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- Lang-Kobayashi model (1)
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We use the traveling wave model for simulating and analyzing
nonlinear dynamics of complex semiconductor ring laser devices.
This modeling allows to consider temporal-spatial distributions
of the coun\-ter-pro\-pa\-ga\-ting slowly varying optical fields
and the carriers, what can be important when studying
non-homogeneous ring cavities, propagation of short pulses or fast switching.
By performing numerical integration of the model
equations we observe several dynamic regimes as well as transitions
between them. The computation of ring cavity modes explains some
peculiarities of these regimes.
We investigate a semiconductor laser with delayed optical feedback due
to an external cavity formed by a regular mirror. We discuss
similarities and differences of the well-known Lang-Kobayashi delay
differential equation model and the traveling wave partial
differential equation model. For comparison we locate the continuous
wave states in both models and analyze their stability.
We explore the concept of passive-feedback lasers for direct signal
modulation at 40 Gbit/s. Based on numerical simulation and bifurcation
analysis, we explain the main mechanisms in these devices which are
crucial for modulation at high speed. The predicted effects are
demonstrated experimentally by means of correspondingly designed
devices. In particular a significant improvement of the modulation
bandwidth at low injection currents can be demonstrated.
We study both theoretically and experimentally typical operation
regimes of 40 GHz monolithic mode-locked lasers. The underlying Traveling Wave Equation model reveals quantitative agreement for characteristics of the fundamental mode-locking as pulse width and repetition frequency tuning, as well as qualitative agreement with the experiments for other dynamic regimes. Especially the appearance of stable harmonic mode-locking at 80 GHz
has been predicted theoretically and confirmed by measurements.
Furthermore, we derive and apply a simplified Delay-Differential-Equation model
which guides us to a qualitative analysis of bifurcations responsible for the appearance
and the breakup of different mode-locking regimes. Higher harmonics of mode-locking are predicted by this model as well.
We prove the existence, uniqueness, regularity and smooth dependence
of the weak solution on the initial data for a certain class of semilinear first order
dissipative hyperbolic systems with spacially discontinuous coefficients. Such
kind of hyperbolic problems have succesfully been used to describe the dynamics
of distributed feedback multisection semiconductor lasers in recent years. We
show that in a suitable function space of continuous functions the weak solutions
generate a smooth semiflow.
Im Zentrum der Arbeiten soll die Chaos- und Kohärenzkontrolle von Halbleiterlasern mit gegenseitiger optischer Kopplung stehen. Diese Fragestellung ist von erheblicher praktischer Relevanz, da Rauschen und chaotisches Verhalten generelle Probleme in der optischen Hochgeschwindigkeitskommunikation sind. Die Kontrolle von optischen Systemen mit komplexer Selbstorganisation stellt aber auch aus grundsätzlicher Sicht Neuland dar. Hierfür geeignete Konzepte sind bisher weder überzeugend theoretisch beschrieben noch experimentell umgesetzt.
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.
We simulate and analyse a 1D-PDE model describing the dynamics of multisection semiconductor lasers. We demonstrate how a semi-analytical computation of the spectrum and the corresponding eigenfunction expansion of the computed solutions provides a useful information allowing to achieve a better understanding of the laser dynamics. Basic algorithms implemented into a corresponding software tool are described.
An in-depth theoretical as well as experimental analysis of the nonlinear dynamics in semiconductor lasers
with active optical feedback is presented. Use of a monolithically integrated multisection device of submillimeter
total length provides access to the short-cavity regime. By introducing an amplifier section as a special
feature, phase and strength of the feedback can be separately tuned. In this way, the number of modes involved
in the laser action can be adjusted. We predict and observe specific dynamical scenarios. Bifurcations mediate
various transitions in the device output, from single-mode steadystate to self-pulsation and between different
kinds of self-pulsations, reaching eventually chaotic behavior in the multimode limit.