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.

Effect of self assembly on the nonlinear optical characteristics of ZnO thin films

In the present work, we report the third order nonlinear optical properties of ZnO thin films deposited using self assembly, sol gel process as well as pulsed laser ablation by z scan technique. ZnO thin films clearly exhibit a negative nonlinear index of refraction at 532 nm and the observed nonlinear refraction is attributed to two photon absorption followed by free carrier absorption. Although the absolute nonlinear values for these films are comparable, there is a change in the sign of the absorptive nonlinearity of the films. The films developed by dip coating and pulsed laser ablation exhibit reverse saturable absorption whereas the self assembled film exhibits saturable absorption. These different nonlinear characteristics in the self assembled films can be mainly attributed to the saturation of linear absorption of the ZnO defect states.

Spectral dependence of third order nonlinear optical susceptibility of zinc phthalocyanine

Wavelength dependence of saturable absorption (SA) and reverse saturable absorption (RSA) of zinc phthalocyanine was studied using 10 Hz, 8 ns pulses from a tunable laser, in the wavelength range of 520–686 nm, which includes the rising edge of the Q band in the electronic absorption spectrum. The nonlinear response is wavelength dependent and switching from RSA to SA has been observed as the excitation wavelength changes from the low absorption window region to higher absorption regime near the Q band. The SA again changes back to RSA when we further move over to the infrared region. Values of the imaginary part of third order susceptibility are calculated for various wavelengths in this range. This study is important in identifying the spectral range over which the nonlinear material acts as RSA based optical limiter.

Spectral dependence of third order nonlinear optical susceptibility of zinc phthalocyanine

Wavelength dependence of saturable absorption (SA) and reverse saturable absorption (RSA) of zinc phthalocyanine was studied using 10 Hz, 8 ns pulses from a tunable laser, in the wavelength range of 520–686 nm, which includes the rising edge of the Q band in the electronic absorption spectrum. The nonlinear response is wavelength dependent and switching from RSA to SA has been observed as the excitation wavelength changes from the low absorption window region to higher absorption regime near the Q band. The SA again changes back to RSA when we further move over to the infrared region. Values of the imaginary part of third order susceptibility are calculated for various wavelengths in this range. This study is important in identifying the spectral range over which the nonlinear material acts as RSA based optical limiter.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Finite Element Analysis of Warship Structures

Warships are generally sleek, slender with V shaped sections and block coefficient below 0.5, compared to fuller forms and higher values for commercial ships. They normally operate in the higher Froude number regime, and the hydrodynamic design is primarily aimed at achieving higher speeds with the minimum power. Therefore the structural design and analysis methods are different from those for commercial ships. Certain design guidelines have been given in documents like Naval Engineering Standards and one of the new developments in this regard is the introduction of classification society rules for the design of warships.The marine environment imposes subjective and objective uncertainties on ship structure. The uncertainties in loads, material properties etc.,. make reliable predictions of ship structural response a difficult task. Strength, stiffness and durability criteria for warship structures can be established by investigations on elastic analysis, ultimate strength analysis and reliability analysis. For analysis of complicated warship structures, special means and valid approximations are required.Preliminary structural design of a frigate size ship has been carried out . A finite element model of the hold model, representative of the complexities in the geometric configuration has been created using the finite element software NISA. Two other models representing the geometry to a limited extent also have been created —- one with two transverse frames and the attached plating alongwith the longitudinal members and the other representing the plating and longitudinal stiffeners between two transverse frames. Linear static analysis of the three models have been carried out and each one with three different boundary conditions. The structural responses have been checked for deflections and stresses against the permissible values. The structure has been found adequate in all the cases. The stresses and deflections predicted by the frame model are comparable with those of the hold model. But no such comparison has been realized for the interstiffener plating model with the other two models.Progressive collapse analyses of the models have been conducted for the three boundary conditions, considering geometric nonlinearity and then combined geometric and material nonlinearity for the hold and the frame models. von Mises — lllyushin yield criteria with elastic-perfectly plastic stress-strain curve has been chosen. ln each case, P-Delta curves have been generated and the ultimate load causing failure (ultimate load factor) has been identified as a multiple of the design load specified by NES.Reliability analysis of the hull module under combined geometric and material nonlinearities have been conducted. The Young's Modulus and the shell thickness have been chosen as the variables. Randomly generated values have been used in the analysis. First Order Second Moment has been used to predict the reliability index and thereafter, the probability of failure. The values have been compared against standard values published in literature.

Third order elastic constants of bcc Cu-Al-Ni

We have measured the changes in the ultrasonic wave velocity, induced by the application of uniaxial stresses in a Cu-Al-Ni single crystal. From these measurements, the complete set of third-order elastic constants has been obtained. The comparison of results for Cu-Al-Ni with available data for other Cu-based alloys has shown that all these alloys exhibit similar anharmonic behavior. By using the measured elastic constants in a Landau expansion for elastic phase transitions, we have been able to give an estimation of the value of a fourth-order elastic constants combination. The experiments have also shown that the application of a stress in the [001] direction, reduces the material resistance to a (110)[110] shear and thus favors the martensitic transition.

Studies on Spatial and Temporal solitons with varying dispersion,diffraction and nonlinearity

Department of Physics, Cochin University of Science and Technology

Edge excitations and topological order in rotating Bose gas

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

Comment on "Reappraisal of experimental values of third-order elastic constants of some cubic semiconductors and metals"

In a recent paper A. S. Johal and D. J. Dunstan [Phys. Rev. B 73, 024106 (2006)] have applied multivariate linear regression analysis to the published data of the change in ultrasonic velocity with applied stress. The aim is to obtain the best estimates for the third-order elastic constants in cubic materials. From such an analysis they conclude that uniaxial stress data on metals turns out to be nearly useless by itself. The purpose of this comment is to point out that by a proper analysis of uniaxial stress data it is possible to obtain reliable values of third-order elastic constants in cubic metals and alloys. Cu-based shape memory alloys are used as an illustrative example.

Evidence of extended orientational order in amorphous Fe/Sm thin films

Amorphous thin films of Fe/Sm, prepared by evaporation methods, have been magnetically characterized and the results were interpreted in terms of the random magnets theory. The samples behave as 2D and 3D random magnets depending on the total thickness of the film. From our data the existence of orientational order, which greatly influences the magnetic behavior of the films, is also clear.

Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention