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- long delay (2)
- pseudo-continuous spectrum (2)
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- Duffing oscillator (1)
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- Lang-Kobayashi model (1)
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- laser with delayed optical feedback (1)
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- passive feedback (1)
- semiconductor laser (1)
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Application Area
- D (9)
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 the dynamics of a ring of unidirectionally coupled autonomous
Duffing oscillators. Starting from a situation where the individual
oscillator without coupling has only trivial equilibrium dynamics,
the coupling induces complicated transitions to periodic, quasiperiodic,
chaotic, and hyperchaotic behavior. We study these transitions in
detail for small and large numbers of oscillators. Particular attention
is paid to the role of unstable periodic solutions for the appearance
of chaotic rotating waves, spatiotemporal structures and the Eckhaus
effect for a large number of oscillators. Our analytical and numerical
results are confirmed by a simple experiment based on the electronic
implementation of coupled Duffing oscillators.
In this paper we study the destabilization mechanism in a ring of unidirectionally coupled oscillators. We derive an amplitude equation of Ginzburg-Landau type that describes the destabilization of the stationary state for systems with a large number of oscillators. Based on this amplitude equation, we are able to provide an explanation for the fast transition to chaos (or hyperchaos)
that can be observed in such systems. We show that the parameter interval, where the transition from a stable periodic state to chaos occurs, scales like the inverse
square of the number of oscillators in the ring. In particular, for a sufficiently large
number of oscillators a practically immediate transition to chaos can be observed.
The results are illustrated by a numerical study of a system of unidirectionally
coupled Duffing oscillators.
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.
Chimera states are particular trajectories
in systems of phase oscillators with non-local coupling
that display a spatio-temporal pattern of coherent and incoherent motion.
We present here a detailed analysis
of the spectral properties for such trajectories.
First, we study numerically their Lyapunov spectrum
and its behavior for an increasing number of oscillators.
The spectra demonstrate the hyperchaotic nature of the chimera states
and show a correspondence of the Lyapunov dimension
with the number of incoherent oscillators.
Then, we pass to the thermodynamic limit equation
and present an analytic approach
to the spectrum of a corresponding linearized evolution operator.
We show that in this setting, the chimera state is neutrally stable
and that the continuous spectrum coincides with the limit
of the hyperchaotic Lyapunov spectrum obtained for the finite size systems.
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.
We show that the spectrum of linear delay differential equations with
large delay splits into two different parts. One part, called the
strong spectrum, converges to isolated points when the delay parameter
tends to infinity. The other part, called the pseudocontinuous spectrum,
accumulates near criticality and converges after rescaling to a set
of spectral curves, called the asymptotic continuous spectrum. We
show that the spectral curves and strong spectral points provide a
complete description of the spectrum for sufficiently large delay
and can be comparatively easily calculated by approximating expressions.
The Lang-Kobayashi model is a system of delay differential equations (DDEs) describing the dynamics of a semiconductor laser under delayed optical feedback. In this paper, we study the stability of so called external cavity modes (ECMs), which are harmonic oscillations corresponding to stationary lasing states. We focus on experimentally relevant situations, when the delay is large compared to the internal time scales of the laser. In this case, both the number of ECMs and the number of critical eigenvalues grows to infinity. Applying a newly developed asymptotic description for the spectrum of linearized DDEs with long delay, we are able to overcome this difficulty and to give a complete description of the stability properties of all ECMs. In particular, we distinguish between different types of weak and strong instabilities and calculate bifurcation diagrams that indicate the regions with different stability properties and the transitions between them.