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.

Laser induced surface damage, thermal transport and microhardness studies on certain organic and semiorganic nonlinear optical crystals

N-alkyl-2,6-dimethyl-4(1H)-pyridinones, salts of 4-dimethylaminopyridine and 2-amino-5-nitropyridine are considered to be potential candidates for nonlinear optical (NLO) applications, in particular for the generation of blue-green laser radiation. Single crystals were grown following the slow evaporation technique at constant temperature. Single-shot laserinduced surface damage thresholds in the range 3–10 GW/cm2 were measured using a 18 ns Q-switched Nd:YAG laser. The surface morphologies of the damaged crystals were examined under an optical microscope and the nature of damage identified. The Vicker’s microhardness was determined at a load of 98.07 mN. The thermal transport properties, thermal diffusivity (α), thermal effusivity (e), thermal conductivity (K) and heat capacity (Cp), of the grown crystals were measured by an improved photopyroelectric technique at room temperature. All the results are presented and discussed.

Effect of annealing on the spectral and nonlinear optical characteristics of thin films of nano-ZnO

The annealing effect on the spectral and nonlinear optical NLO characteristics of ZnO thin films deposited on quartz substrates by sol-gel process is investigated. As the annealing temperature increases from 300–1050 °C, there is a decrease in the band gap, which indicates the changes of the interface of ZnO. ZnO is reported to show two emission bands, an ultraviolet UV emission band and another in the green region. The intensity of the UV peak remains the same while the intensity of the visible peak increases with increase in annealing temperature. The role of oxygen in ZnO thin films during the annealing process is important to the change in optical properties. The mechanism of the luminescence suggests that UV luminescence of ZnO thin films is related to the transition from conduction band edge to valence band, and green luminescence is caused by the transition from deep donor level to valence band due to oxygen vacancies. The NLO response of these samples is studied using nanosecond laser pulses at off-resonance wavelengths. The nonlinear absorption coefficient increases from 2.9 ×10−6 to 1.0 ×10−4 m/W when the annealing temperature is increased from 300 to 1050 °C, mainly due to the enhancement of interfacial state and exciton oscillator strength. The third order optical susceptibility x(3) increases with increase in annealing temperature (T) within the range of our investigations. In the weak confinement regime, T2.4 dependence of x(3) is obtained for ZnO thin films. The role of annealing temperature on the optical limiting response is also studied.

Nonlinear optical characteristics of self-assembled films of ZnO

In the present work, we have investigated the nonlinear optical properties of self-assembled films formed from ZnO colloidal spheres by z-scan technique. The sign of the nonlinear component of refractive index of the material remains the same; however, a switching from reverse saturable absorption to saturable absorption has been observed as the material changes from colloid to self-assembled film. These different nonlinear characteristics can be mainly attributed to ZnO defect states and electronic effects when the colloidal solution is transformed into self-assembled monolayers. We investigated the intensity, wavelength and size dependence of saturable and reverse saturable absorption of ZnO self-assembled films and colloids. Values of the imaginary part of third-order susceptibility are calculated for particles of size in the range 20–300 nm at different intensity levels ranging from 40 to 325MW/cm2 within the wavelength range of 450–650 nm.

Spectral and nonlinear optical characteristics of nanocomposites of ZnO-CdS

In this article, we present the spectral and nonlinear optical properties of ZnO–CdS nanocomposites prepared by colloidal chemical synthesis. The optical band gap (Eg) of the material is tunable between 2.62 and 3.84 eV. The emission peaks of ZnO–CdS nanocomposites change from 385 to 520 nm almost in proportion to changes in Eg. It is possible to obtain a desired luminescence color from UV to green by simply adjusting the composition. The nonlinear optical response of these samples is studied by using nanosecond laser pulses from a tunable laser at the excitonic resonance and off-resonance wavelengths. The nonlinear response is wavelength dependent, and switching from saturable absorption (SA) to reverse SA (RSA) has been observed for samples as the excitation wavelength changes from the excitonic resonance to off-resonance wavelengths. Such a changeover in the sign of the nonlinearity of ZnO–CdS nanocomposites is related to the interplay of exciton bleach and optical limiting mechanisms. The ZnO–CdS nanocomposites show self-defocusing nonlinearity and good nonlinear absorption behavior at off-resonant wavelengths. The nonlinear refractive index and the nonlinear absorption increase with increasing CdS volume fraction at 532 nm. The observed nonlinear absorption is attributed to two photon absorption followed by weak free carrier absorption. The enhancement of the third-order nonlinearity in the composites can be attributed to the concentration of exciton oscillator strength. This study is important in identifying the spectral range and composition over which the nonlinear material acts as a RSA based optical limiter. ZnO–CdS is a potential nanocomposite material for the tunable light emission and for the development of nonlinear optical devices with a relatively small limiting threshold.

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.

Signatures of Higher Functions of Brain Dynamics in Electroencephalogram: A Nonlinear Analysis

The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.

Information Discovery in Distributed Systems-A Novel Concept Based on Modelling of Information Elements

Sharing of information with those in need of it has always been an idealistic goal of networked environments. With the proliferation of computer networks, information is so widely distributed among systems, that it is imperative to have well-organized schemes for retrieval and also discovery. This thesis attempts to investigate the problems associated with such schemes and suggests a software architecture, which is aimed towards achieving a meaningful discovery. Usage of information elements as a modelling base for efficient information discovery in distributed systems is demonstrated with the aid of a novel conceptual entity called infotron.The investigations are focused on distributed systems and their associated problems. The study was directed towards identifying suitable software architecture and incorporating the same in an environment where information growth is phenomenal and a proper mechanism for carrying out information discovery becomes feasible. An empirical study undertaken with the aid of an election database of constituencies distributed geographically, provided the insights required. This is manifested in the Election Counting and Reporting Software (ECRS) System. ECRS system is a software system, which is essentially distributed in nature designed to prepare reports to district administrators about the election counting process and to generate other miscellaneous statutory reports.Most of the distributed systems of the nature of ECRS normally will possess a "fragile architecture" which would make them amenable to collapse, with the occurrence of minor faults. This is resolved with the help of the penta-tier architecture proposed, that contained five different technologies at different tiers of the architecture.The results of experiment conducted and its analysis show that such an architecture would help to maintain different components of the software intact in an impermeable manner from any internal or external faults. The architecture thus evolved needed a mechanism to support information processing and discovery. This necessitated the introduction of the noveI concept of infotrons. Further, when a computing machine has to perform any meaningful extraction of information, it is guided by what is termed an infotron dictionary.The other empirical study was to find out which of the two prominent markup languages namely HTML and XML, is best suited for the incorporation of infotrons. A comparative study of 200 documents in HTML and XML was undertaken. The result was in favor ofXML.The concept of infotron and that of infotron dictionary, which were developed, was applied to implement an Information Discovery System (IDS). IDS is essentially, a system, that starts with the infotron(s) supplied as clue(s), and results in brewing the information required to satisfy the need of the information discoverer by utilizing the documents available at its disposal (as information space). The various components of the system and their interaction follows the penta-tier architectural model and therefore can be considered fault-tolerant. IDS is generic in nature and therefore the characteristics and the specifications were drawn up accordingly. Many subsystems interacted with multiple infotron dictionaries that were maintained in the system.In order to demonstrate the working of the IDS and to discover the information without modification of a typical Library Information System (LIS), an Information Discovery in Library Information System (lDLIS) application was developed. IDLIS is essentially a wrapper for the LIS, which maintains all the databases of the library. The purpose was to demonstrate that the functionality of a legacy system could be enhanced with the augmentation of IDS leading to information discovery service. IDLIS demonstrates IDS in action. IDLIS proves that any legacy system could be augmented with IDS effectively to provide the additional functionality of information discovery service.Possible applications of IDS and scope for further research in the field are covered.

Investigations on Nonlinear and Radiative Properties of Certain Photonic Materials

International School of Photonics, Cochin University of Science & Technology

Investigations of Nonlinear Optical Properties of certain organic photonic materials using Z-Scan and DFWM techniques

Nonlinear optical processes in organic compounds have attracted considerable interest in the field of science and technology because of their compelling technological promises in fields of optical communication,computing,switching and signal processing.As a result of the synthesis of novel organic compounds with varying degree of nonlinear optical strength, many practical devices based on these are getting realised giving new theoretical insights into the nonolinear optical behaviour of materials.Organic compounds like phthalocyanines and porphyrins have evoked great deal of interest in the field of photonic technology.The present thesis describes the results obtained from the investigations carried out on the nonlinear optical properties of certain organo-metallic compounds using Z-Scan and DFWM techniques.

Thermo-Structural Analysis of 3D Composites

Three dimensional (3D) composites are strong contenders for the structural applications in situations like aerospace,aircraft and automotive industries where multidirectional thermal and mechanical stresses exist. The presence of reinforcement along the thickness direction in 3D composites,increases the through the thickness stiffness and strength properties.The 3D preforms can be manufactured with numerous complex architecture variations to meet the needs of specific applications.For hot structure applications Carbon-Carbon(C-C) composites are generally used,whose property variation with respect to temperature is essential for carrying out the design of hot structures.The thermomechanical behavior of 3D composites is not fully understood and reported.The methodology to find the thermomechanical properties using analytical modelling of 3D woven,3D 4-axes braided and 3D 5-axes braided composites from Representative Unit Cells(RUC's) based on constitutive equations for 3D composites has been dealt in the present study.High Temperature Unidirectional (UD) Carbon-Carbon material properties have been evaluated using analytical methods,viz.,Composite cylinder assemblage Model and Method of Cells based on experiments carried out on Carbon-Carbon fabric composite for a temparature range of 300 degreeK to 2800degreeK.These properties have been used for evaluating the 3D composite properties.From among the existing methods of solution sequences for 3D composites,"3D composite Strength Model" has been identified as the most suitable method.For thegeneration of material properies of RUC's od 3D composites,software has been developed using MATLAB.Correlaton of the analytically determined properties with test results available in literature has been established.Parametric studies on the variation of all the thermomechanical constants for different 3D performs of Carbon-Carbon material have been studied and selection criteria have been formulated for their applications for the hot structures.Procedure for the structural design of hot structures made of 3D Carbon-Carbon composites has been established through the numerical investigations on a Nosecap.Nonlinear transient thermal and nonlinear transient thermo-structural analysis on the Nosecap have been carried out using finite element software NASTRAN.Failure indices have been established for the identified performs,identification of suitable 3D composite based on parametric studies on strength properties and recommendation of this material for Nosecap of RLV based on structural performance have been carried out in this Study.Based on the 3D failure theory the best perform for the Nosecap has been identified as 4-axis 15degree braided composite.

Stochastic Modelling Using Markov Chains

Department of Statistics, Cochin University of Science and Technology

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.