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

Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell-Bloch laser
Explicit centre manifold reduction and full bifurcation analysis for an astigmatic Maxwell-Bloch laser
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.
centre manifold, spatial patterns in nonlinear optics, symmetric bifurcation theory, takens–bogdanov, maxwell–bloch lasers
0167-2789
175-202
Chillingworth, D.R.J.
39d011b7-db33-4d7d-8dc7-c5a4e0a61231
D'Alessandro, G.
bad097e1-9506-4b6e-aa56-3e67a526e83b
Papoff, F.
1c4e9e0a-8210-49b3-86e2-1d0323b21268
Chillingworth, D.R.J.
39d011b7-db33-4d7d-8dc7-c5a4e0a61231
D'Alessandro, G.
bad097e1-9506-4b6e-aa56-3e67a526e83b
Papoff, F.
1c4e9e0a-8210-49b3-86e2-1d0323b21268

Chillingworth, D.R.J., 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), 175-202. (doi:10.1016/S0167-2789(02)00786-8).

Record type: Article

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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More information

Published date: 2003
Keywords: centre manifold, spatial patterns in nonlinear optics, symmetric bifurcation theory, takens–bogdanov, maxwell–bloch lasers
Organisations: Pure Mathematics, Applied Mathematics

Identifiers

Local EPrints ID: 29305
URI: https://eprints.soton.ac.uk/id/eprint/29305
ISSN: 0167-2789
PURE UUID: bea58221-a393-4481-a478-db76bfe5727c
ORCID for G. D'Alessandro: ORCID iD orcid.org/0000-0001-9166-9356

Catalogue record

Date deposited: 12 May 2006
Last modified: 16 Jul 2019 18:55

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