Pere Colet

Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop

We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electrooptical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as a function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy.

Stochastic Numerical Methods: An Introduction for Students and Scientists

1. Review of Probability Concepts 2. Monte Carlo Integration 3. Generation of Non-uniform Random Numbers: Non-correlated Values 4. Dynamical Methods 5. Applications to Statistical Mechanics 6. Introduction to Stochastic Processes 7. Numerical Simulation of Stochastic Differential equations 8.Introduction to Master Equations 9. Numerical Simulations of Master Equations 10. Hybrid Monte Carlo 11. Stochastic Partial Differential Equations A. Generation of Uniform ^U (0 1) Random Numbers B. Generation of n-dimensional Correlated Gaussian Variables C. Calculation of the Correlation Function of a Series D. Collective Algorithms for Spin Systems E. Histogram Extrapolation F. Multicanonical Simulations G. Discrete Fourier Transform

Information Encoding and Decoding Using Unidirectionally Coupled Chaotic Semiconductor Lasers Subject to Filtered Optical Feedback

We present a detailed numerical study of the dynamics of two unidirectionally coupled semiconductor lasers subject to filtered optical feedback. We show that this chaos-based communication scheme allows for an improvement in the decoding of encrypted messages in comparison with the conventional feedback scheme. We found that the performance of the system is optimal when the closed-loop configuration and similar filters are used in the emitter and receiver systems.

Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delay feedback loop

We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electro-optical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy.

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.

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.

Sub-diffraction-limited localized structures: influence of linear non-local interactions

Cavity solitons are controllable two-dimensional transverse Localized Structures (LS) in dissipative optical cavities. Such LS have been suggested for use in optical data storage and information processing. Typically, diffraction constrains the size of these light spots to be of the order of the square root of the diffraction coefficient of the system. Due to recent advances in the development of metamaterials, the diffraction strength in a cavity could be controlled by adding a left-handed material layer in a Fabry-Perot resonator together with a traditional nonlinear material. This system thus potentially allows for LS beyond the size limit imposed by natural diffraction. However, when the diffraction strength becomes smaller, the non-local response of the left-handed metamaterial starts to dominate the nonlinear spatiotemporal dynamics. Considering a typical linear non-local response, we develop a mean-field model describing the spatiotemporal evolution of LS. First, the influence of this non-local response on the minimal attainable width of the LS is studied [Gelens et al., Phys. Rev. A 75, 063812 (2007)]. Secondly, we elaborate on the different possible mechanisms that can destabilize the LS, leading to stable oscillations, expanding patterns, or making the LS disappear. Furthermore, we also show multiple routes towards excitability present in the system. We demonstrate that these different regions admitting stationary, oscillating or excitable LS unfold from two Takens-Bogdanov codimension-2 points [Gelens et al., Phys. Rev. A 77 (2008)].

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

Dynamical entrainment of unidirectionally coupled single mode diode lasers

We numerically study the entrainment of two unidirectional coupled single-mode semiconductor lasers in a master-slave configuration. The emitter laser is an external-cavity laser subject to optical feedback that operates in a chaotic regime while the receiver has no optical feedback and consequently operates under CW when it is uncoupled (open loop scheme). We compare the performance of this scheme with the close loop one in which both emitter and receiver are subjected to optical feedback and operate in a chaotic state. We compute the degree of entrainment or synchronization of the two lasers as a function of the detuning, the emitter-receiver coupling constant and the feedback rate of the receiver. We find that the close loop scheme has, in general, a larger region of synchronization when compared with the open loop. We also study the possibility of message encoding and decoding in the both open and close loops and their robustness against parameters mismatch. Finally we compute the time it takes the system to recover the synchronization or entrainment state when the coupling between the two subsystems is lost. We find that this time is much larger in the close loop than in the open one.