Cloaking using complementary media for electromagnetic waves

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 of Lai et al. [Phys. Rev. Lett. 102 (2009) 093901] 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