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

## TL;DR

This paper introduces a novel inverse design method for isotropic media that independently controls wave amplitude and phase, enabling scattering-free electromagnetic wave manipulation without relying on transformation optics.

## Contribution

It presents a new inverse design approach for creating isotropic, inhomogeneous materials that precisely control wave amplitude and phase, avoiding transformation optics approximations.

## Key findings

- Successfully designed isotropic media with tailored wave properties
- Demonstrated control over amplitude and phase in electromagnetic waves
- Validated the methodology with practical examples

## Abstract

In this article we propose a new design methodology allowing us to control both ampli- tude and phase of electromagnetic waves from a cylindrical incident wave. This results in isotropic materials and does not resort to transformation optics or its quasi-conformal approximations. Our method leads 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.