Symmetry in the equations of nonlinear dynamics of semiconductor laser subject to delayed optical feedback

TL;DR

This paper investigates the symmetry properties of nonlinear dynamics in semiconductor lasers with delayed optical feedback, revealing dual systems with equivalent behaviors through mathematical transformations.

Contribution

It introduces a symmetry-based approach to analyze laser dynamics, demonstrating that dual laser systems with anticipated feedback share the same characteristics as those with delayed feedback.

Findings

Dual laser systems exhibit identical dynamics.

Lyapunov transformation simplifies the analysis.

Symmetry reveals equivalence of delayed and anticipated feedback.

Abstract

Delayed feedback laser dynamics is described by means of Lang-Kobayashi equation model. Since a lot of initial states asymptotically approach to periodic attractor in the phase space, only periodic steady-state regimes have been studied here. Lyapunov transformation allows us to reduce problem to the differential equation of the first order whereas the spectrum of laser oscillation is governed by the appropriate eigen value problem. Using the symmetry proves that there is the dual laser system with anticipated feedback which has the same dynamic characteristics as laser with delayed feedback.