Efficient integral equation modeling of scattering by a gradient dielectric metasurface

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.