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

D.R.J. Chillingworth, G. D'Alessandro, F. Papoff

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
LanguageEnglish
Pages175-202
Number of pages27
JournalPhysica D: Nonlinear Phenomena
Volume177
Issue number1-4
DOIs
Publication statusPublished - 15 Mar 2003

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lasers
symmetry
locking
simulation
interactions

Keywords

  • centre manifold
  • spatial patterns in nonlinear optics
  • symmetric bifurcation theory
  • Takens-Bogdanov
  • Maxwell-Bloch lasers

Cite this

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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.",
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Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell-Bloch laser. / Chillingworth, D.R.J.; D'Alessandro, G.; Papoff, F.

In: Physica D: Nonlinear Phenomena, Vol. 177, No. 1-4, 15.03.2003, p. 175-202.

Research output: Contribution to journalArticle

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