Breathing,spiking and chaos in a laser with injected signal

We consider the behavior of a laser driven by an injected cw field detuned from the operating laser frequency. Our analysis covers the entire range of incident power levels from zero to the injection locking threshold. In this domain, the output intensity exhibits regular and chaotic oscillations, a period doubling cascade in reverse order, envelope breathing and spiking.     

Random bit generation using an optically injected semiconductor laser in chaos with oversampling

Random bit generation is experimentally demonstrated using a semiconductor laser driven into chaos by optical injection. The laser is not subject to any feedback so that the chaotic waveform possesses very little autocorrelation. Random bit generation is achieved at a sampling rate of 10 GHz even when only a fractional bandwidth of 1.5 GHz within a much broader chaotic bandwidth is digitized. By retaining only 3 least significant bits per sample, an output bit rate of 30 Gbps is attained. The approach requires no complicated postprocessing and has no stringent requirement on the electronics bandwidth.     

Deterministic chaos in entangled eigenstates

We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.     

Irregular phase slipping in a model for a laser with injected signal

In a model for a single mode laser with injected signal we find irregular pulsing of the output signal. During the turbulent time intervals the relative phase between the internal and the external field slips by an integer multiple of 2pi, where the multiplicity varies irregularly from pulse to pulse. Between the pulses, in the laminar time intervals, the relative phase is locked. We compare this behavior with the results of various other laser models. By the investigation of this interesting mechanism for the creation of phase chaos in a driven oscillator, we learn which properties are responsible for the irregular interruption of the phase locking. (c) 1997 American Institute of Physics.     

Global bifurcations in a laser with injected signal: Beyond Adler's approximation

We discuss the dynamics in the laser with an injected signal from a perturbative point of view showing how different aspects of the dynamics get their definitive character at different orders in the perturbation scheme. At the lowest order Adler's equation [Proc. IRE 34, 351 (1946)] is recovered. More features emerge at first order including some bifurcations sets and the global reinjection conjectured in Physica D 109, 293 (1997). The type of codimension-2 bifurcations present can only be resolved at second order. We show that of the two averaging approximations proposed [Opt. Commun. 111, 173 (1994); Quantum Semiclassic. Opt. 9, 797 (1997); Quantum Semiclassic. Opt. 8, 805 (1996)] differing in the second order terms, only one is accurate to the order required, hence, solving the apparent contradiction among these results. We also show in numerical studies how a homoclinic orbit of the Sil'nikov type, bifurcates into a homoclinic tangency of a periodic orbit of vanishing amplitude. The local vector field at the transition point contains a Hopf-saddle-node singularity, which becomes degenerate and changes type. The overall global bifurcation is of codimension-3. The parameter governing this transition is theta, the cavity detuning (with respect to the atomic frequency) of the laser. (c) 2001 American Institute of Physics.     

Deterministic chaos and natural phenomena

The natural time seriesf ₀ F ₂, F10.7, and AE are analyzed and low-dimensional attractors are found, characterized by the correlation dimension and the lower bound of the Kolmogorov entropy. Sources of noise in natural time series are discussed and the concept of extended systems is introduced and used to explain why the number of data required to calculate the correlation dimension of natural time series is higher than that reported by other authors.     

Deterministic chaos and noise in optical bistability

The time-dependent solutions of the mean-field Maxwell-Bloch equations for optical bistability are studied numerically for the deterministic equations and the stochastic equations with additional noise sources. From the solutions of the deterministic equations, a discrete map is constructed showing that the periodic and chaotic solutions form a Feigenbaum scenarium. Inclusion of noise sources leads to a finite lifetime of the states in the upper bistable branch and to destabilization of higher periodic solutions.     

Optically injected laser system: characterization of chaos, bifurcation, and control

A single mode semiconductor laser subjected to optical injection, described by a set of three coupled nonlinear ordinary differential equations, exhibiting chaos is considered. By means of a recurrence analysis, quantification of the strange attractor is made. Analytical studies of the system using asymptotic averaging technique, derive certain conditions describing the prediction of 1-->2 bifurcation, which have subsequently been verified on numerical simulation. Furthermore, the locus of points on the parameter phase space representing Hopf bifurcation has been derived. The problem of control of chaos by a new procedure based on adaptive stabilization is also addressed. The results of such control are shown explicitly. Though this analysis deals with a very specific set of equations, the overall features that come out of the study remains valid for almost all laser systems.     

Photonic ultrawideband signal generator using an optically injected chaotic semiconductor laser

We propose and demonstrate a method to generate ultrawideband (UWB) signals in the optical domain based on the chaotic dynamics of an optically injected semiconductor laser with optical feedback. The chaotic-UWB pulses with a fractional bandwidth of 116% and central frequency of 6.88?GHz are experimentally generated by controlling the injection strength and frequency detuning of the chaotic laser. The spectrum of the UWB signals is in full compliance with the Federal Communications Commission spectral mask, and the experimental results are qualitatively consistent with the simulated results.     

Tailoring enhanced chaos in optically injected semiconductor lasers

We demonstrate theoretically and experimentally that the injection of two optical signals into a semiconductor laser can be a feasible and practical method of enhancing chaos, influencing the stability map and generating various nonlinear dynamics.     

Deterministic mode alternation,giant pulses and chaos in a bidirectional CO2 ring laser

A CO₂ ring laser with a single longitudinal mode propagating in each direction shows a variety of stable, periodic, and aperiodic phenomena depending on gas pressure, cavity detuning and relative excitation. Three distinct low frequency time scales for dynamical behavior are observed and are explained by numerical solutions of an appropriate model.     

Deterministic chaos in the Belousov-Zhabotinsky reaction: Experiments and simulations

An account of the experimental discovery of complex dynamical behavior in the continuous-flow, stirred tank reactor (CSTR) Belousov-Zhabotinsky (BZ) reaction, as well as numerical simulations based on the BZ chemistry are given. The most recent four- and three-variable models that are deduced from the well-accepted, updated chemical mechanism of the BZ reaction and which exhibit robust chaotic states are summarized. Chaos has been observed in experiments and simulations embedded in the regions of complexities at both low and high flow rates. The deterministic nature of the observed aperiodicities at low flow rates is unequivocally established. However, controversy still remains in the interpretation of certain aperiodicities observed at high flow rates.     

Deterministic patterns of noise and the control of chaos

Real systems in physics, chemistry and biology are always subject to fluctuations that change qualitatively the systems' dynamics. In particular, rare large fluctuations are responsible for the nucleation at phase transitions, mutations in DNA sequences, protein transport in cells and failure of electronic devices. In many cases of practical interest systems are away from thermal equilibrium, and understanding the fluctuations in such systems is one of the fundamental problems of statistical physics that has challenged researchers for decades. Recent progress in the solution of this problem is closely related to the emerging understanding of patterns of deterministic trajectories underlying non-equilibrium fluctuations. These trajectories correspond to the Hamilton equations of motion written for the asymptotic solution of the Fokker - Planck equation and were often thought of as a mere mathematical abstraction. The possibility of quantitative experiments could not be entertained until the appropriate statistical quantity (prehistory probability distribution) had been introduced. In this paper it is shown how such trajectories can be measured experimentally in a number of systems and how the knowledge of these trajectories can be used to solve long standing problems in the theory of fluctuations and in the control theory.     

Intracavity chaotic dynamics in ring lasers with an injected signal

The intracavity dynamics of optically injected ring lasers is studied by means of an extended delay-differential Ikeda model. The behavior of this kind of lasers is, in some aspects, strikingly different from that of a nonlinear absorber placed in a ring cavity, for which the Ikeda model was originally derived. In particular, chaotic behavior in the laser case is seen to occur on much faster time scales than for the absorber. The scenario in which the transition to chaos occurs is also different.     

Deterministic chaos in a diode-pumped Nd:YAG laser passively Q switched by a Cr4+:YAG crystal

We report the experimental observation and numerical simulation of deterministic chaos in a diode-pumped Nd:YAG solid-state laser that is passively Q switched by a Cr4+:YAG crystal saturable absorber. We show that apart from the stable Q-switched operation the laser can also exhibit complicated nonlinear dynamics, including the period-doubling route to chaos and periodic windows.     

Deterministic chaos in one-dimensional maps—the period doubling and intermittency routes

This paper is a review of the present status of studies relating to occurrence of deterministic chaos and its characterization in one-dimensional maps. As our primary aim is to introduce the nonspecialists into this fascinating world of chaos we start from very elementary concepts and give sufficient arguments for clarity of ideas. The two main scenarios during onset of chaos viz. the period doubling and intermittency are dealt with in detail. Although the logistic map is often discussed by way of illustration, a few more interesting maps are mentioned towards the end.