Nonlinear transformation optics and engineering of the Kerr effect

TL;DR

This paper extends transformation optics to nonlinear regimes, particularly analyzing the Kerr effect, and demonstrates how it can be used to engineer self-interaction effects like self-focusing in nonlinear optical materials.

Contribution

It introduces a framework for applying transformation optics to nonlinear electrodynamics, emphasizing energy density relations over field squared terms, and explores Kerr nonlinearity engineering.

Findings

Transformation optics favors energy density relations over field squared terms.

Kerr nonlinearity can be engineered using transformation optics techniques.

Self-focusing effects can be manipulated through this new approach.

Abstract

The concept of transformation optics is extended to nonlinear electrodynamics. It is shown that transformation optics favors implicit constitutive relations in terms of energy densities D.E and B.H rather than E^2 and H^2. The Kerr nonlinearity is studied in detail and the transformation optics based engineering of self-interaction effects is discussed. As a specific example we introduce transformation optics applied on a self-focusing field configuration.