# A Unified Approach to Nonlinear Transformation Materials

## TL;DR

This paper extends transformation optics to nonlinear media, enabling novel effects like cloaking solitons and modeling nonlinear gravitational solutions, thus broadening the scope of optical device design.

## Contribution

It introduces a consistent method to incorporate nonlinearity into transformation optics, expanding its application to nonlinear backgrounds and transformations.

## Key findings

- Cloaking of optical solitons demonstrated.
- Modeling of nonlinear Einstein solutions achieved.
- Development of nonlinear constitutive relations for relativistic cloaks.

## Abstract

The advances in geometric approaches to optical devices due to transformation optics has led to the development of cloaks, concentrators, and other devices. It has also been shown that transformation optics can be used to gravitational fields from general relativity. However, the technique is currently constrained to linear devices, as a consistent approach to nonlinearity (including both the case of a nonlinear background medium and a nonlinear transformation) remains an open question. Here we show that nonlinearity can be incorporated into transformation optics in a consistent way. We use this to illustrate a number of novel effects, including cloaking an optical soliton, modeling nonlinear solutions to Einstein's field equations, controlling transport in a Debye solid, and developing a set of constitutive to relations for relativistic cloaks in arbitrary nonlinear backgrounds.