The DC Kerr Effect in Nonlinear Optics

TL;DR

This paper models the DC Kerr effect using nonlinear geometric optics, proving the existence of solutions to Maxwell's equations with Kerr nonlinearity and addressing the inverse problem of determining nonlinear susceptibility.

Contribution

It provides a rigorous mathematical analysis of the Kerr effect in nonlinear optics, including existence proofs and inverse problem solutions.

Findings

Existence of exact solutions to Maxwell's equations with Kerr nonlinearity.

Justification of the Kerr effect within the proposed model.

Solution to the inverse problem for nonlinear susceptibility recovery.

Abstract

We use weakly nonlinear geometric optics to study a model for the DC Kerr effect (the Kerr electro-optic effect), in which a light beam propagating through a material with strong nonlinear optical properties can have its polarization rotated by applying a strong external electric field. This effect is used to build fast switches (Kerr cells). We prove existence of an exact solution of the nonlinear Maxwell system with a cubic Kerr nonlinearity, with the wavelength $h$ being a small parameter. We justify the effect within this model, and also solve the inverse problem of recovery of the nonlinear susceptibility $\chi^{(3)}$ from the change of the polarization.