  In this paper, we consider near cloaking for the full Maxwell equations. We
extend the recent results, where the quasi-static limit case and the Helmholtz
equation are considered, to electromagnetic scattering problems. We construct
very effective near cloaking structures for the electromagnetic scattering
problem at a fixed frequency. These new structures are, before using the
transformation optics, layered structures and are designed so that their first
scattering coefficients vanish. Inside the cloaking region, any target has
near-zero scattering cross section for a band of frequencies. We analytically
show that our new construction significantly enhances the cloaking effect for
the full Maxwell equations.
