Stability of temporal solitons in uniform and "managed" quadratic nonlinear media with opposite group-velocity dispersions at fundamental and second harmonics

TL;DR

This paper investigates the stability of quadratic solitons in media with opposite group-velocity dispersions, demonstrating that stability can be enhanced through dispersion and GVM management techniques.

Contribution

It introduces a numerical method to identify the stability range of solitons in chi^(2) media and shows how management techniques extend this stability.

Findings

Full stability range identified via numerical simulations

Stability limited by tail growth in the second-harmonic component

Management techniques effectively expand soliton stability domains

Abstract

The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available chi^(2) materials, is revisited. Using an iterative numerical scheme to construct stationary soliton solutions, and direct simulations to test their stability, we identify a full soliton-stability range in the space of the system's parameters, including the coefficient of the group-velocity-mismatch (GVM). The soliton stability is limited by an abrupt onset of growth of tails in the SH component, the relevant stability region being defined as that in which the energy loss to the tail generation is negligible under experimentally relevant conditions. We demonstrate that the stability domain can be readily expanded with the help of two "management" techniques (spatially periodic compensation of destabilizing effects) - the dispersion management (DM) and GVM management. In comparison with their counterparts in optical fibers, DM solitons in the chi^(2) medium feature very weak intrinsic oscillations.