Title: A Unified Approach to Nonlinear Transformation Materials,
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.