  We investigate the scattering of 2D cylindrical invisibility cloaks with
simplified constitutive parameters with the assistance of scattering
coefficients. We show that the scattering of the cloaks originates not only
from the boundary conditions but also from the spatial variation of the
component of permittivity/permeability. According to our formulation, we
propose some restrictions to the invisibility cloak in order to minimize its
scattering after the simplification has taken place. With our theoretical
analysis, it is possible to design a simplified cloak by using some peculiar
composites like photonic crystals (PCs) which mimic an effective refractive
index landscape rather than offering effective constitutives, meanwhile
canceling the scattering from the inner and outer boundaries.
