Bifurcation analysis of a semiconductor laser subject to phase conjugate feedback

• Main Author: Green, Kirk
• Published: University of Bristol 2002
• Subjects: 621; Optics & masers & lasers
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251035

In this thesis we present a detailed bifurcation analysis of a semiconductor laser subject to phase-conjugate feedback (PCF). Mathematically, lasers with feedback are modelled by delay differential equations (DDEs) with an infinite-dimensional phase space. This is why, in the past, systems described by DDEs were only studied by numerical simulation. We employ new numerical bifurcation tools for DOEs that go much beyond mere simulation. More precisely, we continue steady states and periodic orbits, irrespective of their stability with the package DDE-BIFTOOL, and present here the first algorithm for computing unstable manifolds of saddle-periodic orbits with one unstable Floquet multiplier in systems of DDEs. Together, these tools make it possible, for the first time, to numerically study global bifurcations in ODEs. Specifically, we first show how periodic solutions of the PCF laser are all connected to one another via a locked steady state solution. A one-parameter study of these steady states reveals heteroclinic bifurcations, which tum out to be responsible for bistability and excitability at the locking boundaries. We then perform a full two-parameter investigation of the locking range, where we continue bifurcations of steady states and heteroclinic bifurcations. This leads to the identification of a number of codirnensiontwo bifurcation points. Here, we also make a first attempt at providing a two-parameter study of bifurcations of periodic orbits in a system of DDEs. Finally, our new method for the computation of unstable manifolds of saddle periodic orbits is used to show how a torus breaks up with a sudden transition to chaos in a crisis bifurcation. In more general terms, we believe that the results presented in this thesis showcase the usefulness of continuation and manifold computations and will contribute to the theory of global bifurcations in DDEs.