High frequency integrable regimes in nonlocal nonlinear optics

TL;DR

This paper introduces an integrable model for high frequency light propagation in nonlocal nonlinear media, revealing self-guided beams and phase deformations, and connects nonlocal optics with quasiconformal mappings.

Contribution

It derives a high frequency limit model for nonlocal nonlinear optics and analyzes nonlocal perturbations using the dispersionless Veselov-Novikov hierarchy with novel mathematical methods.

Findings

Existence of self-guided light beams in the model

Nonlocal perturbations manifest as phase deformations

Connection established between nonlocal optics and quasiconformal mappings

Abstract

We consider an integrable model which describes light beams propagating in nonlocal nonlinear media of Cole-Cole type. The model is derived as high frequency limit of both Maxwell equations and the nonlocal nonlinear Schroedinger equation. We demonstrate that for a general form of nonlinearity there exist selfguided light beams. In high frequency limit nonlocal perturbations can be seen as a class of phase deformation along one direction. We study in detail nonlocal perturbations described by the dispersionless Veselov-Novikov (dVN) hierarchy. The dVN hierarchy is analyzed by the reduction method based on symmetry constraints and by the quasiclassical Dbar-dressing method. Quasiclassical Dbar-dressing method reveals a connection between nonlocal nonlinear geometric optics and the theory of quasiconformal mappings of the plane.