Metasurfaces and Optimal transport

TL;DR

This paper introduces a theoretical and numerical framework for designing metalenses using optimal transport theory, demonstrating existence, uniqueness, and computational methods for controlling radiation patterns.

Contribution

It combines optimal transport theory with numerical algorithms to solve the metalens design problem, including near and far field refraction analysis.

Findings

Proves existence and uniqueness of solutions for metalens design.

Develops a damped Newton algorithm for numerical solution.

Provides detailed analysis for near field refraction and extensions to far field.

Abstract

This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for the numerical solution we study and implement a damped Newton algorithm to solve the semi discrete problem. A detailed analysis is carried out to solve the near field one source refraction problem and extensions to the far field are also mentioned.