How carrier memory enters the Haus master equation of mode-locking

TL;DR

This paper generalizes the Haus master equation by incorporating dynamical boundary conditions, enabling the modeling of complex pulse behaviors and interactions in mode-locked lasers, including Q-switching and harmonic transitions.

Contribution

It introduces a novel approach to include carrier memory effects into the Haus master equation, expanding its applicability to complex pulse dynamics and interactions.

Findings

Analyzes the impact of group velocity dispersion on Q-switching stability.

Demonstrates the model's ability to describe weak interactions between localized states.

Compares the generalized model with time-delayed systems for validation.

Abstract

We present a generalization of the Haus master equation in which a dynamical boundary condition allows to describe complex pulse trains such as the Q-switched and harmonic transitions of passive mode-locking as well as the weak interactions between localized states. As an example, we investigate the influence of group velocity dispersion on the stability boundaries of the Q-switched regime. We compare our results with that of a time-delayed system.