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.

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.

Investigation of nonlinear absorption and aggregation in aqueous solutions of rhodamine B using thermal lens technique

Thermal lensing effect was studied in aqueous solutions of rhodamine B using 532 nm, 9 ns pulses from a Nd:YAG laser. A low intensity He-Ne laser beam was used for probing the thermal lens. Results obtained show that it is appropriate to use this technique for studying nonlinear absorption processes like two photon absorption or excited state absorption and for analyzing dimerization equilibria.

Studies of nonlinear absorption and aggregation in aqueous solutions of rhodamine 6G using a transient thermal lens technique

Dual-beam transient thermal lens studies were carried out in aqueous solutions of rhodamine 6G using 532 nm pulses from a frequency-doubled Nd:YAG laser. The analysis of the observed data showed that the thermal lens method can effectively be utilized to study the nonlinear absorption and aggregation which are taking place in a dye medium.

Thermal lens spectrum of organic dyes using optical parametric oscillator

The wavelength dependence of thermal lens signal from organic dyes are studied using dual beam thermal lens technique. It is found that the profile of thermal lens spectrum widely differ from the conventional absorption spectrum in the case of rhodamine B unlike in the case of crystal violet. This is explained on the basis of varying contribution of nonradiative relaxations from the excited vibronic levels.

Pulsed photoacoustic technique to study nonlinear processes in liquids: Results in toluene

Pulsed photoacoustic measurements have been carried out in toluene at 532 nm wavelength using a Q-switched frequency doubled Nd:YAG laser. The variation of photoacoustic signal amplitude with incident laser power indicates that at lower laser powers one photon absorption takes place at this wavelength while a clear two photon absorption occurs in this liquid at higher laser powers. The studies made here demonstrate that pulsed photoacoustic technique is simple and effective for the investigation of multiphoton processes in liquids.

Possibility of waveguide formation on organic nonlinear crystal methyl para-hydroxy benzoate using high energy ion irradiation

Organic nonlinear optical single crystals of Methyl para-Hydroxy Benzoate (MHB) have been grown using gel-solution technique. These crystals are cut along z-axis and are bombarded with Ag14+ ions of energy 100 MeV. The results show an increase in refractive index at the ion irradiated region. The dielectric constant of the irradiated crystal is increased more than 15 times compared to that of a nonirradiated crystal. The result of these changes and comparative study of second harmonic generation (SHG) efficiency before and after irradiation is discussed.

Third order nonlinear optical studies in europium naphthalocyanine using degenerate four wave mixing and Z-scan

Third order nonlinear susceptibility χ(3) and second hyperpolarizability (γ) of a bis-naphthalocyanine viz. europium naphthalocyanines, Eu(Nc)2, were measured in dimethyl formamide solution using degenerate four wave mixing at 532 nm under nanosecond pulse excitation. Effective nonlinear absorption coefficient, βeff and imaginary part of nonlinear susceptibility, Im(χ(3)) were obtained using open aperture /Z-scan technique at the same wavelength. Optical limiting property of the sample was also investigated. The role of excited state absorption in deciding the nonlinear properties of this material is discussed.

Thermal lens spectrum of organic dyes using optical parametric oscillator

The wavelength dependence of thermal lens signal from organic dyes are studied using dual beam thermal lens technique. It is found that the profile of thermal lens spectrum widely differ from the conventional absorption spectrum in the case of rhodamine B unlike in the case of crystal violet. This is explained on the basis of varying contribution of nonradiative relaxations from the excited vibronic levels.

Studies on Two-Photon Absorption of Aniline Using Thermal Lens Effect

Two-photon absorption spectrum of aniline is recorded using thermal lens effect with optical parametric oscillator as the pump source. Studies show that the two-photon absorption spectrum observed corresponds to I Al -. I B2 transition of aniline.

Studies on Some Aspects of Light Beam Propagation Through Certain Nonlinear Media

This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.

Template assisted fabrication of I-D nanostructures of Nickel,Cobalt, Iron Oxide and Carbon nanotubes and a study on their structural, magnetic and nonlinear optical properties for applications

Department of Physics, Cochin University of Science & Technology

The quantum effects in quadratically damped systems

A dynamical system with a damping that is quadratic in velocity is converted into the Hamiltonian format using a nonlinear transformation. Its quantum mechanical behaviour is then analysed by invoking the Gaussian effective potential technique. The method is worked out explicitly for the Duffing oscillator potential.

Metastable States and Irregular Behaviour in a Josephson Junction with Nonlinear Resistance

We consider a resistively shunted Josephson junction with a resistance that depends inversely on voltage. It is shown that such a junction in the underdamped case can give rise to extremely long-lived metastable states even in the absence of external noise. We investigate numerically this metastable state and its transition to a chaotic state. The junction voltages corresponding to these states are studied.