Ultrafast Optically Tunable GaAs Metasurfaces for Analog Image Processing

Abstract

Optical metasurfaces offer unprecedented potential for miniaturizing conventional bulk optics into compact, energy-efficient devices suitable for advanced edge computing applications. However, current implementations lack the dynamic tunability essential for real-time optical processing functions. Here, we numerically demonstrate a gallium arsenide metasurface that achieves subpicosecond switching between dual complex-valued transfer functions through ultrafast photoinduced carrier modulation. Our device exploits specially designed Mie-resonant nanoantennas for nonuniform amplitude and phase profile change under pump pulses with typical energies about 4.8 nJ. The metasurface enables real-time Fourier filtering with switching frequency exceeding 100 GHz, providing a pathway to ultrafast neuromorphic vision sensors and live image processing applications.

Introduction

Metasurfaces represent a versatile and powerful platform for the manipulation and processing of optical signals, enabling precise control over the amplitude and phase of light at subwavelength scales. − Recent advances have demonstrated their effectiveness in a wide range of applications, including spatial light control, such as in metalenses − meta-holograms , and structured beam generation ,− as well as frequency-domain engineering for structural coloration and harmonic generation. Furthermore, novel fabrication techniques , have paved the way for scalable and cost-effective production of metasurface devices, facilitating their integration into practical photonic systems. These innovations open new perspectives for optical signal processing and advanced photonic functionalities.

In particular, the development of metasurfaces for analog optical computing , has received significant attention due to their potential for high-speed operation and inherently compact architectures. Various strategies have been explored to realize these functionalities , with some of the most prominent approaches including the Green’s function method − , Fourier filtering − and diffractive neural networks. Although Green’s function approach enables highly compact device designs, Fourier filtering offers greater versatility for implementing complex computational functions in the optical domain.

However, the static optical response of conventional metasurfaces limits their widespread application in analog optical computing. To address this limitation, a variety of reconfiguration mechanisms have been explored, including phase-change materials , , liquid crystal coatings , , mechanical deformation , , and dynamic modulation through free-carrier injection. The optical properties of semiconductor metasurfaces can be tuned via electrical biasing − , magnetic fields , , or optical excitation. − Notably, optical excitation offers significantly faster switching speeds compared to electrical control, provided that the constituent material exhibits a large refractive index modulation under external stimulus. Direct-gap semiconductors such as GaAs, AlGaAs, and InP are particularly well-suited for this purpose due to their strong optical response near the bandgap. While changes in the overall transmission of metasurfaces under optical excitation have been demonstrated, dynamic image filtering using optically reconfigurable metasurfaces remains largely unexplored. Achieving switching between distinct filter functions demands precise engineering of nonuniform free carrier distributions at subdiffraction spatial scales. This, in turn, requires complex, high-dimensional parametric optimization of the metasurface topology to realize the targeted spatial absorption profilea challenge that has remained unsolved to date.

In this work, we present a numerical investigation of an ultrafast, tunable metastructure design for analog optical computing. Specifically, we propose a gallium arsenide-based metasurface that functions as a switchable derivative filter within a spatial Fourier filtering configuration (Figure ). It operates as a transmissive amplitude and phase filter, enabling the implementation of first- and second-order differentiation: in the absence of optical pumping, it performs second-derivative filtering, while under optical pumping, it switches to first-derivative filtering. The design of the metasurface resonators is optimized using a fully connected artificial neural network (ANN) trained on a data set generated via finite-difference time-domain (FDTD) simulations, allowing prediction of optical responses for various geometries. To ensure polarization insensitivity, the resonators are realized in the form of nanorings.

1.

Schematic illustration of analog optical differentiation using an ultrafast, optically tunable GaAs metasurface. A collimated probe beam passes through an H-shaped amplitude mask to generate the input image, which is then focused by a lens onto a nanoring-based GaAs metasurface serving as a spatial Fourier filter. The metasurface’s optical response is dynamically tuned by external pump pulses (yellow). The filtered light is subsequently imaged onto a detector. The left side of the detector shows the output when the probe and pump pulses are uncorrelated in time, corresponding to second-derivative filtering of the input image. The right side displays the result for coincident probe and pump pulses, where the metasurface performs first-derivative filtering of the probe via pump-induced modulation.

The performance of the proposed metasurface is validated numerically using the input image in the form of the letter “H”. In the absence of optical pumping, regions where image boundaries are perpendicular to the specified axis exhibit zero intensity, consistent with the behavior of a second-derivative filter. In contrast, under optical pumping, these boundaries are prominently highlighted, demonstrating first-derivative filtering. Such differential operations are foundational in image processing, as they effectively enhance edges and delineate boundariescrucial features for applications such as object detection and image segmentation. These results highlight the potential of ultrafast, tunable metasurfaces as compact and versatile platforms for real-time, on-chip image processing and advanced photonic computing applications.

Results

Concept

The metasurface filter tuning is implemented within a standard 4f optical scheme, as illustrated in Figure . The output pulse from a femtosecond laser is split into separate probe and pump beams. The probe beam travels through a variable delay line and enters the 4f Fourier filtering setup such that the input image is positioned at the front focal plane of the first lens, while the metasurface characterized by a complex transmission coefficient is placed at the Fourier (focal) plane, and the resulting filtered image is subsequently recorded by a detector. The coordinates in the focal plane are defined as u (horizontal axis) and v (vertical axis) for describing the transmission coefficient’s spatial variation. The pump beam, with polarization orthogonal to that of the probe, is directed onto the metasurface from the opposite side. By adjusting the temporal delay between the pump and probe beams, the complex transmission profile of the metasurface can be dynamically modulated via optical injection of free carriers.

The metasurface is engineered in the way that the function of its optical filtering depends on the temporal correlation between the probe and pump pulses. When the probe and pump pulses are uncorrelated at the metasurface, the optical system performs a second derivative operation on the input image along the u-axis. In this regime, the target transmission function is given by T ₀(u, v) ∝ u ², exploiting the Fourier transform property that maps a spatial-domain second derivative to a quadratic function in the spatial frequency domain. By contrast, when the probe and pump pulses are temporally coincident (controlled via the delay line), the metasurface switches its transfer function to T ₁(u, v) ∝ iu = |u|e ^iπsgn(u)/2 corresponding to a first derivative operation along the u-axis. As a result, applying the second derivative suppresses intensity at boundaries perpendicular to the u-axis in the input image, producing zero output there, while the first derivative operation, engaged under optical pumping, accentuates these boundaries by enhancing their intensity. This reconfigurability enables on-demand selection between fundamental image processing operations essential for edge detection and feature extraction.

Free Carriers Modulation

Photoinduced generation of free carriers in gallium arsenide leads to changes in both the refractive index (n) and extinction coefficient (k). Their dependence on free carrier concentration and wavelength is calculated by accounting for both interband and intraband effects, as detailed in refs , , and and can be found in Supporting Information. GaAs is selected as the platform due to its substantial modulation of n and k, resulting from a combination of the Drude response and interband phenomena, including the Burstein–Moss effect and band gap shrinkage under ultrafast optical pumping in the near-infrared spectral range. Near the bandgap energy (E _{g ap} = 1.42 eV, λ _gap = 873 nm) at a wavelength of 850 nm optical pumping can reduce absorption to nearly zero, while the refractive index exhibits a modulation of Δn ≈ 0.13 at a free carrier concentration of 10¹⁹ cm^–3. Typical relaxation times for such carrier-induced modulation in GaAs metasurfaces can be as short as a few picoseconds, enabling switching frequencies that exceed 100 GHz.

Metasurface Design

The proposed metasurface is partitioned into rectangular regions (pixels), each comprising a two-dimensional array of gallium arsenide nanorings characterized by an inner diameter b, outer diameter d, and lattice period a. An additional tunable parameter is the free carrier concentration N, which modulates the refractive index (n) and extinction coefficient (k) of gallium arsenide and is controlled by the intensity of the incident optical pump. We set the minimum pixel size to 10 μm to mitigate boundary effects that disrupt the collective response of the nanoring resonators. Although a smaller pixel size would improve the accuracy of the transfer function for a given metasurface area, it would also reduce the number of disks per pixel, thereby altering their collective Mie resonance. Based on our prior estimation in the work ref in the Supplementary note 2 for a 905 nm wavelength, and given the similar 850 nm wavelength used here, we maintained a 10 μm pixel size. Due to computational constraints, the maximum metasurface size is limited to 110 μm, resulting in a design comprising 11 rectangular pixels, each measuring 110 μm × 10 μm. For more complex transfer functions, this approach is not entirely correct. This is because a 10 μm resolution for a metasurface size of 110 μm will introduce progressively larger errors as the transfer function increases in complexity. For such tasks, alternative metasurface topology optimization methods should be employed. , The reflection R, transmission T, absorption A, and phase shift Δφ of each pixel are calculated for various free carrier concentrations N using the FDTD method. Optimizing the metasurface topology requires smooth, continuous functional dependences for R(a,d,b,N), T(a,d,b,N), A(a,d,b,N), and Δφ­(a,d,b,N). To achieve this, a fully connected neural network is trained on the FDTD simulation data to provide a continuous approximation of the metasurface’s optical response. The network consists of an input layer with 4 neurons corresponding to parameters a, d, b, and N, followed by two hidden layers with 32 and 16 neurons respectively, both employing hyperbolic tangent activation functions. The output layer contains 4 neurons with linear activation, representing the target parameters R, T, Δφ, and A. This architecture is implemented using the PyTorch framework and trained over 5 × 10⁴ epochs with Adam optimization at a learning rate of 10^–3, minimizing the mean squared error loss function. The data set is partitioned into 80% training and 20% testing subsets, with all features normalized to the [−1, 1] range using min-max scaling. A quantitative evaluation of the model’s performance demonstrates good approximation across all output parameters. The network achieves an average coefficient of determination of R ² = 0.95, and an average relative mean absolute error of 1.2%, demonstrating high accuracy. The demonstrated performance with an average accuracy of 98.8% confirms the suitability of the neural network-based approach for practical application in this task. In Supporting Information, a convergence graph is also presented; the training process exhibited a stable and monotonic decrease in the loss function indicating proper learning dynamics.

To demonstrate the neural network’s approximation of the obtained dependences, we analyzed transmission and phase shift profiles as functions of lattice period a and disk diameter d with fixed inner hole diameter b = 0 nm (Figure ). This was performed for both intrinsic GaAs and doped GaAs with free-carrier concentrations N = 10¹⁹ cm^–3. The resonance features in the transmission and phase shift spectra arise from the emergence of Mie resonances in the nanodisks. Specifically, transmission exhibits three sharp minima at periods and diameters, caused by the spectral overlap of electric dipole (ED), electric quadrupole (EQ), magnetic dipole (MD), and magnetic quadrupole (MQ) resonances. For a small variation of the nanoresonator parameters, the phase shift undergoes abrupt transitions with 2π magnitude (marked by roman numerals) in the spectral proximity of the EQ+MD or EQ+MQ mode overlap (see Figure ). Increasing the free-carrier concentration mostly enhances transmission, which is attributed to a decreasing in the extinction coefficient. The obtained resonant dependences enable the implementation of various switchable amplitude-phase Fourier filters. More details on the decomposition of Mie scattering coefficients for GaAs nanodisks can be found in Supporting Information.

2.

Predicted transmission T and phase shift Δφ of the GaAs metasurface as a function of nanodisk diameter d and lattice period a obtained using the neural network model trained on FDTD simulation results. Top row: results without optical pumping. Bottom row: results with optical pumping corresponding to a free carrier concentration of N = 10¹⁹ cm^–3. The markers I, II, and III denote transmission minima corresponding to the overlap of resonances: electric quadrupole and magnetic dipole for I, and both electric and magnetic quadrupole for II and III.

Since the target transmission functions T ₀(u, v) ∝ u ² and T ₁(u, v) ∝ iu vary smoothly along the u-axis (Figure , blue curves) while the metasurface consists of only 11 pixels, it is necessary to approximate these continuous functions with discrete transmission values, $T_{0i}^{\mathrm{target}}$ and $T_{1i}^{\mathrm{target}}$ , corresponding to each pixel. These discretized target transmission profiles, which closely follow the ideal T ₀(u, v) and T ₁(u, v) functions, are illustrated in Figure (red curves). The phase discrepancy at the center of the metasurface does not significantly impact the filtering operation, as the transmission amplitude in this region is nearly zero.

3.

Transmission (a, c) and phase shift (b, d) profiles for the metasurface-based Fourier filter in the 4f optical scheme. The top row (a, b) shows the response in the absence of optical pumping, while the bottom row (c, d) corresponds to the condition when the pump and probe pulses are coincident. The blue curve indicates the ideal Fourier filter transmissions, T ₀(u, v) and T ₁(u, v). The red curve represents the discretized target filter profiles, $T_{0i}^{\mathrm{target}}$ and $T_{1i}^{\mathrm{target}}$ . Black markers indicate the transmission and phase values calculated for the optimal parameters using the neural network’s smoothed predictions, red markers show the corresponding values as confirmed by FDTD simulations for the same geometries.

Under homogeneous optical pumping, the free carrier concentration in each pixel is uniquely determined by its geometry. Our model accounts for the nonuniform absorption across the metasurface, calculating it for each individual periodic cell and the volume of the absorbing material. In cells with high absorption, the free carrier concentration can reach up to 10¹⁹ cm^–3, while in others, it is lower due to reduced absorption. The concentration of 10¹⁹ cm^–3 is chosen as an upper limit because, as known from the literature, exceeding this value may leads to irreversible sample damage. The absorption mechanisms considered in our calculations are modeled for room temperature, we do not account for the heating of the sample’s phonon subsystem resulting from the femtosecond laser pulse.

The design parameter ranges are set as follows: the lattice period a spans from 300 to 550 nm, the outer diameter d ranges from 150 to 400 nm, and the inner diameter b varies from 0 to 250 nm. Optimization constraints are defined by fabrication capabilities: the period must exceed the outer diameter by at least 100 nm, and the minimum width of the ring (i.e., the hole in the disk) must be no less than 50 nm. To achieve the target refractive index modulation without irreversible structural damage, the laser pulse energy is 4.8 nJ and fluence 25.4 μJ cm^–2. Compared to literature values (e.g., ref [] where fluence reached 310 μJ cm^–2), lower pulse fluence in our case enables energy-efficient nondestructive metasurface switching.

For optimal structure topology design, we apply differential evolution optimization. The detailed description of the optimization approach can be found in Supporting Information. As a result of the optimization, the periods a, outer diameters d, and inner diameters b for each pixel are obtained such that their transmission functions closely match the target profiles $T_{0i}^{\mathrm{target}}$ and $T_{1i}^{\mathrm{target}}$ . The corresponding values of transmission and phase shift for the optimized geometries are indicated by black markers in Figure . For each optimized nanoring geometry, transmission and phase shift values were validated using FDTD simulations. The resulting values deviate from the target ones due to approximation inaccuracies, as indicated by the red markers in Figure . The most significant discrepancy appears as a phase shift near the center of the metasurface, where the transmittance coefficient is close to zero, and the phase of the transmitted electromagnetic field becomes ill-defined. The reason for this is the choice of an optimization function that, as the transmittance (and consequently the field amplitude) decreases toward zero, disregards the phase discrepancy regardless of its magnitude. There is also a deviation in the transmittance coefficient. These discrepancies could be reduced by using a more complex neural network architecture. However, this deviation remains within acceptable limits and has a negligible impact on performance, which is further demonstrated in the Fourier filtering analysis performed using the designed metasurface.

Fourier Filtering of the Input Image

The optimized metasurface is then employed to simulate light propagation in a Fourier filtering setup. The interaction of the Fourier-transformed input image with the metasurface is modeled using the FDTD method. To simulate materials with various concentrations of free carriers N, a library of materials with different refractive index n and extinction k depending on the doping level is created. As a test case, a homogeneously illuminated letter “H” is chosen as the input image.

The intensity distributions of the filtered input image obtained using the metasurface with the optimized geometryboth without and with optical pumpingare presented in the top row of Figure . For comparison, the bottom row shows results produced by applying the ideal filters, corresponding to the target profiles depicted by the red line in Figure , and computed using the discrete Fourier transform. The change in transmission and phase shift after 2 ps since the pump pulse excited the metasurface can be found in Supporting Information. The left column illustrates the output for the second derivative operation applied to the input image in the absence of pumping, while the right column shows the result for the first derivative operation when the metasurface is optically pumped.

4.

Spatial Fourier filtering of an input image in a 4f optical system utilizing all-optical switching of the GaAs metasurface response. The boundaries of the input image (the letter “H”) are indicated by white dashed lines. (a) Output image corresponding to the second derivative operation applied via the metasurface without optical pumping. (b) Output image after applying the first derivative operation along the horizontal axis, realized by switching the metasurface response through optical pumping. (c) Reference: second derivative of the input image calculated by discrete Fourier transform. (d) Reference: first derivative of the input image calculated by discrete Fourier transform.

The structural similarity index (SSIM) is employed to quantitatively assess image similarity. A comparison between the simulated and ideal filtered images achieves SSIM values of 0.73 and 0.76 for the metasurface in the states without pump (second derivative) and with pump (first derivative), respectively. These values, exceeding the threshold of 0.7, indicate a high degree of visual correspondence. Observed differences between the metasurface-based and ideal filter results are attributed to deviations between the actual and the target filter profiles realized in the designed metasurface.

Discussion

The proposed structures are intended to be fabricated using molecular beam epitaxy, epitaxial lift-off, electron beam lithography, reactive ion etching. Lithography and etching are performed before the lift-off step (preprocessing). When appropriately executed, this method enhances structural stability by embedding etched nanostructures in transparent dielectrics prior to lift-off, passivating dangling bonds with the surrounding dielectric matrix. Based on the cited literature, the carrier relaxation times for these processes are on the order of several picoseconds. For disk nanoresonators with an aspect ratio close to unity, etching a central hole with a diameter of 50 nm or larger is feasible. However, creating holes with diameters below 50 nm is challenging due to the fundamental resolution limits of lithography. A similar limitation applies to the minimal edge-to-edge separation between neighboring nanoresonators. A key manufacturing detail is the application of the SiO ₂ passivation layer. Inhomogeneous application, resulting in incomplete filling of the nanoring holes, can alter the optical response. We numerically evaluated the impact of such geometric changes on the transmission and phase shift of our optimized nanoresonators and found that the average absolute deviation of the amplitude is 0.07, and the average absolute deviation of the phase shift is 0.26 radians. At this level, we do not expect significant degradation of the metasurface’s performance.

As a logical extension of this work, alternative approaches for dynamically switching metasurfaces in the context of optical analog image processing merit exploration. One direct approach is electrical control; however, it is important to acknowledge the substantial limitations associated with electrical charge carrier injection. These include significant Joule heatingwhich is considerably reduced under femtosecond optical excitationinefficient free carrier generation due to leakage currents, and inherently lower modulation speeds on the order of hundreds of megahertz, in contrast to the picosecond-scale switching achievable via optical pumping. Furthermore, the fabrication complexity of an actively tuned, electrically driven metasurface is markedly greater than that of a purely optically pumped device. Thus, although electrical control offers conceptual versatility, it is unlikely to represent an efficient or practical route for rapid metasurface reconfiguration. An alternative and promising strategy involves integrating phase-change material (PCM) films with metasurfaces. A primary advantage of PCM-based control is its nonvolatile nature; the metasurface can be maintained in distinct optical states without continuous power input, thereby offering substantially improved energy efficiency relative to the methods discussed above.

In this work, we numerically demonstrate two-dimensional filtering of spatially structured femtosecond probe pulses using the tunable GaAs metasurface. An important challenge can be achieving even more sophisticated ultrafast control over the optical wavefront via transient amplitude and phase modulation during the pump-induced switching process. Owing to the spectral characteristics of Mie resonances, the metasurface exhibits a nonlinear nonuniform dependence of both amplitude and phase shift on the refractive index. Consequently, the transmission spectrum of a periodic nanoresonator array exhibits a spectral peak whose position depends on transient free-carrier concentration and, thus, on the temporal overlap of pump and probe pulses. This property can be exploited for dynamic control of light in 2D+1 space (two spatial and time dimensions) by means of specially engineered metasurfaces, enabling advanced functionalities such as arbitrary pulse shaping, full dispersion control, and real-time wavefront correction. , Ultrafast tunable metasurfaces, therefore, hold significant promise for a wide range of applications, including miniaturized pulse compressors, adaptive optics, real-time signal processing, and next-generation laser systems.

Conclusion

In summary, we have numerically modeled an ultrafast, switchable gallium arsenide metasurface engineered for Fourier-filtering of optical images. Comprehensive calculations of the metasurface’s transmission, reflection, phase shift, and absorption coefficients were performed as functions of nanoring topology and lattice period for initial and photoinduced conditions. By optimizing the metasurface geometrical parameters, we achieved a filter that performs second-derivative image processing in the unpumped state and first-derivative filtering under optical pumping. The characteristic switching time between these filtering states is on the order of several picoseconds, enabling ultrafast reconfigurability. The functionality of the designed meta-filters was validated using a test image with an “H” pattern, demonstrating the metasurface’s capability for ultrafast, reconfigurable analog image processing. These results highlight the potential of dynamically tunable semiconductor metasurfaces for real-time optical computing and advanced machine vision applications.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c10340.

• Detailed description of the modulation of the refractive index and the extinction coefficient for GaAs; FDTD simulation data used for neural network model training; decomposition of Mie-type modes for resonant nanodisks; approach for creating a metasurface topology optimization function; intermediate Fourier filter profiles observed during carrier relaxation (PDF)

The authors declare no competing financial interest.