# Single evolution equation describing nonlinear dynamics of nonlocal optical medium under two-wave mixing

## TL;DR

This paper derives a single nonlinear Schrödinger equation to describe the complex nonlinear dynamics of a nonlocal optical medium with relaxation under two-wave mixing, providing a new analytical framework for understanding energy transport.

## Contribution

It presents the first analytical derivation of a unified evolution equation for nonlinear dynamical media with relaxation in two-wave mixing scenarios.

## Key findings

- Explicit coefficients of the evolution equation are expressed in terms of initial parameters.
- The study offers new insights into energy transport scenarios in nonlinear media.
- Provides a foundation for future analytical and experimental investigations.

## Abstract

In this Letter we study theoretically the interaction of optical waves in nonlinear dynamical medium, i.e. medium with relaxation. Taking into account the relaxation of the photoinduced nonlinearity we derive a single evolution equation, namely the nonlinear Schr\"{o}dinger equation with coefficients depending on parameters, for the case of degenerate two-wave mixing at the reflection geometry in bulk Kerr-like medium possessing a nonlocal nonlinear response. All coefficients of the single evolution equation for our system are written out explicitly in terms of initial parameters. This is the first analytical study of the evolution of nonlinear dynamical medium under the action of two wave mixing; usually, it is studied numerically or experimentally making use of some empirical assumptions. We briefly discuss various possible scenarios of energy transport in the frame of the novel equation.