Frequency locking of modulated waves

We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals

Mode oscillation and harmonic distortions associated with sinusoidal modulation of semiconductor lasers

This paper investigates mode dynamics, operation characteristics and signal distortions associated with sinusoidal modulation of semiconductor lasers. The study is based on intensive integrations of the multimode rate equation model of semiconductor lasers over wide ranges of the modulation frequency and depth. The rate equations take into account both spectral symmetric and asymmetric suppressions of modal gain. The higher harmonic distortions as well as the half harmonic distortion associated with the period doubling effect are investigated. The study is applied to both cases of single-mode and multimode oscillations of the non-modulated laser. The obtained results showed that the modulated signal has six distinct waveforms depending on the modulation conditions; three types have continuous periodic waveforms and the others have periodic pulsing waveforms. The modulated laser is found to oscillate in a single mode under weak modulation where the modulated signal is continuous, whereas the pulsing signals are associated with multimode oscillation. The higher harmonic distortions of single-mode laser are lower than those of two-mode lasers, and become serious at modulation frequencies around the relaxation oscillation frequency. These distortions are highest when the laser output is pulsating and the pulses are superposed by relaxation oscillations. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012

First demonstration of multi-vendor and multi-domain EON with S-BVT and control interoperability over Pan-European testbed

The operation of multi-domain and multi-vendor EONs can be achieved by interoperable Sliceable Bandwidth Variable Transponders, a GMPLS / BGP-LS-based control plane and a planning tool. This paper reports the first full demonstration and validation this end-to-end architecture

Symmetry breaking in dynamical systems

Symmetry breaking bifurcations and dynamical systems have obtained a lot of attention over the last years. This has several reasons: real world applications give rise to systems with symmetry, steady state solutions and periodic orbits may have interesting patterns, symmetry changes the notion of structural stability and introduces degeneracies into the systems as well as geometric simplifications. Therefore symmetric systems are attractive to those who study specific applications as well as to those who are interested in a the abstract theory of dynamical systems. Dynamical systems fall into two classes, those with continuous time and those with discrete time. In this paper we study only the continuous case, although the discrete case is as interesting as the continuous one. Many global results were obtained for the discrete case. Our emphasis are heteroclinic cycles and some mechanisms to create them. We do not pursue the question of stability. Of course many studies have been made to give conditions which imply the existence and stability of such cycles. In contrast to systems without symmetry heteroclinic cycles can be structurally stable in the symmetric case. Sometimes the various solutions on the cycle get mapped onto each other by group elements. Then this cycle will reduce to a homoclinic orbit if we project the equation onto the orbit space. Therefore techniques to study homoclinic bifurcations become available. In recent years some efforts have been made to understand the behaviour of dynamical systems near points where the symmetry of the system was perturbed by outside influences. This can lead to very complicated dynamical behaviour, as was pointed out by several authors. We will discuss some of the technical difficulties which arise in these problems. Then we will review some recent results on a geometric approach to this problem near steady state bifurcation points

Investigations on the stability of an all-optically extracted clock at 18 GHz using a selfpulsating DFB-laser

The performance of the extracted clock is characterized. The initial transient behaviour of the clock is measured when a long sequence of zero bits is present in the injected signal. The dephasing of the extracted clock due to inherent noise and the lock-up time are studied. The main goal is an estimate for the maximum tolerable zero bit sequence