Metasurfaces are thin optical materials consisting of tiny meta-atoms that locally change the phase, amplitude, and polarization of light. Such metasurfaces have been shown to exhibit optical responses beyond what is possible with natural materials, e.g. in thin achromatic lenses, holograms, reflectors, and the generation of structured light. A considerable challenge lies in designing the sometimes thousands of meta-atoms that are needed to locally modify the wavefronts of light. Here we use a conditional generative adversarial network to demonstrate for the first time a way to design metasurfaces where the scattering responses of different meta-atoms are interdependent, i.e. some of the individual scattering parameters are unimportant, and it is the relative values between different meta-atoms that matter. We illustrate our approach with a design of a broadband phase mask for a Zernike wavefront sensor, with complex requirements on the phase relationship between the scattering parameters of an inner disk and the surrounding region. Our inverse design method offers increased design freedom, since it does not require specifying absolute scattering parameters, and allows for metasurfaces with large bandwidths.

Using inverse-design and a novel design pattern which breaks crystal periodicity, we demonstrate experimentally the, to our knowledge, highest vacuum optomechanical interaction rate for release-free systems at 770 kHz.

Neural networks have been demonstrated to be able to accelerate the modeling and inverse design of optical and electromagnetic devices by serving as fast surrogates for electromagnetic solvers. Nevertheless, such neural networks can be unreliable and normally require extreme amounts of data to train. Here it is shown that these limitations can be alleviated by constraining neural-network models using prior knowledge about the governing physics. We propose a universal physics-informed neural network framework for electromagnetic scattering based on the quasinormal mode expansion of the scattering matrix. The neural networks learn the resonant structure underlying the scattering spectrum, are guaranteed to obey energy conservation and causality, and are shown to have significantly improved data efficiency for photonic-crystal slabs and all-dielectric free-form metasurfaces. Furthermore, the framework allows additional problem-specific constraints, such as losslessness, symmetries, and number of modes, to be imposed manually when they are available. The method can be applied to a wide range of optical and electromagnetic devices owing to the generality of the quasinormal mode formalism.

Interactions between light and mechanics provide a powerful interface between optical and microwave-frequency signals, with applications spanning classical signal processing and quantum technologies. High-performance optomechanical devices require both strong photon-phonon coupling and tolerance to parasitic laser heating. Release-free optomechanical crystals provide improved thermal anchoring compared to suspended nanobeams, but have so far exhibited weaker vacuum optomechanical coupling rates, leaving a trade-off between coupling strength and thermal robustness. Here, we largely close this gap: we design and experimentally demonstrate a release-free silicon optomechanical crystal with a record vacuum optomechanical coupling rate of about g_OM / (2 π) = 800 kHz, comparable to suspended state-of-the-art devices. The resulting optomechanical scattering rate Γ_OM/(2 π)= 1.1 kHz is nearly twice that of previous release-free implementations. This performance is achieved by combining physics-guided human intuition with a multiphysics inverse-design algorithm introduced here for resonant optomechanical structures. Beyond the specific device demonstrated, the inverse-design framework is applicable to co-optimizing optical and mechanical resonances and eigenmodes more broadly. These results strengthen release-free optomechanical crystals as a platform for fast, low-noise classical and quantum optomechanics.

Deep learning can accelerate the modeling of electromagnetic devices by replacing costly simulations with neural networks trained to map design parameters to scattering parameters. However, data efficiency remains a central bottleneck, as training data is typically generated through expensive numerical simulations. Here we show that symmetry provides a powerful and largely untapped route to overcoming this limitation in electromagnetic scattering problems. Leveraging the equivariance of Maxwell's equations, we obtain general transformation rules that map symmetries of electromagnetic devices to corresponding transformations of their scattering parameters. This enables both systematic data augmentation and the construction of exactly equivariant neural networks. We implement the framework for both discrete and continuous symmetry groups and demonstrate its effectiveness on photonic-crystal slabs and free-form diffraction gratings. Incorporating symmetry improves data efficiency by an order of magnitude compared to standard architectures, while equivariant models additionally enforce physical constraints exactly. Our approach is general and complementary to existing physics-informed strategies, provides a first-principles framework for constructing physically grounded surrogate models, and establishes symmetry as a unifying inductive bias for data-efficient and physically consistent learning in computational electromagnetics and beyond.

As nanophotonic devices become increasingly complex, computer simulations of such devices are becoming ever more important. Unfortunately, computer simulations of nanophotonic devices are computationally expensive, especially if many simulations are necessary, e.g., when optimizing or inverse designing a device. Here we study adaptive mesh refinement for finite-element method simulations using an a posteriori error estimation method. We demonstrate that the use of adaptive meshing leads to faster convergence with lower memory footprint for complex three-dimensional nanophotonic structures. Nevertheless, one needs to be careful to avoid a mesh propagation effect for adaptive mesh refinement to be a successful strategy.

We present a detailed study of mechanically compliant, photonic-crystal-based microcavities featuring a quasi-bound state in the continuum. Such systems have recently been predicted to reduce the optical loss in Fabry-Perot-type optomechanical cavities. However, they require two identical photonic-crystal slabs facing each other, which poses a considerable challenge for experimental implementation. We investigate how such an ideal system can be simplified and still exhibit a quasi-bound state in the continuum. We find that a suspended photonic-crystal slab facing a distributed Bragg reflector realizes an optomechanical system with a quasi-bound state in the continuum. In this system, the radiative cavity loss can be eliminated to the extent that the cavity loss is dominated by dissipative loss originating from material absorption only. These proposed optomechanical cavity designs are predicted to feature optical quality factors in excess of 10^5.

Due to their low mass and high reflectivity, photonic-crystal membranes are excellent candidates for vibrating end mirrors in optomechanical cavities. Cavities with photonic-crystal membranes can support a quasi-bound state in the continuum (BIC), i.e., a resonance exhibiting an optical quality factor only limited by dissipative loss. Such cavities promise to access new regimes in optomechanics [1], e.g., the single-photon strong-coupling regime for applications in precision sensing [2] and quantum information processing [3]. However, previously proposed designs turned out to be difficult to fabricate with state-of-the-art nanolithography techniques. Furthermore, it is difficult to find new nanophotonic structures with a bound state in the continuum, in particular if a substrate breaks the mirror symmetry of the cavity.

We present methods for designing optical metasurfaces. First we focus on metasurfaces manipulating curved wave fronts, e.g., confocal metamirrors. Then we show how metamaterials with multiple design objectives can be designed using machine learning.

Increasing the interaction between light and mechanical resonators is an ongoing endeavor in the field of cavity optomechanics. Optical microcavities allow for boosting the interaction strength through their strong spatial confinement of the optical field. In this work, we follow this approach by realizing a sub-wavelength-long, free-space optomechanical microcavity on-chip fabricated from an (Al,Ga)As heterostructure. A suspended GaAs photonic crystal mirror is acting as a highly reflective mechanical resonator, which together with a distributed Bragg (DBR) reflector forms an optomechanical microcavity. We demonstrate precise control over the microcavity resonance by change of the photonic crystal parameters. We find that the microcavity mode can strongly couple to the transmissive modes of the DBR. The interplay between the microcavity mode and a guided resonance of the photonic crystal modifies the cavity response and results in a stronger dynamical backaction on the mechanical resonator compared to conventional optomechanical dynamics.

We show that the free-form inverse design of nanophotonic matasurfaces can be solved with a modified CGAN machine learning method that balances the accuracy of desired optical properties with experimental feasibility.

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We show that a modified CGAN machine learning method that balances the accuracy of desired optical properties with experimental feasibility can solve the free-form inverse design of nanophotonic matasurfaces.

Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large computer simulations for anything beyond the simplest geometries. The inverse problem, determining the coefficients from a field on a boundary, is even more demanding, since traditional optimization requires a large number of forward problems be solved sequentially. Here we show that the free-form inverse problem of wave equations can be solved with machine learning. First we show that deep neural networks can be used to predict the optical properties of nanostructured materials such as metasurfaces. Then we demonstrate the free-form inverse design of such nanostructures and show that constraints imposed by experimental feasibility can be taken into account. Our neural networks promise automated design in several technologies based on the wave equation.

We propose a versatile, free-space cavity optomechanics platform built from two photonic crystal membranes, one of which is freely suspended, and designed to form a microcavity less than one wavelength long. This cavity features a series of photonic bound states in the continuum that, in principle, trap light forever and can be favorably used together with evanescent coupling for realizing various types of optomechanical couplings, such as linear or quadratic coupling of either dispersive or dissipative type, by tuning the photonic crystal patterning and cavity length. Crucially, this platform allows for a quantum cooperativity exceeding unity in the ultrastrong single-photon coupling regime, surpassing the performance of conventional Fabry-Perot-based cavity optomechanical devices in the non-resolved sideband regime. This conceptually novel platform allows for exploring new regimes of the optomechanical interaction, in particular in the framework of pulsed and single-photon optomechanics.

We characterize the opto-mechanical properties of double-layer mechanical devices. These closely spaced photonic crystal membranes can exhibit photonic bound states in the continuum, which could enable the realization of a strongly coupled, integrated op-tomechanical system.

In this contribution, we will show how nanophotonic structures can be used to gain access to previously inaccessible regimes in cavity optomechanics [1] . We introduce a novel optomechanics platform, built from two photonic crystal membranes [2] , one of which is freely suspended (see Fig. 1 ). This cavity supports a series of photonic bound states in the continuum (BICs) that, in principle, trap light forever [3] and can be favourably used together with evanescent coupling for realizing various types of optomechanical couplings, such as linear or quadratic coupling of either dispersive or dissipative type, by tuning the photonic crystal patterning and cavity length. By combining light propagation in both free-space (between the photonic-crystal membranes) and guided-mode (over the photonic-crystal membranes) form, our platform merges the strengths offered by in-plane and out-of-plane optomechanical systems.

We fabricated and characterized suspended bi-layered photonic crystal slabs in AlGaAs heterostructures. Our approach allows to create integrated, closely spaced membranes, which can exhibit photonic bound states in the continuum to increase light-matter interaction.

We present high-reflectivity mechanical resonators fabricated from AlGaAs heterostructures for use in free-space optical cavities operating in the telecom wavelength regime. The mechanical resonators are fabricated in slabs of GaAs and patterned with a photonic crystal to increase their out-of-plane reflectivity. Characterization of the mechanical modes reveals residual tensile stress in the GaAs device layer. This stress results in higher mechanical frequencies than in unstressed GaAs and can be used for strain engineering of mechanical dissipation. Simultaneously, we find that the finite waist of the incident optical beam leads to a dip in the reflectance spectrum. This feature originates from coupling to a guided resonance of the photonic crystal, an effect that must be taken into account when designing slabs of finite size. The single-layer and sub-μm-spaced double-layer slabs demonstrated here can be directly fabricated on top of a distributed Bragg reflector mirror in the same material platform. Such a platform opens a route for realizing integrated multi-element cavity optomechanical devices and optomechanical microcavities on chip.

Phase-gradient metasurfaces have the potential to revolutionize photonics by offering ultrathin alternatives to a wide range of common optical elements, including bulky refractive optics, waveplates, and axicons. However, the fabrication of state-of-the-art metasurfaces typically involves several expensive, time-consuming, and potentially hazardous processing steps. To address this limitation, a facile methodology to construct phase-gradient metasurfaces from an exposed standard electron beam resist is developed. The method dramatically cuts the required processing time and cost as well as reduces safety hazards. The advantages of the method are demonstrated by constructing high-performance flat optics based on the Pancharatnam-Berry phase gradient concept for the entire visible wavelength range. Manufactured devices include macroscopic (1 cm diameter) positive lenses, gratings exhibiting anomalous reflection, and cylindrical metalenses on flexible plastic substrates.