Cloaking with optimized homogeneous anisotropic layers

We present a method to reduce the scattering from arbitrary objects by surrounding them with shells composed of several layers of homogeneous anisotropic materials. An optimization procedure is used to find the material parameters for each layer, the starting point of which is a discretized approximation of a coordinate transformation cloaking shell. We show that an optimized, three-layer shell can reduce the maximum scattering of an object by as much as 15 dB more than a 100-layer realization of a coordinate transformation cloaking shell. Moreover, using an optimization procedure can yield high-performance cloaking shell solutions that also meet external constraints, such as the maximum value of permittivity or permeability. This design approach can substantially simplify the fabrication of moderate-size cloaking shells.