Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks

An analytical method of electromagnetic wave interactions with a general radially anisotropic cloak is established. It is able to deal with arbitrary parameters [epsilon(r)(r), mu(r)(r), epsilon(t)(r), and mu(t)(r)] of a radially anisotropic inhomogeneous shell. The general cloaking condition is proposed from the wave relations, in contrast to the method of transformation optics. Spherical metamaterial cloaks with improved invisibility performance are achieved with optimal nonlinearity in transformation and core-shell ratio.