Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation

TL;DR

This paper derives a cubic generalized Kadomtsev-Petviashvili equation from Maxwell-Bloch equations to describe ultrashort pulse collapse in Kerr media, analyzing thresholds and spectral evolution during collapse.

Contribution

It introduces a novel derivation of the cubic generalized Kadomtsev-Petviashvili equation for ultrashort pulses without the slowly varying envelope approximation, and analyzes collapse thresholds and spectral broadening.

Findings

Collapse threshold determined numerically and analytically

Spectral broadening during collapse is strongly asymmetric

Ultrashort pulse evolution characterized without envelope approximation

Abstract

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.