Nonlinear envelope equation for broadband optical pulses in quadratic media

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 ${\ensuremath{\chi}}^{(2)}$ phenomena and provides an accurate modeling of the evolution of ultra-broadband pulses also when the separation into different coupled frequency components is not possible or not profitable.