Quasiperiodic Multicolor Solitons in Quasi-Phase-Matched Quadratic Media

TL;DR

This paper investigates quasiperiodic multicolor solitons in quadratic nonlinear media, demonstrating their stability and dynamics through analytical and Lyapunov methods in quasiperiodic optical superlattices.

Contribution

It introduces a comprehensive analysis of quasiperiodic multicolor solitons, including stability criteria and dynamic behavior in generalized quasiperiodic waveguides.

Findings

Demonstrated stability of multicolor solitons via Lyapunov analysis.

Predicted stable propagation using virial identity.

Established analytic stability criterion for the solitons.

Abstract

We study the (1+1)-dimensional quasiperiodic multicolor solitons due to cascading quadratic nonlinear response in generalized one-dimensional quasiperiodic optical superlattice waveguides and show that the dynamic equations describing the quasi-phase-matched multicolor solitons include quasiperiodicity-induced Kerr effects, such as self- and cross-phase modulation, third harmonic generation and four-wave mixing. We demonstrate the stability of this multicolor solitons by means of a Lyapunov analysis based on the energy integral of the wave coupling equations and investigate the dynamics of the multicolor solitons using a virial identity, which predicts a stable propagation of the mutually trapped solitons. We finally establish the analytic stability criterion for the multicolor solitons by applying a multiscale asymptotic method.