Modulation Instability of Ultrashort Pulses in Quadratic Nonlinear Media beyond the Slowly Varying Envelope Approximation

TL;DR

This paper analyzes modulational instability of ultrashort pulses in quadratic nonlinear media beyond traditional approximations, demonstrating control over MI and soliton formation in few-cycle regimes through theoretical and numerical methods.

Contribution

It introduces a model for ultrashort pulses beyond the slowly varying envelope approximation and explores MI control and soliton stability in cascaded quadratic-cubic media.

Findings

MI properties agree with numerical simulations

Control over MI and soliton formation is possible

Stable soliton-like pulse propagation depends on MI criteria

Abstract

We report a modulational instability (MI) analysis of a mathematical model appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media beyond the so-called slowly varying envelope approximation. Theoretically predicted MI properties are found to be in good agreement with numerical simulation. The study shows the possibility of controlling the generation of MI and formation of solitons in a cascaded quadratic-cubic media in the few cycle regimes. We also find that stable propagation of soliton-like few-cycle pulses in the medium is subject to the fulfilment of the modulation instability criteria.