Adrian Jacobo

Effects of a localized beam on the dynamics of excitable cavity solitons

(Dated: August 19, 2008)We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerrmedium when a localized beam is applied on top of the homogeneous pumping. In particular, wereport on the excitability regime that cavity solitons exhibits which is emergent property since thesystem is not locally excitable. The resulting scenario differs in an important way from the caseof a purely homogeneous pump and now two different excitable regimes, both Class I, are shown.The whole scenario is presented and discussed, showing that it is organized by three codimension-2points. Moreover, the localized beam can be used to control important features, such as the excitablethreshold, improving the possibilities for the experimental observation of this phenomenon.

Model of the Self-Q-Switching Instability of Passively Phased Fiber Laser Arrays

We present a simple model for self-pulsation instability in passively phased high power optical fiber amplifier arrays with external feedback. Its key features are, first, the feedback levels sensitivity, and thus that of the cavity Q-value, to small phase changes of the array fields, and, second, the effect of refractive index nonlinearity in the amplifiers. The models prediction of an instability threshold for arrays of at least two amplifiers is confirmed by a linearized stability analysis of a system in ring-cavity geometry, and the magnitudes of predicted power levels are well within the domain of recent experiments.

Simple model to explain instabilities in passively-phased high-power fiber laser arrays

We propose a simple physical mechanism to explain observed instabilities in the dynamics of passively phased fiber amplifier arrays that arises from two properties: First that a weak phase disturbance of the output field of the array is converted into a strong intensity disturbance through the mode-selective feedback mechanism. Second, that this intensity fluctuation regenerates a phase fluctuation due to the nonlinear properties of the amplifying media. At sufficiently high operating power levels this cyclic disturbance continues to grow upon each cavity round trip, creating instability. This simple picture is supported by the results of a linear stability analysis of the set of propagation and population rate equations, which are in good agreement with observed critical power levels. A third level of quantitative confirmation was obtained by comparison to the results of numerical integration of the original set of nonlinear equations. This predicted instability is entirely a property of passively phased arrays of more than one element.

Space-time-dynamic model of passively-phased ring-geometry fiber laser array

We performed a linearized stability analysis and preliminary simulations of passive phasing in a CW operating ring-geometry fiber laser array coupled in an external cavity with a single-mode feedback fiber that functions as spatial filter. A two-element array with path length error is predicted to have a dynamically stable stationary operating state at the compputer operating wavelength.

Logical Operations Using Excitable Cavity Solitons

We show theoretically that dissipative solitons arising in the transverse plane of nonlinear optical cavities show oscillatory and excitable regimes that can be used to perform all-optical logical operations. This allows for the construction of reconfigurable optical gates that can operate in parallel.

Dynamic Stability Analysis Of Passively-phased Ring-geometry Fiber Laser Array

Based on stability analysis of passive phasing in an externally coupled, ring-geometry fiber laser array, we predict a dynamicaly stable operating state of a 2-element array at wavelengths of relative maxima in output power.

Excitability Mediated by Localized Structures in Kerr Cavities

We characterize a scenario where localized structures in nonlinear optical cavities display an oscillatory behavior which becomes unstable leading to an excitable regime. Ex- citability emerges from spatial dependence since the system locally is not excitable. We show the existence of difierent mechanisms leading to excitability depending on the proflle of the pump fleld. DOI: 10.2529/PIERS060907134206 Localized structures (LS) in dissipative optical cavities arise as a consequence of the interplay between difiraction, nonlinearity, driving, and dissipation (1). These structures, also known as cavity solitons, are unique once the parameters of the system have been flxed. This fact makes this structures potentially useful in optical storage and processing of information (2,3). LS may develop a number of instabilities, for instance their amplitude can oscillate in time while remaining static in space. Here we report on a novel regime of excitability associated to the existence of localized structures in a nonlinear optical system (4,5). Excitability has been found in a variety of systems (6), including optical systems (7), and is characterized by a nonlinear response under applied external perturbation. Perturbations exceeding a certain threshold are able to elicit in the system a full and well deflned response. Furthermore after one perturbation the system cannot be excited again within a refractory period of time. Excitability is behind excitation waves in heart tissue and the existence of action potentials in neurons, and, so, may confer new computational capabilities to optical systems beyond information storage. In this paper we show the existence of difierent mechanisms leading to excitability depending on the proflle of the pump fleld. For a homogeneous pump the mechanism leading to excitable behavior is a saddle-loop bifurcation through which an stable oscillating LS collides with an unstable LS (4). For a system pumped by a localized Gaussian beam on top of homogeneous background the scenario is richer and one flnds two difierent mechanisms leading to excitability. One is based on a saddle- loop bifurcation as above while the other takes place through a saddle-node in the invariant circle (SNIC) bifurcation. This second mechanism has excitability threshold which can be much lower. We consider a ring cavity fllled with a nonlinear self-focusing Kerr medium pumped by an external fleld. In the mean fleld approximation, the dynamics of the electric fleld inside the cavity can be described by a single partial difierential equation for the scaled slowly varying amplitude E(~) (8) @tE = i(1 + iµ)E + ir 2 E + E0 + ijEj 2 E;

Optical Image Processing in Second-Harmonic Generation

Although the processing of an image by all-optical means is quite less com-mon than the well-developed techniques for digital image processing [1], ithas nevertheless been around for quite a some time. At a classical level earlyworks demonstrated frequency transfer of an optical image from the infraredto the visible domain [2, 3], and later from the visible to the UV domain[4, 5], as well as parametric amplification of an UV image [6, 7], and contrastinversion [8]. In these schemes, an optical image at a frequency ω is directlyinjected into a nonlinear crystal illuminated with a strong monochromaticpump wave at frequency ω