Stationary, harmonic, and pulsed operations of an optically bistable laser with saturable absorber. I

Journal Article · Mon Oct 01 04:00:00 EDT 1984 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.30.1893· OSTI ID:6153046

Mandel, P; Erneux, T

We study the semiclassical equations for a laser with a saturable absorber in the mean-field limit, assuming homogeneously broadened two-level atoms, for a set of parameters where the system displays optical bistability and time-periodic solutions. In the first part the bifurcation diagram for stationary and periodic solutions is obtained by numerical integration. Two different classes of stable periodic solutions arise: small-amplitude solutions and passive Q switching. We observe hysteresis domains involving up to three solutions (stationary and/or periodic). We also discuss the validity of some standard approximations and show that even in the absence of detuning the phases play an important role. We also discuss the influence of the initial conditions whose symmetry properties induce important modifications of the bifurcation diagram. In the second part we introduce an alternative adiabatic elimination scheme which allows us to construct the small-amplitude periodic solutions over nearly their whole range of existence. We then study these solutions near the Hopf bifurcation from which they emerge and derive analytic conditions for their stability. When they are stable, we also give the conditions under which a secondary Hopf bifurcation will occur, leading to quasiperiodic solutions.

• Research Organization: Service de Chimie-Physique II, Universite Libre de Bruxelles, Campus de la Plaine, Code Postal No. 231, B-1050 Brussels, Belgium
• OSTI ID: 6153046
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 30:4; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
ABSORPTION
ANALYTICAL SOLUTION
HARMONICS
INSTABILITY
LASERS
MEAN-FIELD THEORY
OSCILLATIONS
PULSES
SATURATION
STEADY-STATE CONDITIONS