Spaceless description of active optical media

TL;DR

This paper introduces a simplified modeling approach for active optical media that reduces complex spatially-dependent Maxwell-Bloch equations to a few ordinary differential equations, enabling faster analysis of laser dynamics.

Contribution

The authors propose a novel method that removes spatial variability from Maxwell-Bloch equations, simplifying the analysis of nonlinear optical media and laser systems.

Findings

Accurately reproduces Maxwell-Bloch dynamics with simplified equations

Enables efficient simulation of active optical networks

Facilitates analysis of laser instabilities and feedback effects

Abstract

The acclaimed Maxwell-Bloch (or Arecchi-Bonifacio) equations are a valid dynamical model, effectively describing wave propagation in nonlinear optical media: from the amplification in input-output devices to multimode instabilities arising in laser systems. However, the inherent spatial variability of the physical observables represents an obstacle to fast simulations and analysis, especially whenever networks of active elements have to be considered. In this paper, we propose an approach which, stripping the spatial dependence of its role as a generator of dynamical richness, allows for a compelling simple portrait. It leads to (a few) ordinary differential equations in input-output configurations, complemented by a time-delayed feedback in closed-loop setups. Such scheme reproduces accurately the dynamics, paving the way to a plain treatment of the wealth of phenomena described by the Maxwell-Bloch equations.