The scattering of a cylindrical invisibility cloak: reduced parameters and optimization

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 using some peculiar composites such as photonic crystals which mimic an effective refractive index landscape rather than offering effective constitutives, meanwhile cancelling the scattering from the inner and outer boundaries.