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Singular Hopf bifurcation to strongly pulsating oscillations in lasers containing a saturable absorber

Published online by Cambridge University Press:  30 July 2003

GREGORY KOZYREFF  and
THOMAS ERNEUX
GREGORY KOZYREFF
Affiliation:
Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine, C.P. 231, 1050 Bruxelles, Belgium Current address: OCIAM, Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK.
THOMAS ERNEUX
Affiliation:
Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine, C.P. 231, 1050 Bruxelles, Belgium
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Abstract

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The equations describing the pulsating output of a laser containing a saturable absorber are investigated numerically and analytically. The laser admits a singular Hopf bifurcation to a nearly vertical branch of periodic solutions. Using asymptotic methods, we determine a simplified problem that describes the transition from harmonic to pulsating oscillations as the bifurcation parameter is changed. This transition occurs in a layer bounded by the Hopf bifurcation point, and by a critical point near which the branch of solutions becomes vertical.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 14 , Issue 4 , August 2003 , pp. 407 - 420
Copyright
2003 Cambridge University Press