Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

Dynamics of free-running, pump-modulated and coupled semiconductor and solid-state lasers

The output of a laser is a high frequency propagating electromagnetic field with superior coherence and brightness compared to that emitted by thermal sources. A multitude of different types of lasers exist, which also translates into large differences in the properties of their output. Moreover, the characteristics of the electromagnetic field emitted by a laser can be influenced from the outside, e.g., by injecting an external optical field or by optical feedback. In the case of free-running solitary class-B lasers, such as semiconductor and Nd:YVO4 solid-state lasers, the phase space is two-dimensional, the dynamical variables being the population inversion and the amplitude of the electromagnetic field. The two-dimensional structure of the phase space means that no complex dynamics can be found. If a class-B laser is perturbed from its steady state, then the steady state is restored after a short transient. However, as discussed in part (i) of this Thesis, the static properties of class-B lasers, as well as their artificially or noise induced dynamics around the steady state, can be experimentally studied in order to gain insight on laser behaviour, and to determine model parameters that are not known ab initio. In this Thesis particular attention is given to the linewidth enhancement factor, which describes the coupling between the gain and the refractive index in the active material. A highly desirable attribute of an oscillator is stability, both in frequency and amplitude. Nowadays, however, instabilities in coupled lasers have become an active area of research motivated not only by the interesting complex nonlinear dynamics but also by potential applications. In part (ii) of this Thesis the complex dynamics of unidirectionally coupled, i.e., optically injected, class-B lasers is investigated. An injected optical field increases the dimensionality of the phase space to three by turning the phase of the electromagnetic field into an important variable. This has a radical effect on laser behaviour, since very complex dynamics, including chaos, can be found in a nonlinear system with three degrees of freedom. The output of the injected laser can be controlled in experiments by varying the injection rate and the frequency of the injected light. In this Thesis the dynamics of unidirectionally coupled semiconductor and Nd:YVO4 solid-state lasers is studied numerically and experimentally.

Quadrature generation techniques for frequency multiplication based oscillators

Frequency multiplication (FM) can be used to design low power frequency synthesizers. This is achieved by running the VCO at a much reduced frequency, while employing a power efficient frequency multiplier, and also thereby eliminating the first few dividers. Quadrature signals can be generated by frequency- multiplying low frequency I/Q signals, however this also multiplies the quadrature error of these signals. Another way is generating additional edges from the low-frequency oscillator (LFO) and develop a quadrature FM. This makes the I-Q precision heavily dependent on process mismatches in the ring oscillator. In this paper we examine the use of fewer edges from LFO and a single stage polyphase filter to generate approximate quadrature signals, which is then followed by an injection-locked quadrature VCO to generate high- precision I/Q signals. Simulation comparisons with the existing approach shows that the proposed method offers very good phase accuracy of 0.5deg with only a modest increase in power dissipation for 2.4 GHz IEEE 802.15.4 standard using UMC 0.13 mum RFCMOS technology.

Spectroscopic ellipsometry investigations of the optical properties of manganese doped bismuth vanadate thin films

The optical properties of Bi(2)V(1-x)MnxO(5.5-x) (x=0.05, 0.1, 0.15 and 0.2 at.%) thin films fabricated by pulsed laser deposition on platinized Silicon Substrates were Studied in UV-visible spectral region (1.51-4.17 CV) using spectroscopic ellipsometry. The optical constants and thicknesses of these films have been obtained by fitting the ellipsometric data (Psi and Delta) using a multilayer four-phase model system and a relaxed Lorentz oscillator dispersion relation. The surface roughness and film thickness obtained by spectroscopic ellipsometry were found to be consistent with the results obtained by atomic force and scanning electron microscopy. The refractive index measured at 650 nm does not show any marginal increase with Mn content. Further, the extinction coefficient does not show much decrease with increasing Mn content. An increase in optical band gap energy from 2.52 to 2.77 eV with increasing Mn Content from x = 0.05 to 0.15 was attributed to the increase in oxygen ion vacancy disorder. (C) 2009 Elsevier Ltd. All rights reserved.

A Simple Instrumentation Calibration Technique for Electrical Impedance Tomography (EIT) Using A 16-Electrode Phantom

A simple analog instrumentation for Electrical Impedance Tomography is developed and calibrated using the practical phantoms. A constant current injector consisting of a modified Howland voltage controlled current source fed by a voltage controlled oscillator is developed to inject a constant current to the phantom boundary. An instrumentation amplifier, 50 Hz notch filter and a narrow band pass filter are developed and used for signal conditioning. Practical biological phantoms are developed and the forward problem is studied to calibrate the EIT-instrumentation. An array of sixteen stainless steel electrodes is developed and placed inside the phantom tank filled with KCl solution. 1 mA, 50 kHz sinusoidal current is injected at the phantom boundary using adjacent current injection protocol. The differential potentials developed at the voltage electrodes are measured for sixteen current injections. Differential voltage signal is passed through an instrumentation amplifier and a filtering block and measured by a digital multimeter. A forward solver is developed using Finite Element Method in MATLAB7.0 for solving the EIT governing equation. Differential potentials are numerically calculated using the forward solver with a simulated current and bathing solution conductivity. Measured potential data is compared with the differential potentials calculated for calibrating the instrumentation to acquire the voltage data suitable for better image reconstruction.

A Study of Practical Biological Phantoms with Simple Instrumentation for Electrical Impedance Tomography (EIT)

16-electrode phantoms are developed and studied with a simple instrumentation developed for Electrical Impedance Tomography. An analog instrumentation is developed with a sinusoidal current generator and signal conditioner circuit. Current generator is developed withmodified Howland constant current source fed by a voltage controlled oscillator and the signal conditioner circuit consisting of an instrumentation amplifier and a narrow band pass filter. Electronic hardware is connected to the electrodes through a DIP switch based multiplexer module. Phantoms with different electrode size and position are developed and the EIT forward problem is studied using the forward solver. A low frequency low magnitude sinusoidal current is injected to the surface electrodes surrounding the phantom boundary and the differential potential is measured by a digital multimeter. Comparing measured potential with the simulated data it is intended to reduce the measurement error and an optimum phantom geometry is suggested. Result shows that the common mode electrode reduces the common mode error of the EIT electronics and reduces the error potential in the measured data. Differential potential is reduced up to 67 mV at the voltage electrode pair opposite to the current electrodes. Offset potential is measured and subtracted from the measured data for further correction. It is noticed that the potential data pattern depends on the electrode width and the optimum electrode width is suggested. It is also observed that measured potential becomes acceptable with a 20 mm solution column above and below the electrode array level.

Raman spectra of single crystals of adipic and sebacic acids and a study of the hydrogen bond vibrations in carboxylic acid dimers

Raman spectra of single crystals of adipic and sebacic acids have been photographed for the first time using λ 2537 excitation. The spectra have been divided into four regions: (a) internal frequencies; (b) summations and overtones; (c) external vibrations; and (d) low-frequency hydrogen bond oscillations. Tentative correlations have been given for all the internal frequencies and summations and overtones. A series of diffuse weak bands observed in the spectra of both these acids in the not, vert, similar2400–2800 cm−1 have been explained as a superposition of O---H frequencies lowered due to hydrogen bond formation over the summations and overtones of fundamentals mainly in the not, vert, similar1000–1500 cm−1 region. Rotatory type of external oscillations of the two formula units of these molecules in their unit cells have been identified at 76, 99, 118 and 165 cm−1 in adipic acid and 66, 95, 117 and 177 cm−1 in the spectrum of sebacic acid. A brief discussion of the low frequency hydrogen bond vibrations in these acids has been made. Making use of the Lippincott—Schroeder potential and assuming a highly anharmonic potential curve for the hydrogen bond, the vibrational frequencies of the bond have been theoretically evaluated. There is very good agreement between these and the experimental values. The results for adipic acid in cm−1 are: 304 (0 → 1), 270 (1 → 2), 241 (2 → 3), 222 (3 → 4) 201 (4 → 5), 183 (5 → 6). In the case of sebacic acid some of the intermediate and higher transitions are absent in the spectrum recorded by the author. From the above data for adipic acid the dissociation energy of the hydrogen bond was evaluated as 5·9 kcal/mole in fair agreement with the values derived from conventional methods.

Force constants and thermodynamic functions of iodine heptafluoride

Normal coordinate analysis of a molecule of the type XY7 (point group D5h) has been carried out using Wilson's FG, matrix method and the results have been utilized to calculate the force constants of IF7 from the available Raman and infrared data. Some of the assignments made previously by Lord and others have been revised and with the revised assignments the thermodynamic quantities of IF7 have been computed from 300°K to 1000°K under rigid rotator and harmonic oscillator approximation.

Free-to-bound and bound exciton transitions at isoelectronic impurities: GaP(Zn,O)

We show, for sufficiently high temperatures and sufficiently weak majority-carrier binding energies, that the dominant radiative transition at an isoelectronic acceptor (donor) in p-type (n-type) material consists of the recombination of singly trapped minority carriers (bound by central-cell forces) with free majority carriers attracted by a Coulomb interaction. There are two reasons why the radiative recombination rate of the free-to-bound process is greater than the bound exciton process, which dominates at lower temperatures: (i) The population of free majority-carrier states greatly exceeds that of exciton states at higher temperatures, and (ii) the oscillator strength of the free-to-bound transition is greatly enhanced by the Coulomb attraction between the free carrier and the charged isoelectronic impurity. This enhancement is important for isoelectronic centers and is easily calculable from existing exciton models. We show that the free carrier attracted by a Coulomb interaction can be viewed as a continuum excited state of the bound exciton. When we apply the results of our calculations to the GaP(Zn, O) system, we find that the major part of the room-temperature luminescence from nearest-neighbor isoelectronic Zn-O complexes results from free-to-bound recombination and not exciton recombination as has been thought previously. Recent experiments on impulse excitation of luminescence in GaP(Zn, O) are reevaluated in the light of our calculations and are shown to be consistent with a strong free-to-bound transition. For deep isoelectronic centers with weakly bound majority carriers, we predict an overwhelming dominance of the free-to-bound process at 300°K.

First passage probability during random vibration

The probability that a random process crosses an arbitrary level for the first time is expressed as a Gram—Charlier series, the leading term of which is the Poisson approximation. The coefficients of this series are related to the moments of the number of level crossings. The results are applicable to both stationary and non-stationary processes. Some numerical results are presented for the response process of a linear single-degree-of-freedom oscillator under Gaussian white noise excitation.

A particle filtering approach for structural system identification in vehicle–structure interaction problems

The problem of identification of parameters of a beam-moving oscillator system based on measurement of time histories of beam strains and displacements is considered. The governing equations of motion here have time varying coefficients. The parameters to be identified are however time invariant and consist of mass, stiffness and damping characteristics of the beam and oscillator subsystems. A strategy based on dynamic state estimation method, that employs particle filtering algorithms, is proposed to tackle the identification problem. The method can take into account measurement noise, guideway unevenness, spatially incomplete measurements, finite element models for supporting structure and moving vehicle, and imperfections in the formulation of the mathematical models. Numerical illustrations based on synthetic data on beam-oscillator system are presented to demonstrate the satisfactory performance of the proposed procedure.

Worst inputs and a bound on the highest peak statistics of a class of non-linear systems

A method is developed by which the input leading to the highest possible response in an interval of time can be determined for a class of non-linear systems. The input, if deterministic, is constrained to have a known finite energy (or norm) in the interval under consideration. In the case of random inputs, the energy is constrained to have a known probability distribution function. The approach has applications when a system has to be put to maximum advantage by getting the largest possible output or when a system has to be designed to the highest maximum response with only the input energy or the energy distribution known. The method is also useful in arriving at a bound on the highest peak distribution of the response, when the excitation is a known random process.As an illustration the Duffing oscillator has been analysed and some numerical results have also been presented.

Response of nonlinear systems to narrow-band excitation

The hardening cubic spring oscillator is studied under narrow-band gaussian excitation. Equivalent linearization leads to multiple steady states. The realizability of the solution is discussed through stochastic stability analysis. Theoretical results are supported by numerical simulation.

Undamped oscillations of homogeneous collisionless stellar systems

The Lewis (1968) invariant of the time-dependent harmonic oscillator is used to construct exact time-dependent, uniform density solutions of the collisionless Boltzmann equation. The spatially bound solutions are time-periodic.

Infrared Spectra of Dimethylquinolines in the Gas Phase: Experiment and Theory

Infrared spectra of atmospherically important dimethylquinolines (DMQs), namely 2,4-DMQ, 2,6-DMQ, 2,7-DMQ, and 2,8-DMQ in the gas phase at 80 degrees C were recorded using a long variable path-length cell. DFT calculations were carried out to assign the bands in the experimentally observed spectra at the B3LYP/6-31G* level of theory. The spectral assignments particularly for the C-H stretching modes could not be made unambiguously using calculated anharmonic or scaled harmonic frequencies. To resolve this problem, a scaled force field method of assignment was used. Assignment of fundamental modes was confirmed by potential energy distributions (PEDs) of the normal modes derived by the scaled force fields using a modified version of the UMAT program in the QCPE package. We demonstrate that for large molecules such as the DMQs, the scaling of the force field is more effective in arriving at the correct assignment of the fundamentals for a quantitative vibrational analysis. An error analysis of the mean deviation of the calculated harmonic, anharmonic, and force field fitted frequencies from the observed frequency provides strong evidence for the correctness of the assignment.