Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell-Bloch laser

Abstract

We set up a general framework to study the bifurcations of nearly degenerate modes of a Maxwell-Bloch laser model, and we apply it specifically to the study of interactions of two modes of a laser with broken circular symmetry. We use an explicit centre manifold reduction to analyse the behaviour of this laser. Complex bifurcation sequences involving single mode solutions, mode locking and mode beating regimes are predicted. These sequences are organized by a Hopf bifurcation with 1:1 resonance and a Z_2-symmetric Takens-Bogdanov bifurcation. Numerical simulations of the original system show good agreement with theory.