Efficient integral equation modeling of scattering by a gradient dielectric metasurface

Abstract

-Plane-wave scattering by a gradient dielectric metasurface, composed of a dielectric slab on which has been etched an infinitely periodic grating, is analyzed by means of rigorous semi-analytical integral equation techniques based on the Method of Moments with entire domain basis functions. The electric field integral equation is considered with unknown function the electric field on the grating and is then solved by applying an entire domain Galerkin's technique. The proposed methodology is characterized by high numerical stability and controllable accuracy; the obtained solution is analytic with the sole approximation of the final truncation of the expansion functions sets. The operation of the metasurface as a narrow-band reflection frequency filter is investigated. Moreover, it is also shown that under certain conditions anomalous reflection and transmission can be generated even for a metasurface composed of conventional materials. The numerical results obtained provide design guidelines, which may pave the way for more systematic investigations of gradient dielectric metasurfaces assisting the control and manipulation of electromagnetic waves.

Anomalous reflection of visible light by all-dielectric gradient metasurfaces

“…The total electric field induced in every region of the scattering problem is of the form Ex; z Ψx; zŷ, and the unknown scalar electric field factor Ψ admits the integral representation [24][25][26][27] …”

“…Furthermore, S denotes the total transverse cross section of the rectangular inclusions. Functions Ψ 0 and G have been analytically determined (for more complicated geometries) in [24,25]. According to the Floquet-Bloch theorem [28], the electric field factor is expressed as Ψx; z exp−ik 0 n 0 cos θzux; z;…”

“…A rigorous and highly accurate entire-domain integral equation methodology is employed for the analysis of the associated scattering and diffraction phenomena by such a metasurface. The methodology was initially introduced and developed in [24] for the analysis of dielectric grating structures and was subsequently extended to the scattering analysis of metasurfaces in [25]. We focus on the determination of suitable geometrical and electromagnetic parameters of the metasurface in order for it to exhibit significant anomalous reflection.…”

Mitigating Snell's-Law reflection and transmission with metasurfaces of ordinary dielectrics

“…To this end, we consider that only the 0-and the −1-reflection and transmission orders propagate, which lead by (8) to the following conditions…”

“…The total electric field induced in every region of the scattering problem is of the form E(x, z) = Ψ(x, z)ŷ, and the unknown electric field factor Ψ admits the integral representation [6]- [8] Ψ…”