Instabilities, Self-Pulsing and Chaos in Optical Bistability and Laser with Injected Signal.

Optical systems that are sufficiently removed from thermal equilibrium are known to undergo instabilities, self-pulsing, and even chaotic oscillations. Optically bistable systems and lasers driven by an external coherent source are prototype optical devices where strong coupling between the elementary components can be insured. The nonlinear nature of the interaction between light and matter coupled to the presence of feedback from the optical resonator forms the basis for the emergence of unstable behavior. We have explored in detail the mechanism behind the output pulsations and the phenomenology of several bifurcation sequences, using time dependent solutions of the Maxwell -Bloch equations, their associated power spectra and Lyapunov exponents. Single-mode optically bistable systems display chaotic behavior for very large values of the cooperation parameter with a period doubling route to chaos. Experimentally accessible values of the cooperation parameter, instead, are predicted to produce simple periodic oscillations. A laser driven by an external signal displays the expected heterodyne beat signature for low incident field amplitudes. For larger incident signals, a complicated sequence of higher-order bifurcations can be observed.