Subharmonic bifurcation and bistability of periodic solutions in a periodically modulated laser
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 lambda 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 (lambda = 1) and the first subharmonic resonance (lambda = (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 lambda = (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.
- Research Organization:
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60201
- OSTI ID:
- 5914555
- Journal Information:
- Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 35:3; ISSN PLRAA
- Country of Publication:
- United States
- Language:
- English
Similar Records
Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity
Double-Period Breathers in a Driven-Damped Lattice