Nonlinear envelope equation for broadband optical pulses in quadratic media

TL;DR

This paper introduces a nonlinear envelope equation that accurately models the propagation of ultra-broadband optical pulses in quadratic media, extending beyond traditional coupled wave methods for wide bandwidths.

Contribution

It presents a first-order nonlinear envelope equation valid for arbitrarily wide pulse bandwidths, improving modeling of broadband pulses in second-order nonlinear materials.

Findings

Provides an accurate model for ultra-broadband pulse evolution

Goes beyond coupled wave descriptions for wide bandwidths

Applicable to scenarios where frequency component separation is impractical

Abstract

We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse bandwidth. Our approach goes beyond the usual coupled wave description of $\chi^{(2)}$ phenomena and provides an accurate modelling of the evolution of ultra-broadband pulses also when the separation into different coupled frequency components is not possible or not profitable.