Semianalytic theory of self-similar optical propagation and mode locking using a shape-adaptive model pulse

TL;DR

This paper introduces a semianalytic, shape-adaptive model for pulse dynamics in optical amplifiers and lasers, enabling simplified analysis and optimization of self-similar and soliton-like pulses.

Contribution

It presents a flexible, semi-analytic pulse model that interpolates between Gaussian, parabolic, and sech profiles, facilitating analysis of pulse evolution in various regimes.

Findings

Validated the model against numerical simulations of a soliton-similariton laser.

Enabled extensive parameter optimization with reduced complexity.

Provided insights into pulse shape evolution in self-similar regimes.

Abstract

A semianalytic theory for the pulse dynamics in similariton amplifiers and lasers is presented, based on a model pulse with adaptive shape. By changing a single parameter, this test function can be continuously tweaked between a pure Gaussian and a pure parabolic profile and can even represent sech-like pulses, the shape of a soliton. This approach allows us to describe the pulse evolution in the self-similar and other regimes of optical propagation. Employing the method of moments, the evolution equations for the characteristic pulse parameters are derived from the governing nonlinear Schr\"odinger or Ginzburg-Landau equation. Due to its greatly reduced complexity, this description allows for extensive parameter optimization, and can aid intuitive understanding of the dynamics. As an application of this approach, we model a soliton-similariton laser and validate the results against numerical simulations. This constitutes a semianalytic model of the soliton-similariton laser. Due to the versatility of the model pulse, it can also prove useful in other application areas.