General laws of reflection and refraction for subwavelength phase grating

TL;DR

This paper derives general laws for reflection and refraction at metasurfaces with abrupt phase shifts, revealing critical angles and conditions for anomalous phenomena like negative refraction, and designs a metasurface for controlling light propagation.

Contribution

It introduces a comprehensive theoretical framework for reflection and refraction at subwavelength metasurfaces using Fermat's principle and boundary conditions, including conditions for anomalous effects.

Findings

Existence of critical angles for total internal reflection.

Conditions for negative reflection and refraction.

Design of a metasurface for light control.

Abstract

The general reflection and refraction laws at the metasurface with the abrupt phase shift were derived by two different methods of Fermat's principle and the boundary conditions respectively. It is found that one or two critical angles for total internal reflection exist when a light hits on the optical sparse material from the optical denser material, and one such a critical angle exists when light spreads from the optical sparse material to the optical denser material. Anomalous reflection and refraction, such as, negative reflection and negative refraction may occur when a light passes through the metasurface, and the conditions of their occurrence were given. Finally, a kind of metasurface based on one-dimensional phase mask was designed to control the light propagation.