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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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.
Author(s): | Chillingworth, D.R.J., D'Alessandro, G. and Papoff, F. | Item type: | Article |
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ID code: | 2961 |
Keywords: | centre manifold, spatial patterns in nonlinear optics, symmetric bifurcation theory, Takens-Bogdanov, Maxwell-Bloch lasers, Optics. Light, Statistical and Nonlinear Physics, Condensed Matter Physics |
Subjects: | Science > Physics > Optics. Light |
Department: | Faculty of Science > Physics |
Depositing user: | Mr Derek Boyle |
Date deposited: | 23 Feb 2007 |
Last modified: | 30 Jan 2019 08:37 |
URI: | https://strathprints.strath.ac.uk/id/eprint/2961 |
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