Direct manipulation of wave amplitude and phase through inverse design of isotropic media

In this article we propose a new design methodology to control both amplitude and phase of electromagnetic waves from cylindrical incidence, which utilizes engineered media that does not resort to transformation optics or its quasi-conformal approximations. This method can lead to two-dimensional isotropic, inhomogeneous material profiles of permittivity and permeability, to which a general class of scattering-free wave solutions arise. Our design is based on the separation of the complex wave solution into amplitude and phase. We give two types of examples to validate our methodology.