Controlling electromagnetic waves in a class of invisible materials

We propose a general methodology to manipulate the amplitude of an electromagnetic wave in a pre-defined way, without introducing any scattering. This leads to a whole class of isotropic spatially varying permittivity and permeability profiles that are invisible to incident waves. The theory is illustrated through various numerical examples, including the non-magnetic case. The implementation of the required material properties using metamaterials is discussed, as well as extensions of the method for controlling the phase of electromagnetic fields.