Subharmonic bifurcation and bistability of periodic solutions in a periodically modulated laser

T. Erneux, S. M. Baer, Paul Mandel

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52 Scopus citations


We consider the effect of periodically modulated cavity losses on the bifurcation diagram of the laser rate equations. The double limit of very slow atomic inversion relaxation and small modulation amplitude is investigated. Our control parameter is the ratio of the damped oscillation frequency of the rate equations (at zero modulation amplitude) to the forcing frequency. We concentrate on the case of pure resonance (=1) and the first subharmonic resonance (=(1/2)) because they are most representative of the effects of the periodic control. We first reformulate the laser problem as a weakly perturbed conservative system and construct harmonic and subharmonic large-amplitude periodic solutions by a regular perturbation analysis. The conditions for the existence of these solutions are analyzed and evaluated numerically. We show that harmonic and subharmonic solutions may coexist. We then determine a small-amplitude periodic solution oscillating at the forcing frequency. We show that perturbations of this basic state lead to slowly decaying quasiperiodic oscillations except in the vicinity of the critical points =(1/2) and 1. In the first case, subharmonic bifurcation may occur and the period of the oscillations suddenly doubles. In the second case, bistability of periodic solutions is observed.

Original languageEnglish (US)
Pages (from-to)1165-1171
Number of pages7
JournalPhysical Review A
Issue number3
StatePublished - 1987
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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