Cloaking using complementary media for electromagnetic waves

TL;DR

This paper demonstrates electromagnetic cloaking using complementary media with negative index materials, extending previous two-dimensional results to full Maxwell equations through advanced mathematical techniques.

Contribution

It establishes cloaking for electromagnetic waves with negative index materials, extending prior two-dimensional findings to the full Maxwell equations.

Findings

Cloaking achieved using complementary media for electromagnetic waves.

Extension of 2D cloaking results to 3D Maxwell equations.

Application of advanced mathematical techniques to analyze cloaking.

Abstract

Negative index materials are artificial structures whose refractive index has negative value over some frequency range. The study of these materials has attracted a lot of attention in the scientific community not only because of their many potential interesting applications but also because of challenges in understanding their intriguing properties due to the sign-changing coefficients in equations describing their properties. In this paper, we establish cloaking using complementary media for electromagnetic waves. This confirms and extends the suggestions in two dimensions of Lai et al. for the full Maxwell equations. The analysis is based on the reflecting and removing localized singularity techniques, three-sphere inequalities, and the fact that the Maxwell equations can be reduced to a weakly coupled second order elliptic equations.