Spatio-Temporal Mode-locking in Quadratic Nonlinear Media

TL;DR

This paper introduces a new theoretical model for spatio-temporal mode-locking in quadratic nonlinear media, demonstrating the existence and stability of astigmatic soliton solutions through numerical and bifurcation analysis.

Contribution

It develops a novel extension of the master mode-locking model using a 2D nonlinear Schrödinger equation with mean coupling, specifically for quadratic nonlinear media.

Findings

Existence of steady state astigmatic soliton solutions.

Spatio-temporal mode-locking is achievable and stable in quadratic nonlinear media.

Bifurcation analysis confirms the stability of these solutions.

Abstract

A new theoretical model is developed to characterize spatio-temporal mode-locking (ML) in quadratic nonlinear media. The model is based on the two-dimensional nonlinear Schr\"odinger equation with coupling to a mean term (NLSM) and constructed as an extension of the master mode-locking model. It is numerically demonstrated that there exists steady state soliton solutions of the ML-NLSM mode-locking model that are astigmatic in nature. A full stability analysis and bifurcation study is performed for the ML-NLSM model and it is manifest that spatio-temporal mode-locking of the astigmatic steady-state solutions is possible in quadratic nonlinear media.