off gratings. For a $5$ ns probe pulse width, the maximum near-field extinction of targeted cavities (7.4 dB and 9.8 dB for horizontal and vertical gratings, respectively) occurs within a $\mathord{\sim}6$ ns delay; i.e. just after the pump and probe pulses completely overlap. This minimum probe pulse width is limited by the requirement for high imaging contrast between probe pulses and leakage (due to the imperfect probe modulator extinction) given the instrument-limited trigger repetition rate ($\mathord{\sim}$MHz) and camera integration time.

As expected, the input field is primarily scattered into first-order diffraction peaks within the (greater than $10^{\circ}$) 2D field-of-view of $S(\vec{k})$. The illustrated cross sectional beam profiles again agree with analytic results for a 80% filled linear array of uniform apertures (black dashed lines). For the horizontal grating Fig. 7e, the fit is scaled by a factor of $\mathord{\sim}2$ to account for the increased reflectivity of unactuated cavities during switching events, which we attribute to residual coupling between adjacent cavities. In both cases, the pattern diffraction efficiencies — measured as the fraction of integrated power within the outlined regions in Fig. 7 — $(\eta_{x},\eta_{y})=(0.22,0.20)$ compare favorably to the efficiency of the fitted uniform aperture array. Even with amplitude-dominant modulation, these metrics exceed the efficiencies of previous resonator-based experiments due to our high-directivity PhC antenna array [17].

These proof-of-concept experiments demonstrate near-complete spatiotemporal control of a narrow-band optical field filtered in space and time by an array of wavelength-scale, high-speed resonant modulators. While the general resonant architecture (Fig. 1c) is applicable to a range of microcavity geometries and modulation schemes, the combination of our high-$Q$, vertically-coupled PhC cavities with efficient, all-optical free-carrier modulation achieves (C1-5) with an ultrahigh per-pixel spatiotemporal bandwidth $\nu\approx 5.6~\text{MHz}\cdot\text{sr}$. This MHz-order modulation bandwidth per aperture-limited spatial mode corresponds to a more than ten-fold improvement over the 2D spatial light modulators reviewed in Fig 1b. Our wafer-scale fabrication and parallel trimming offer a direct route towards scaling this performance to spectrally-multiplexed, $\mathcal{O}(\text{cm}^{2})$ apertures for exascale interconnects beyond the reach of current electronic systems, thus motivating the continued development of optical addressing and control techniques.

The PhC-SLM opens the door to a number of applications and opportunities, including: high-definition, high-frame-rate holographic displays by the integration of a back-reflector (see Appendices E-G) for one-sided, phase-only, and full-DoF spatiotemporal modulation; compact device integration via direct transfer printing of our cavity arrays onto a high-bandwidth $\upmu$LED array [94]; three-dimensional optical addressing and imaging by combining on-demand $\upmu$LED control with statically trimmed detuning profiles that continuously steer pre-programmed patterns [95]; large-scale programmable unitary transformations for universal linear optics processors [96]; focal plane array sensors for high-spatial-resolution readout of refractive index perturbations in imaging applications from endoscopy to bolometry and quantum-limited superresolution [97, 98, 99]; optical neural network acceleration via low-power, high-density unitary transformation of free-space optical inputs [5, 100]; and high-speed adaptive optics enabling free-space compressive sensing, deep-brain neural stimulation, and real-time scattering matrix inversion in complex media [101, 102]. Moreover, whereas we have so far considered only mode transformations, the PhC-SLM’s high-$Q/V$ resonant enhancement suggests the possibility of programming the quantum optical excitations/fields of these modes for applications ranging from multimode squeezed light generation [103], to multiplexed single photon sources for linear optics quantum computing [6, 104] or deterministic photonic logic [105, 106].