Gaussian pulse dynamics in gain media with Kerr nonlinearity

TL;DR

This paper develops a comprehensive variational framework using the Kantorovitch method and Gaussian ansatz to model Gaussian pulse dynamics in dispersive Kerr media with gain, applicable to fibers and bulk media.

Contribution

It introduces a novel set of equations and ABCD matrices for analyzing spatiotemporal Gaussian pulses in Kerr gain media, unifying various effects in a flexible model.

Findings

Derived equations for pulse dynamics in Kerr media with gain

Applied model to Kerr-lens mode-locked laser resonator

Provided a versatile tool for pulse evolution analysis

Abstract

Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications include the temporal pulse dynamics in gain fibers and the beam propagation or spatiotemporal pulse evolution in bulk gain media. As an example, the steady-state spatiotemporal Gaussian pulse dynamics in a Kerr-lens mode-locked laser resonator is studied.