We show that silicon-based metagratings capable of large-angle, multifunctional performance can be realized using inverse freeform design. These devices consist of nonintuitive nanoscale patterns and support a large number of spatially overlapping optical modes per unit area. The quantity of modes, in combination with their optimized responses, provides the degrees of freedom required to produce high-efficiency devices. To demonstrate the power and versatility of our approach, we fabricate metagratings that can efficiently deflect light to 75° angles and multifunctional devices that can steer beams to different diffraction orders based on wavelength. A theoretical analysis of the Bloch modes supported by these devices elucidates the spatial mode profiles and coupling dynamics that make high-performance beam deflection possible. This approach represents a new paradigm in nano-optical mode engineering and utilizes different physics from the current state-of-the-art, which is based on the stitching of noninteracting waveguide structures. We envision that inverse design will enable new classes of high-performance photonic systems and new strategies toward the nanoscale control of light fields.

A key challenge in metasurface design is the development of algorithms that can effectively and efficiently produce high performance devices. Design methods based on iterative optimization can push the performance limits of metasurfaces, but they require extensive computational resources that limit their implementation to small numbers of microscale devices. We show that generative neural networks can train from images of periodic, topology-optimized metagratings to produce high-efficiency, topologically complex devices operating over a broad range of deflection angles and wavelengths. Further iterative optimization of these designs yields devices with enhanced robustness and efficiencies, and these devices can be utilized as additional training data for network refinement. In this manner, generative networks can be trained, with a onetime computation cost, and used as a design tool to facilitate the production of near-optimal, topologically-complex device designs. We envision that such data-driven design methodologies can apply to other physical sciences domains that require the design of functional elements operating across a wide parameter space.

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Metasurfaces are ultrathin optical elements that are highly promising for constructing lightweight and compact optical systems. For their practical implementation, it is imperative to maximize the metasurface efficiency. Topology optimization provides a pathway for pushing the limits of metasurface efficiency; however, topology optimization methods have been limited to the design of microscale devices due to the extensive computational resources that are required. We introduce a new strategy for optimizing large-area metasurfaces in a computationally efficient manner. By stitching together individually optimized sections of the metasurface, we can reduce the computational complexity of the optimization from high-polynomial to linear. As a proof of concept, we design and experimentally demonstrate large-area, high-numerical-aperture silicon metasurface lenses with focusing efficiencies exceeding 90%. These concepts can be generalized to the design of multifunctional, broadband diffractive optical devices and will enable the implementation of large-area, high-performance metasurfaces in practical optical systems.

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The absorption coefficient α for GaAs at room temperature was determined in the spectral range from 1.3 to 1.6 eV by transmission measurements for 10⩽α⩽103 cm−1 and by a Kramers−Kronig analysis of the reflectance for α≳103 cm−1. Measurements were made on high−purity n−type samples, n−type samples with free−electron concentrations from 5×1016 to 6.7×1018 cm−3, p−type samples with free−hole concentrations from 1.5×1016 to 1.6×1019 cm−3, and p−type samples heavily doped with the amphoteric impurity Si. These data show that near the direct energy gap Eg the shape of the α−vs−photon−energy curve is strongly dependent on the impurity concentration.

Metasurfaces are thin-film optical devices for tailoring the phase fronts of light. The extension of metasurfaces to multiple wavelengths has remained a major challenge, and existing design techniques do not yield devices with high efficiency. We report a

Semiconducting nanostructures are promising as components in high-performance metasurfaces. We show that single-crystal silicon can be used to realize efficient metasurface devices across the entire visible spectrum, ranging from 480 to 700 nm. Alternative forms of silicon, such as polycrystalline and amorphous silicon, suffer from higher absorption losses and do not yield efficient metasurfaces across this wavelength range. To demonstrate, we theoretically and experimentally characterize the resonant scattering peaks of individual single-crystal silicon nanoridges. In addition, we design high-efficiency metagratings and lenses based on nanoridge arrays, operating at visible wavelengths, using a stochastic optimization approach. We find that at wavelengths where single-crystal silicon is effectively lossless, devices based on high aspect ratio nanostructures are optimal. These devices possess efficiencies similar to those made of titanium oxide, which is an established material for high-efficiency visible wavelength metasurfaces. At blue wavelengths, where single-crystal silicon exhibits absorption losses, optimal devices are instead based on coupled low aspect ratio resonant nanostructures and are able to provide reasonably high efficiencies. We envision that crystalline silicon metasurfaces will enable compact optical systems spanning the full visible spectrum.