  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.
