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

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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 (http://dx.doi.org/10.1016/S0167-2789(02)00786-8)

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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.

ORCID iDs

Chillingworth, D.R.J., D'Alessandro, G. and Papoff, F. ORCID logoORCID: https://orcid.org/0000-0002-3456-343X;
  • Item type:Article
    ID code:2961
    Dates:
    Date
    Event
    15 March 2003
    Published
    Subjects:Science > Physics > Optics. Light
    Department:Faculty of Science > Physics
    Depositing user: Mr Derek Boyle
    Date deposited:23 Feb 2007
    Last modified:02 Apr 2025 18:39
    URI:https://strathprints.strath.ac.uk/id/eprint/2961
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