Nonlinear Dynamics of Semiconductor Laser Systems with Feedback: Applications to Optical Chaos Cryptography, Radar Frequency Generation, and Transverse Mode Control

Abstract

The simple fact to introduce and account for a delay time in a dynamical system increases its dimensionality to infinity, and thereby opens the way to a wide variety of very complex behaviors. Despite the huge advances of physics and mathematics in the twentieth century, in is only at the early sixties that delay differential equations gained sufficient attention from the scientific community. In the first years, though, the interest was purely mathematical and these equations where studied under the terminology of Functional Differential Equations, mainly by Krasovskii and Hale. Then, these new ideas rapidly started to spread in various areas of applied science, particularly in control theory. In physics, in particular, delay differential equations have been found to be the idoneous tool to investigate the behavorial properties of dynamical systems where delays had to be taken into account. Far beyond the scope of physics, delay differential systems have been successfully used to investigate a very large spectrum of problems, ranging from predator/prey ecosystems to neurology.

It has resulted from thirty years of theoretical and experimental investigations that the delay may globally have two opposite effects: either a destabilization effect, through the excitation of many of the latent degrees of freedom; or either a stabilization effect by somehow acting as a selective energy sink. In both cases, there is a plethora of applications where one of these effects may be highly desired. Within the frame of this thesis, we will lay emphasis upon those of these applications which are related to semiconductor laser systems.