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

Chillingworth, D.R.J. and D'Alessandro, G. and Papoff, F. (2003) Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell-Bloch laser. Physica D: Nonlinear Phenomena, 177 (1-4). pp. 175-202. ISSN 0167-2789

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Abstract

Using an explicit centre manifold reduction, we set up a general framework to study the bifurcations of nearly degenerate modes of a rather general laser model. We then apply it specifically to the study of interactions of two modes of a Maxwell-Bloch laser with broken circular symmetry. Complex bifurcation sequences involving single-mode solutions, mode locking and mode beating regimes are predicted. These sequences are organised by a Z2-symmetric Takens-Bogdanov bifurcation together with a zero-detuning Hopf bifurcation with 1:1 resonance that leads to an unexpected cyclic spatio-temporal symmetry of order 4. Numerical simulations of the original system show good agreement with theory.