Spatial quadratic solitons guided by narrow layers of a nonlinear material

TL;DR

This paper presents analytical solutions for spatial quadratic solitons in layered nonlinear materials, revealing bifurcation phenomena, stability characteristics, and solutions in both linear and nonlinear waveguides with various nonlinearities.

Contribution

It provides the first comprehensive analytical solutions for spatial solitons in layered quadratic nonlinear media, including bifurcation analysis and stability assessment.

Findings

Symmetric, asymmetric, and antisymmetric soliton modes identified.

Bifurcation from symmetric to asymmetric modes demonstrated.

Stable antisymmetric states confirmed through numerical simulations.

Abstract

We report analytical solutions for spatial solitons supported by layers of a quadratically nonlinear material embedded into a linear planar waveguide. A full set of symmetric, asymmetric, and antisymmetric modes pinned to a symmetric pair of the nonlinear layers is obtained. The solutions describe a bifurcation of the subcritical type, which accounts for the transition from the symmetric to asymmetric modes. The antisymmetric states (which do not undergo the bifurcation) are completely stable (the stability of the solitons pinned to the embedded layers is tested by means of numerical simulations). Exact solutions are also found for nonlinear layers embedded into a nonlinear waveguide, including the case when the uniform and localized nonlinearities have opposite signs (competing nonlinearities). For the layers embedded into the nonlinear medium, stability properties are explained by comparison to the respective cascading limit.