Subharmonic Hysteresis and Period Doubling Bifurcations for a Periodically Driven Laser

The authors consider the laser rate equations for a periodically modulated class B laser. The bifurcation diagram of the periodic solutions is analyzed both numerically and theoretically. The bifurcation parameter is the amplitude of the periodic modulations. Concentration is on the Period 1 and Period 2 branches of solutions that emerge either from a limit point or from a period doubling bifurcation point. The bifurcation diagrams of the driven laser are analyzed with and without dissipation. It is seen that the laser oscillations become pulsating as their amplitude increases, suggesting a new asymptotic analysis ofthe laser oscillations. A large parameter proportional to the amplitude of the oscillations is identified andperiodic solutions using singular perturbation techniques are constructed. Equations for a Poincaré map are derived and an analytical expression of the first period doubling bifurcation is obtained.