Dynamics of Delay Equations, Theory and Applications - Abstract

Vladimirov, Andrei

Delay differential equations in modeling multimode laser dynamics

We discuss an approach to the modeling of nonlinear dynamics in multimode semiconductor lasers based on a set of delay differential equations (DDE). We consider DDE models of different multimode laser devices and present the results of numerical bifurcation analysis of different dynamical regimes in these lasers. Further, we discuss asymptotic approaches to the stability analysis of CW and periodic operation regimes. In particular, basing on a DDE multimode laser model we provide an analytical interpretation of the characteristic features of the dynamical regimes observed experimentally in frequency swept lasers operating in the Fourier domain mode-locked regime. Finally, we present a new model of an FDML laser that takes into account chromatic dispersion of the fiber delay line. This is a system of DDEs, which in addition to a fixed delay contains a distributed delay term and can be reduced to an infinite chain of delay differential equations with a single fixed delay.