P. Colet

Dependence of timing jitter on bias level for single-mode semiconductor lasers under high speed operations

The dependence on the bias level of some quantities characterizing optical pulse statistics, such as the turn-on time, pulsewidth, maximum output photon number, and average output power, of single-mode semiconductor lasers is numerically analyzed at frequencies in the gigahertz range. Periodic modulation and pseudorandom word modulation are considered. In the former regime, timing jitter is shown to be rather independent of the bias current. In the latter regime, timing jitter becomes larger when biasing above threshold than when biasing below threshold. This larger jitter is found to be associated with a bimodal probability distribution of the turn-on time, which yields undesirable pattern effects. A privileged bias, slightly below threshold, suppresses these pattern effects making the laser response almost independent of previous input bits. For such bias value the probability distribution functions of the turn-on time in the case of the periodic and pseudorandom word modulation coincide. >

Parametric dependence of stochastic frequency variations in the gain switching of a single-mode laser diode

The authors have studied the fluctuations in the range of frequency excursions of the optical field from a single-mode laser diode that has been switched-on by a stepwise increase, in the current from a bias level which is below threshold. Both the maximum and the minimum frequencies reached in the transient for each gain-switching event are linear functions of the turn-on time. The statistics of the range of frequency variation for different turn-on events are then easily obtained from the statistics of the turn-on time. The slopes of these functions depend linearly on the injection current of the single-mode laser diode. In addition, they depend not only on the saturation intensity of the single-mode laser diode, but also on the particular form of gain saturation. As a consequence, experimental measurements could be used, in principle, to determine which model of gain saturation best describes the operation of a given single-mode laser diode. >

Stable droplets and dark-ring cavity solitons in nonlinear optical devices

Two kinds of cavity solitons, stable circular domain walls (droplets) and dark-ring cavity solitons, are presented in models of vectorial Kerr resonators and degenerate optical parametric oscillators. These structures are universal in systems with two equivalent homogeneous states and are found for parameter values close to those of a modulational instability of a flat front. Stable droplets owe their existence to curvature effects and, therefore, they are not present in one-dimensional systems. We show that stable droplets nucleate out of dark-ring cavity solitons and that in some systems there are regimes in which they coexist.

Logical operations with localized structures

We show how to use excitable regimes mediated by localized structures (LSs) to perform AND, OR and NOT logical operations providing full logical functionality. Our scheme is general and can be implemented in any physical system displaying LSs. In particular, LSs in nonlinear photonic devices can be used for all-optical computing applications where several reconfigurable logic gates can be implemented in the transverse plane of a single device, allowing for parallel computing.

Passage Time Description of Dynamical Processes

The description of dynamical processes in terms of passage time distributions is generally advocated. Two specific situations are considered, transient relaxation at a pitchfork bifurcation and transport in disordered chains. The scaling description at a supercritical bifurcation is reviewed. For the subcritical case an approximation for the stochastic paths allowing the calculation of the passage time distribution is presented. In the case of disordered chains, a characterization of strong disorder is given in terms of the long tail of the passage time distribution to escape from a finite interval.

Localized structures in nonlinear optical cavities

Dissipative localized structures, also known as cavity solitons, arise in the transverse plane of several nonlinear optical devices. We present two general mechanisms for their formation and some scenarios for their instability. In situations of coexistence of a homogeneous and a pattern state, we characterize excitable behavior mediated by localized structures. In this scenario, excitability emerges directly from the spatial dependence since it is absent in the purely temporal dynamics. In situations of coexistence of two homogeneous states, we discuss localized structures either due to the interaction of front tails (dark ring cavity solitons) or due to a balance between curvature effects and modulational instabilities of front solutions (stable droplets).

Quantum correlations in noise-sustained optical patterns

Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity and an optical parametric oscillator. In these systems a regime of convective instability can appear, in which a transverse pattern arises as a macroscopic manifestation of amplified and spatially structured quantum noise, with magnification factors of several order of magnitudes. We study quantum correlations in the convective regime of a degenerate type-I optical parametric oscillator (OPO) using a time dependent parametric approximation, in which the intracavity pump field is taken as a classical stochastic field.

NON-ADIABATIC ELIMINATION OF VARIABLES IN STOCHASTIC PROCESSES BY MEANS OF PATH INTEGRAL AND INFLUENCE FUNCTIONAL METHODS

We present a novel scheme for the non-adiabatic elimination of variables in stochastic processes, based on a path integral representation of the probability density and the use of an influence functional. We analyze in particular the case of multivariate Fokker-Planck equations, or equivalently a set of coupled Langevin equations driven by white noises, and discuss some examples where exact or approximate results are obtained.

Noise properties of semiconductor ring lasers

This article investigates the interaction of fluctuations and field dynamics in semiconductor ring lasers. The noise spectrum resolved for the intensities of two counterpropagating waves are presented in detail.

Noise properties of Semiconductor Ring Lasers

This article investigates the interaction of fluctuations and field dynamics in semiconductor ring lasers. The noise spectrum resolved for the intensities of two counterpropagating waves are presented in detail.