Dispersion and losses of plasmons along simple metasurfaces: the analysis of dispersion equations

TL;DR

This paper analyzes the dispersion relations and losses of surface plasmons on simple metasurfaces with tensor surface conductivity, using Green's functions and mode matching, including layered and inhomogeneous substrates.

Contribution

It introduces a comprehensive method for analyzing plasmon dispersion and losses on various metasurfaces with complex substrate configurations.

Findings

Derived dispersion equations for plasmons on metasurfaces.

Analyzed effects of layered and gradient substrates on plasmon behavior.

Explored diffraction of surface plasmons on metasurface inhomogeneities.

Abstract

The flat metasurfaces described by tensor surface conductivity, the transverse size of which is small compared to the wavelength, are considered. In this case, we introduce two-dimensional surface conductivity for them, as well as for infinitely thin conductive sheets of graphene type. The method of Green's tensor functions of electrodynamics connecting fields and current densities, as well as the mode matching technique, are used. Conductive films on substrates are considered, including layered substrates of finite thickness with periodic layers and infinite substrates, as well as gradient substrates with a dependence of the dielectric constant on the thickness. Two-dimensional periodic structures of conductive films and dielectric films doped with nanoparticles are also analyzed. The possibility of applying the method to diffraction of surface plasmons on metasurface inhomogeneities is analyzed.