Semiconductor laser with filtered optical feedback: from optical injection to conventional feedback.

Abstract
We study a model for a semiconductor laser subject to filtered optical feedback,
that is a system of delay differential equations (DDEs). In this model the filter is characterised
by a mean frequency Ωm and a filter width λ. In the limit of a narrow filter
(λ → 0) the laser equations reduce to the equations for a laser with optical injection,
whereas they become the Lang-Kobayashi equations in the limit of an unbounded
filterwidth (λ→∞).
We perform a bifurcation analysis of steady state solutions, with the parameter
λ as main bifurcation parameter. In this way, we get insight in the relation between
the filter width and the number of possible steady states. In particular we obtain
the result, that there exist parameter regions in which the number of possible steady
states decreases when λ is increased.
From a mathematical point of view, our approach to combine information about
limiting systems with precise bifurcation results may be of interest for a wider class
of systems of DDEs.