Scattering free graded index profiles and the control of electromagnetic fields

We present a general methodology to arbitrarily manipulate the amplitude and phase of an electromagnetic wave propagating in a two-dimensional medium, without introducing any scattering. This leads to a class of isotropic spatially varying permittivity and permeability profiles that are transparent to an incident plane wave while shaping the field magnitude. Furthermore, we propose a metamaterial structure working in the infrared that demonstrates deep sub-wavelength control of the electric field amplitude and strong reduction of the scattering.