There is today a growing need to accurately model the angular scattering response of metasurfaces for optical analog processing applications. However, the current metasurface modeling techniques are not well suited for such a task since they are limited to small angular spectrum transformations, as shall be demonstrated. The goal of this work is to overcome this limitation by improving the modeling accuracy of these techniques and, specifically, to provide a better description of the angular response of metasurfaces. This is achieved by extending the current methods, which are restricted to dipolar responses and weak spatially dispersive effects, so as to include quadrupolar responses and higher-order spatially dispersive components. The accuracy of the newly derived multipolar model is demonstrated by predicting the angular scattering of a dielectric metasurface. This results in a modeling accuracy that is at least two times better than the standard dipolar model.
We propose a framework that connects the spatial symmetries of a metasurface to its material parameter tensors and its scattering matrix. This provides a simple yet effective way to effortlessly determine properties of a metasurface scattering response, such as chirality or asymmetric transmission, and which of its effective material parameters should be taken into account in the prospect of a homogenization procedure. In contrast to existing techniques, this approach does not require any a priori knowledge of group theory or complicated numerical simulation schemes, hence making it fast, easy…
Optical metasurfaces consist of a 2D arrangement of scatterers, and they control the amplitude, phase, and polarization of an incidence field on demand. Optical metasurfaces are the cornerstone for a future generation of flat optical devices in a wide range of applications. The rapidly growing advances in nanofabrication have made the versatile design and analysis of these ultra-thin surfaces an ever-growing necessity. However, despite their importance, a comprehensive theory to describe the optical response of periodic metasurfaces in closed-form and analytical expressions has not been formul…
Metasurfaces based on resonant subwavelength photonic structures enable novel ways of wavefront control and light focusing, underpinning a new generation of flat-optics devices. Recently emerged all-dielectric metasurfaces exhibit high-quality resonances underpinned by the physics of bound states in the continuum that drives many interesting concepts in photonics. Here we suggest a novel approach to explain the physics of bound photonic states embedded into the radiation continuum. We study dielectric metasurfaces composed of planar periodic arrays of Mie-resonant nanoparticles ("meta-atoms") …
The replacement of bulk refractive optical elements with diffractive planar components enables the miniaturization of optical systems. However, diffractive optics suffers from large chromatic aberrations due to the dispersion of the phase accumulated by light during propagation. We show that this limitation can be overcome with an engineered wavelength-dependent phase shift imparted by a metasurface and demonstrate a design that deflects three wavelengths without dispersion. A planar lens without chromatic aberrations at three wavelengths is also presented. Our design is based on low-loss diel…
We propose a novel class of ultrathin high Q passband filters designed by properly combining different multipolar resonances sustained by an all dielectric metasurface. A rigorous analytical model, based on surface impedance homogenization and accounting for the effects of both dipolar and the quadrupolar contributions to the overall scattering response, is derived and verified through numerical simulations. Then, it is described how it is possible to engineer the interactions between dipoles and quadrupoles in a metasurface made by core shell spherical elements to design ultrathin and broadba…
Non-uniform metasurfaces (electrically thin composite layers) can be used for shaping refracted and reflected electromagnetic waves. However, known design approaches based on the generalized refraction and reflection laws do not allow realization of perfectly performing devices: there are always some parasitic reflections into undesired directions. In this paper we introduce and discuss a general approach to the synthesis of metasurfaces for full control of transmitted and reflected plane waves and show that perfect performance can be realized. The method is based on the use of an equivalent i…
Relating the electromagnetic scattering and absorption properties of an individual particle to the reflection and transmission coefficients of a two-dimensional material composed of these particles is a crucial concept that has driven both fundamental and applied physics. It is at the heart of both the characterization of material properties as well as the phase and amplitude engineering of a wave. Here we propose a multipolar description of the reflection and transmission coefficients across a monolayer of particles using a vector spherical harmonic decomposition. This enables us to provide a…
We present a simple and efficient Finite-Difference Time-Domain (FDFD) scheme for simulating dispersive (Lorentz-Debye) bianisotropic metasurfaces. This scheme replaces the conventional FDTD update equations by augmented update equations where the effect of the metasurface, positioned at a virtual node (or node plane) in the Yee grid, is accounted for by judiciously selected auxiliary polarization functions, based on the Generalized Sheet Transition Conditions (GSTCs). This scheme is computationally -- time- and memory-wise -- more efficient and easier to implement than a previously reported s…
A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, $\boldsymbol{k_{||}}$ with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the st…
In this paper we describe a methodology for tailoring the design of metamaterial dielectric resonators, which represent a promising path toward low-loss metamaterials at optical frequencies. We first describe a procedure to decompose the far field scattered by subwavelength resonators in terms of multipolar field components, providing explicit expressions for the multipolar far fields. We apply this formulation to confirm that an isolated high-permittivity cube resonator possesses frequency separated electric and magnetic dipole resonances, as well as a magnetic quadrupole resonance in close p…
An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, $\boldsymbol{k}$. By representing the angular dependence of the surface susceptibilities in $\boldsymbol{k}$ as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to inclu…
Nonlinear metamaterials show potential for realizing flat nonlinear optical devices but generally lack in terms of achievable conversion efficiencies. Recent work has focused on enhancing nonlinear processes by utilizing high quality factor resonances, such as collective responses known as surface lattice resonances (SLRs) taking place in periodic metal nanoparticle arrays. Here, we investigate how the dispersive nature of SLRs affects the nonlinear responses of SLR-supporting metasurfaces. Particularly, we measure second-harmonic generation from aluminum nanoparticle arrays and demonstrate th…
Dispersion lies at the heart of real-time signal processing systems across the entire electromagnetic spectrum from radio to optics. However, the performance and applicability of such systems have been severely plagued by distortions due to the frequency dependent nature of the amplitude response of the dispersive media used for processing. This frequency dependence is a fundamental consequence of the causality constraint, incarnated by Kramers-Kronig relations or, equivalently, by the Bode relations. In order to resolve this issue, we introduce here the concept of a \emph{perfect dispersive m…
