### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 1165-1171 |

Number of pages | 7 |

Journal | Physical Review A |

Volume | 35 |

Issue number | 3 |

DOIs | |

State | Published - 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*35*(3), 1165-1171. https://doi.org/10.1103/PhysRevA.35.1165

**Subharmonic bifurcation and bistability of periodic solutions in a periodically modulated laser.** / Erneux, T.; Baer, Steven; Mandel, Paul.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 35, no. 3, pp. 1165-1171. https://doi.org/10.1103/PhysRevA.35.1165

}

TY - JOUR

T1 - Subharmonic bifurcation and bistability of periodic solutions in a periodically modulated laser

AU - Erneux, T.

AU - Baer, Steven

AU - Mandel, Paul

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.35.1165

DO - 10.1103/PhysRevA.35.1165

M3 - Article

AN - SCOPUS:0000071424

VL - 35

SP - 1165

EP - 1171

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

ER -