Limiting absorption principle of Helmholtz equation with sign changing coefficients under periodic structure

TL;DR

This paper rigorously establishes the limiting absorption principle for the Helmholtz equation with sign-changing coefficients in periodic structures, ensuring well-posedness of electromagnetic transmission problems involving negative refractive index materials.

Contribution

It introduces a mathematical framework using complementing boundary conditions to derive a priori estimates and prove the limiting absorption principle for such complex materials.

Findings

Established well-posedness of the transmission problem

Derived a priori estimates for Helmholtz equation with sign-changing coefficients

Proved the limiting absorption principle in periodic structures

Abstract

Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complementing boundary condition to establish rigorous a priori estimates for the Helmholtz equation, from which the limiting absorption principle is analytically derived. Within this mathematical framework, we conclusively establish the well-posedness of the electromagnetic transmission problem at the interface between conventional materials and negative refractive index materials in two-dimensional periodic structures.