Nonlinear Wave Equation in Frequency Domain: Accurate Modeling of Ultrafast Interaction in Anisotropic Nonlinear Media

TL;DR

This paper develops a comprehensive frequency domain nonlinear wave equation for ultrafast pulse interactions in anisotropic nonlinear media, demonstrating its effectiveness through simulations of soliton dynamics and spectral phenomena.

Contribution

It introduces a detailed spectral nonlinear wave equation incorporating multiple nonlinear effects and anisotropy, advancing the modeling of ultrafast nonlinear optical interactions.

Findings

Balanced soliton delay achieved through nonlinear effects

Generation of few-cycle compressed solitons in short crystals

Observation of spectral shifts and dispersive waves

Abstract

We interpret the purely spectral forward Maxwell equation with up to 3${^{\rm rd}}$ order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named nonlinear wave equation in frequency domain, includes both quadratic and cubic nonlinearities, delayed Raman effects and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due to competition between self-steepening, Raman effects and self-steepening-like effects from cascading originating in the group-velocity mismatch between the pump and second harmonic. We analyze the first-order contributions, and show that this balance can be broken to create fast or slow pulses. Through further simulations we demonstrate few-cycle compressed solitons in extremely short crystals, where spectral phenomena such as blue/red shifting, non-stationary radiation in accordance with the non-local phase matching condition and dispersive-wave generation are observed and marked, which help improving the experimental knowledge of cascading nonlinear soliton pulse compression.