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

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.