Nonlinear Dynamics of Semiconductor LasersControl and Synchronization of Chaos:

Nonlinear dynamics of laser systems has become an interesting area of research in recent times. Lasers are good examples of nonlinear dissipative systems showing many kinds of nonlinear phenomena such as chaos, multistability and quasiperiodicity. The study of these phenomena in lasers has fundamental scientific importance since the investigations on these effects reveal many interesting features of nonlinear effects in practical systems. Further, the understanding of the instabilities in lasers is helpful in detecting and controlling such effects. Chaos is one of the most interesting phenomena shown by nonlinear deterministic systems. It is found that, like many nonlinear dissipative systems, lasers also show chaos for certain ranges of parameters. Many investigations on laser chaos have been done in the last two decades. The earlier studies in this field were concentrated on the dynamical aspects of laser chaos. However, recent developments in this area mainly belong to the control and synchronization of chaos. A number of attempts have been reported in controlling or suppressing chaos in lasers since lasers are the practical systems aimed to operated in stable or periodic mode. On the other hand, laser chaos has been found to be applicable in high speed secure communication based on synchronization of chaos. Thus, chaos in laser systems has technological importance also. Semiconductor lasers are most applicable in the fields of optical communications among various kinds of laser due to many reasons such as their compactness, reliability modest cost and the opportunity of direct current modulation. They show chaos and other instabilities under various physical conditions such as direct modulation and optical or optoelectronic feedback. It is desirable for semiconductor lasers to have stable and regular operation. Thus, the understanding of chaos and other instabilities in semiconductor lasers and their xi control is highly important in photonics. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated. A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor laser

Studies on the Effect of Randomness on the Synchronization of Coupled Systems and on the Dynamics of Intermittently driven systems

Nonlinear dynamics has emerged into a prominent area of research in the past few Decades.Turbulence, Pattern formation,Multistability etc are some of the important areas of research in nonlinear dynamics apart from the study of chaos.Chaos refers to the complex evolution of a deterministic system, which is highly sensitive to initial conditions. The study of chaos theory started in the modern sense with the investigations of Edward Lorentz in mid 60's. Later developments in this subject provided systematic development of chaos theory as a science of deterministic but complex and unpredictable dynamical systems. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. Here we introduce the concept of noise, and two familiar types of noise are discussed. The classifications and representation of white and colored noise are introduced. Based on this we introduce the concept of randomness that we deal with as a variant of the familiar concept of noise. The dynamical systems introduced are the Rossler system, directly modulated semiconductor lasers and the Harmonic oscillator. The directly modulated semiconductor laser being not a much familiar dynamical system, we have included a detailed introduction to its relevance in Chaotic encryption based cryptography in communication. We show that the effect of a fluctuating parameter mismatch on synchronization is to destroy the synchronization. Further we show that the relation between synchronization error and timescales can be found empirically but there are also cases where this is not possible. Studies show that under the variation of the parameters, the system becomes chaotic, which appears to be the period doubling route to chaos.

Nonlinear Dynamics of Nd:YAG lasers: Hopf bifurcation, Multistability and Chaotic Synchronization

In this thesis we have presented some aspects of the nonlinear dynamics of Nd:YAG lasers including synchronization, Hopf bifurcation, chaos control and delay induced multistability.We have chosen diode pumped Nd:YAG laser with intracavity KTP crystal operating with two mode and three mode output as our model system.Different types of orientation for the laser cavity modes were considered to carry out the studies. For laser operating with two mode output we have chosen the modes as having parallel polarization and perpendicular polarization. For laser having three mode output, we have chosen them as two modes polarized parallel to each other while the third mode polarized orthogonal to them.

Studies on function projective synchronization in chaotic and hyperchaotic systems

FPS is a more general form of synchronization. Hyperchaotic systems possessing more than one positive Lypaunov exponent exhibit highly complex behaviour and are more suitable for some applications like secure communications. In this thesis we report studies of FPS and MFPS of a few chaotic and hyperchaotic systems. When all the parameters of the system are known we show that active nonlinear control method can be efectively used to obtain FPS. Adaptive nonlinear control and OPCL control method are employed for obtaining FPS and MFPS when some or all parameters of the system are uncertain. A secure communication scheme based on MFPS is also proposed in theory. All our theoretical calculations are verified by numerical simulations.

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.

Studies on Chaos and Synchronization in ac-driven Josephson junctions

The main goal of this thesis is to study the dynamics of Josephson junction system in the presence of an external rf-biasing.A system of two chaotically synchronized Josephson junction is studied.The change in the dynamics of the system in the presence of at phase difference between the applied fields is considered. Control of chaos is very important from an application point of view. The role Of phase difference in controlling chaos is discussed.An array of three Josephson junctions iS studied for the effect of phase difference on chaos and synchronization and the argument is extended for a system of N Josephson junctions. In the presence of a phase difference between the external fields, the system exhibits periodic behavior with a definite phase relationship between all the three junctions.Itdeals with an array of three Josephson junctions with a time delay in the coupling term. It is observed that only the outer systems synchronize while the middle system remain uncorrelated with t-he other two. The effect of phase difference between the applied fields and time-delay on system dynamics and synchronization is also studied. We study the influence of an applied ac biasing on a serniannular Josephson junction. It is found the magnetic field along with the biasing induces creation and annihilation of fluxons in the junction. The I-V characteristics of the junction is studied by considering the surface loss term also in the model equation. The system is found to exhibit chaotic behavior in the presence of ac biasing.

Phase effects on synchronization by dynamical relaying in delay-coupled systems

Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant, and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.

Phase synchronization in an array of driven Josephson junctions

We consider an array of N Josephson junctions connected in parallel and explore the condition for chaotic synchronization. It is found that the outer junctions can be synchronized while they remain uncorrelated to the inner ones when an external biasing is applied. The stability of the solution is found out for the outer junctions in the synchronization manifold. Symmetry considerations lead to a situation wherein the inner junctions can synchronize for certain values of the parameter. In the presence of a phase difference between the applied fields, all the junctions exhibit phase synchronization. It is also found that chaotic motion changes to periodic in the presence of phase differences.

Studies on the effect of randoniness on the synchronization of coupled systems and on the dynamics of intermittently driven systems

It has been shown recently that systems driven with random pulses show the signature of chaos ,even without non linear dynamics.This shows that the relation between randomness and chaos is much closer than it was understood earlier .The effect of random perturbations on synchronization can be also different. In some cases identical random perturbations acting on two different chaotic systems induce synchronizations. However most commonly ,the effect of random fluctuations on the synchronizations of chaotic system is to destroy synchronization. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. The author tries to unearth yet another manifestation of randomness on chaos and sychroniztion. This thesis is organized into six chapters.

STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

Nonlinear Dynamics of Multiple Quantum Well Lasers: Chaos and Multistability

This thesis presents analytical and numerical results from studies based on the multiple quantum well laser rate equation model. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated.A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor lasers.

Bidirectional communication using delay coupled chaotic directly modulated semiconductor lasers

Chaotic synchronization of two directly modulated semiconductor lasers with negative delayed optoelectronic feedback is investigated and this scheme is found to be useful for e±cient bidirectional communication between the lasers. A symmetric bidirec- tional coupling is identified as a suitable method for isochronal synchronization of such lasers. The optimum values of coupling and feedback strength that can provide maxi- mum quality of synchronization are identified. This method is successfully employed for encoding/decoding both analog and digital messages. The importance of a symmetric coupling is demonstrated by studying the variation of decoding efficiency with respect to asymmetric coupling.

Effect of a fluctuating parameter mismatch and the associated time-scales on coupled Rossler oscillators

We study the effect of parameter fluctuations and the resultant multiplicative noise on the synchronization of coupled chaotic systems. We introduce a new quantity, the fluctuation rate Ф as the number of perturbations occurring to the parameter in unit time. It is shown that ϕ is the most significant quantity that determines the quality of synchronization. It is found that parameter fluctuations with high fluctuation rates do not destroy synchronization, irrespective of the statistical features of the fluctuations. We also present a quasi-analytic explanation to the relation between ϕ and the error in synchrony.

Dynamical aspects of coupled Rossler systems: effects of noise

Nonlinear time series analysis is employed to study the complex behaviour exhibited by a coupled pair of Rossler systems. Dimensional analysis with emphasis on the topological correlation dimension and the Kolmogorov entropy of the system is carried out in the coupling parameter space. The regime of phase synchronization is identified and the extent of synchronization between the systems constituting the coupled system is quantified by the phase synchronization index. The effect of noise on the coupling between the systems is also investigated. An exhaustive study of the topological, dynamical and synchronization properties of the nonlinear system under consideration in its characteristic parameter space is attempted.

Dynamics of coupled Josephson junctions under the influence of applied fields

We investigate the effect of the phase difference of appliedfields on the dynamics of mutually coupledJosephsonjunctions. A phase difference between the appliedfields desynchronizes the system. It is found that though the amplitudes of the output voltage values are uncorrelated, a phase correlation is found to exist for small values of applied phase difference. The dynamics of the system is found to change from chaotic to periodic for certain values of phase difference. We report that by keeping the value of phase difference as π, the system continues to be in periodic motion for a wide range of values of system parameters. This result may find applications in devices like voltage standards, detectors, SQUIDS, etc., where chaos is least desired.