# A perturbative approach to self-phase modulation and self-steepening of short laser pulses propagating in nonlinear media

## TL;DR

This paper develops a first-order perturbative method to analyze self-phase modulation and self-steepening of short laser pulses in nonlinear media, clarifying the effects of various nonlinear terms on pulse evolution.

## Contribution

It introduces a closed-form, perturbative solution for laser pulse propagation accounting for Kerr effect, ionization, and absorption, providing new insights into nonlinear pulse dynamics.

## Key findings

- Quantitative analysis of femtosecond pulse propagation in air
- Clarification of nonlinear effects on pulse amplitude and frequency
- Scaling parameters for nonlinear effects

## Abstract

The solution of the wave equation in the envelope approximation with temporal corrections for a laser pulse propagating in a medium where the Kerr effect, field ionization, and associated absorption take place, is obtained through a first-order perturbative approach. The closed-form expressions so obtained clarify the influence of the various terms of the equation on the laser amplitude and on the frequency generation as a function of the retarded time. Furthermore, they allow extracting scaling parameters which size the nonlinear effects. The results are illustrated quantitatively on the case of a femtosecond pulse focused in the air with typical parameters.