Silnikov homoclinic orbits in the equations for a semiconductor laser subject to optical injection and detuning.

摘要

In this thesis I investigate the dynamics of a coupled laser system, where light from one laser is injected into the cavity of another. I am interested in analyzing the response of the injected laser.; Semiconductor lasers find important applications in the area of telecommunications, where the beam emanating from an injected laser is used to encode data to be sent through an optical fiber. The data encoding process involves direct intensity modulations at very high speed, which causes noise to appear in the modulated laser's spectrum.; Injecting a low-intensity beam into the lasing cavity has proven to be a very effective way of suppressing the unwanted noise. However, this technique affects the behavior of the injected laser in ways that are not completely understood. Injection introduces another dimension to the dynamics of the laser diode, and semiconductor lasers subjected to injection have been reported to exhibit complex phenomena routinely associated with three-dimensional systems: chaotic dynamics, cascades of period-doubling bifurcation, etc.; This thesis investigates the existence of Šilnikov homoclinic orbits in the rate equations governing the functioning of an injected semiconductor laser. We show that there exists a surface in a three-dimensional parameter space near which the rate equations admit Šilnikov homoclinic orbits.