Modeling Metasurfaces Using Discrete-Space Impulse Response Technique

Abstract

Metasurfaces are arrays of subwavelength meta-atoms that shape waves in a compact and planar form factor. Analysis and design of metasurfaces require methods for modeling their interactions with waves. Conventional modeling techniques assume that metasurfaces are locally periodic structures excited by plane waves, restricting their applicability to gradually varying metasurfaces that are illuminated with plane waves. Here we introduce the discrete-space impulse response concept that enables the development of accurate and general models for metasurfaces. According to the proposed model, discrete impulse responses are assigned to metasurface unit cells and are used to determine the metasurface response to any arbitrary incident waves. We verify the accuracy of the model by comparing its results with full-wave simulations. The proposed concept and modeling technique are applicable to linear metasurfaces with arbitrary meta-atoms, and the resulting system-level models can be used to accurately incorporate metasurfaces into simulation and design tools that use wave or ray optics.

Fast multi-source nanophotonic simulations using augmented partial factorization

“…S1). APF-c can naturally be used with overlappingdomain distribution strategies [73][74][75] when modeling large-area systems. Multi-frontal parallelization can be used through existing packages such as MUMPS [56], and one may further employ hardware accelerations with GPUs [75,91,92].…”

“…The overall response is commonly modeled by ignoring the coupling between meta-atoms [3,4] or with the locally-periodic approximation (LPA) which approximates the local response as that of a periodic array of meta-atoms [4,70]. However, LPA is inaccurate whenever the cell-to-cell variation is large [71][72][73][74][75] and cannot describe nonlocal responses [76,77] and metasurfaces that are not based on unit cells [78][79][80]. Coupled-mode theory can model the coupling between meta-atoms [81] but requires isolated resonances with high quality factors.…”

Thickness bound for nonlocal wide-field-of-view metalenses

“…A formal derivation is provided in the Supplementary Materials. Intuitively, t(y, y ) gives the output at position y given a localized incident wave focused at y ; it has also been called the "discrete-space impulse response" [65]. Its off-diagonal elements capture nonlocal couplings between different elements of a metasurface, which are commonly ignored in conventional metasurface designs but play a critical role for angular diversity.…”

Large-Scale Parametrized Metasurface Design Using Adjoint Optimization

“…In an actual metasurface, the transmission angle varies, and hence the true response would deviate from the response map. 17 These assumptions can lead to significant mismatches between expected and actual responses of a meta-atom in a metasurface. The effect of such mismatch can be seen in reduction of the efficiency of the device; however, it is hard to exactly distinguish the contribution of each assumption without analytical models.…”

“…This approximation also has reduced accuracy in structures comprising meta-atoms with lower refractive index, in which the response of a meta-atom is more strongly affected by variations of its neighbors. , Second, the response map used in unit-cell-based methods records only the normally transmitted response for normally incident light. In an actual metasurface, the transmission angle varies, and hence the true response would deviate from the response map . These assumptions can lead to significant mismatches between expected and actual responses of a meta-atom in a metasurface.…”