A stochastic nonlinear model of the dynamics of actively Q-switched lasers

TL;DR

This paper introduces a new stochastic, reduced-order model for actively Q-switched lasers that captures nonlinear dynamics and spontaneous emission noise, enabling efficient control and prediction of laser behavior.

Contribution

It develops a novel stochastic, spatially lumped multi-mode model with model-order reduction for actively Q-switched lasers, including semi-analytic solutions for pulse dynamics.

Findings

Model accurately predicts laser pulse energy and inversion.

Simulation results validate the model's effectiveness.

Experimental data supports the model's feasibility.

Abstract

In this paper, we present a novel stochastic and spatially lumped multi-mode model to describe the nonlinear dynamics of actively Q-switched lasers and random perturbations due to amplified spontaneous emission. This model will serve as a basis for the design of (nonlinear) control and estimation strategies and thus a high value is set on its computational efficiency. Therefore, a common traveling-wave model is chosen as a starting point and a number of model-order reduction steps are performed. As a result, a set of nonlinear ordinary differential equations for the dynamic behavior of the laser during a switching cycle is obtained. A semi-analytic solution of these differential equations yields expressions for the population inversion after a switching cycle and for the output energy, which are then used to formulate a nonlinear discrete-time model for the pulse-to-pulse dynamics. Simulation studies including models with different levels of complexity and first experimental results demonstrate the feasibility of the proposed approach.