Spectral method for efficient computation of time-dependent phenomena in complex lasers

TL;DR

This paper introduces an efficient spectral method for simulating complex, time-dependent laser phenomena, overcoming computational challenges of traditional approaches and revealing new dynamical behaviors like mode synchronization.

Contribution

The authors develop a spectral method that efficiently models time-dependent phenomena in complex lasers, extending analysis beyond the stationary inversion approximation.

Findings

Inversion remains non-stationary only in a narrow pump power range.

Increased pump power induces a synchronization transition.

The spectral method accurately captures mode synchronization dynamics.

Abstract

Studying time-dependent behavior in lasers is analytically difficult due to the saturating non-linearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time and space in conventional FDTD approaches. We describe here an efficient spectral method to overcome these shortcomings in complex lasers of arbitrary shape, gain medium distribution, and pumping profile. We apply this approach to a quasi-degenerate two-mode laser in different dynamical regimes and compare the results in the long-time limit to the Steady State Ab Initio Laser Theory (SALT), which is also built on a spectral method but makes a more specific ansatz about the long-time dynamical evolution of the semiclassical laser equations. Analyzing a parameter regime outside the known domain of validity of the stationary inversion approximation, we find that for only a narrow regime of pump powers the inversion is not stationary, and that this, as pump power is further increased, triggers a synchronization transition upon which the inversion becomes stationary again. We provide a detailed analysis of mode synchronization (aka cooperative frequency locking), revealing interesting dynamical features of such a laser system in the vicinity of the synchronization threshold.