We prove a necessary and sufficient criterion for the exponential
stability of periodic solutions of delay differential equations with
large delay. We show that for sufficiently large delay the Floquet
spectrum near criticality is characterized by a set of curves, which we
call asymptotic continuous spectrum, that is independent on the
delay.
We describe the basic ideas behind the concept of distributed
feedback (DFB) lasers with short optical feedback for the
generation of high-frequency self-pulsations and show the theoretical
background describing realized devices. It is predicted by
theory that the self-pulsation frequency increases with increasing
feedback strength. To provide evidence for this, we propose a novel
device design which employs an amplifier section in the integrated
feedback cavity of a DFB laser.We present results from numerical
simulations and experiments. It has been shown experimentally
that a continuous tuning of the self-pulsation frequency from 12
to 45 GHz can be adjusted via the control of the feedback strength.
The numerical simulations, which are in good accordance with experimental
investigations, give an explanation for a self-stabilizing
effect of the self-pulsations due to the additional carrier dynamic
in the integrated feedback cavity.
Abstract. We consider a mathematical model (the so-called traveling-wave system) which describes longitudinal
dynamical effects in semiconductor lasers. This model consists of a linear hyperbolic system
of PDEs, which is nonlinearly coupled with a slow subsystem of ODEs. We prove that a corresponding
initial-boundary value problem is well posed and that it generates a smooth infinite-dimensional dynamical
system. Exploiting the particular slow–fast structure, we derive conditions under which there exists a lowdimensional
attracting invariant manifold. The flow on this invariant manifold is described by a system
of ODEs. Mode approximations of that system are studied by means of bifurcation theory and numerical
tools.