Unidirectional Reflection and Invisibility in Nonlinear Media with an Incoherent Nonlinearity

TL;DR

This paper provides explicit criteria for achieving reflectionlessness and invisibility in nonlinear media with incoherent nonlinearity, analyzing how weak Kerr nonlinearity impacts unidirectional invisibility and reflection properties.

Contribution

It introduces explicit criteria for reflectionlessness and invisibility in nonlinear potentials and systematically studies the effects of weak Kerr nonlinearity on unidirectional invisibility.

Findings

Weak Kerr nonlinearity can destroy unidirectional invisibility.

First-order perturbation theory shows nonlinearity does not affect reflectionlessness.

Violation of transmission reciprocity is a second-order effect.

Abstract

We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.