Direct Cartesian-Space Solutions of Generalized Bloch Equations in the Rotating Frame

Analytical solutions of the generalized Bloch equations for an arbitrary set of initial values of the x, y, and z magnetization components are given in the rotating frame. The solutions involve the decoupling of the three coupled differential equations such that a third-order differential equation in each magnetization variable is obtained. In contrast to the previously reported solutions given by Torrey, the present attempt paves the way for more direct physical insight into the behavior of each magnetization component. Special cases have been discussed that highlight the utility of the general solutions. Representative trajectories of magnetization components are given, illustrating their behavior with respect to the values of off-resonance and initial conditions. (C) 1995 Academic Press, Inc.

Quasiequilibrium optical nonlinearities from spin-polarized carriers in GaAs

Semiconductor Bloch equations, which microscopically describe the dynamics of a Coulomb interacting, spin-unpolarized electron-hole plasma, can be solved in two limits: the coherent and the quasiequilibrium regimes. These equations have been recently extended to include the spin degree of freedom and used to explain spin dynamics in the coherent regime. In the quasiequilibrium limit, one solves the Bethe-Salpeter equation in a two-band model to describe how optical absorption is affected by Coulomb interactions within a spin unpolarized plasma of arbitrary density. In this work, we modified the solution of the Bethe-Salpeter equation to include spin polarization and light holes in a three-band model, which allowed us to account for spin-polarized versions of many-body effects in absorption. The calculated absorption reproduced the spin-dependent, density-dependent, and spectral trends observed in bulk GaAs at room temperature, in a recent pump-probe experiment with circularly polarized light. Hence, our results may be useful in the microscopic modeling of density-dependent optical nonlinearities due to spin-polarized carriers in semiconductors.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data. (C) 2011 Optical Society of America

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units

Diffuse optical tomographic image reconstruction uses advanced numerical models that are computationally costly to be implemented in the real time. The graphics processing units (GPUs) offer desktop massive parallelization that can accelerate these computations. An open-source GPU-accelerated linear algebra library package is used to compute the most intensive matrix-matrix calculations and matrix decompositions that are used in solving the system of linear equations. These open-source functions were integrated into the existing frequency-domain diffuse optical image reconstruction algorithms to evaluate the acceleration capability of the GPUs (NVIDIA Tesla C 1060) with increasing reconstruction problem sizes. These studies indicate that single precision computations are sufficient for diffuse optical tomographic image reconstruction. The acceleration per iteration can be up to 40, using GPUs compared to traditional CPUs in case of three-dimensional reconstruction, where the reconstruction problem is more underdetermined, making the GPUs more attractive in the clinical settings. The current limitation of these GPUs in the available onboard memory (4 GB) that restricts the reconstruction of a large set of optical parameters, more than 13, 377. (C) 2010 Society of Photo-Optical Instrumentation Engineers. DOI: 10.1117/1.3506216]

Homogenization of periodic structures via Bloch decomposition

In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered. Using Bloch wave decomposition, a new proof of convergence is furnished. It sheds new light and offers an alternate way to view the classical results. In a natural way, this method leads us to work in the Fourier space and thus in a framework dual to the one used by L. Tartar [Problemes d'Homogeneisation dans les Equations aux: Derivees Partielles, Cours Peccot au College de Prance, 1977] in his method of homogenization. Further, this technique offers a nontraditional way of calculating the homogenized coefficients which is easy to implement in the computer.

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

Wheeler-Feynman absorber revisited: a useful technique to calculate decay rates and lifetimes in small scale optical systems

The Wheeler-Feynman (WF) absorber theory of radiation though no more of interest in explaining self interaction of an electron, can be very useful in today's research in small scale optical systems. The significance of the WF absorber is the use of time-symmetrical solution of Maxwell's equations as opposed to only the retarded solution. The radiative coupling of emitters to nano wires in the near field and change in their lifetimes due to small mode volume enclosures have been elucidated with the retarded solutions before. These solutions have also been shown to agree with quantum electrodynamics, thus allowing for classical electromagnetic approaches in such problems. It is here assumed that the radiative coupling of the emitter with a body is in proportion to its contribution to the classical force of radiative reaction as derived in the WF absorber theory. Representing such nano structures as a partial WF absorber acting on the emitter makes the computations considerably easier than conventional electromagnetic solutions for full boundary conditions.

Ultrasound-modulated optical tomography: direct recovery of elasticity distribution from experimentally measured intensity autocorrelation

Based on an ultrasound-modulated optical tomography experiment, a direct, quantitative recovery of Young's modulus (E) is achieved from the modulation depth (M) in the intensity autocorrelation. The number of detector locations is limited to two in orthogonal directions, reducing the complexity of the data gathering step whilst ensuring against an impoverishment of the measurement, by employing ultrasound frequency as a parameter to vary during data collection. The M and E are related via two partial differential equations. The first one connects M to the amplitude of vibration of the scattering centers in the focal volume and the other, this amplitude to E. A (composite) sensitivity matrix is arrived at mapping the variation of M with that of E and used in a (barely regularized) Gauss-Newton algorithm to iteratively recover E. The reconstruction results showing the variation of E are presented. (C) 2015 Optical Society of America

Exact N-wave solutions of generalized Burgers equations

Exact N-wave solutions for the generalized Burgers equation u(t) + u(n)u(x) + (j/2t + alpha) u + (beta + gamma/x) u(n+1) = delta/2u(xx),where j, alpha, beta, and gamma are nonnegative constants and n is a positive integer, are obtained. These solutions are asymptotic to the (linear) old-age solution for large time and extend the validity of the latter so as to cover the entire time regime starting where the originally sharp shock has become sufficiently thick and the viscous effects are felt in the entire N wave.

Spontaneous generation of optical activity in urea inclusion compounds vis-a-vis current theories

A novel test of recent theories of the origin of optical activity has been designed based on the inclusion of certain alkyl 2-methylhexanoates into urea channels.

Anomalous thermal dynamics of Bragg gratings inscribed in germanosilicate optical fiber

An interesting, periodic appearance of a new peak has been observed in the reflected spectrum of a Fiber Bragg Grating (FBG) inscribed in a germanosilicate fiber during thermal treatment. The new peak occurs on the longer wavelength side of the spectrum during heating and on the shorter wavelength side during cooling, following an identical reverse dynamics. Comparison with a commercial grating with 99.9% reflectivity shows a similar decay dynamics. It is proposed that the distortion due to simultaneous erasure and thermal expansion of the index modulation profile may be responsible for the observed anomaly. The reported results help us in understanding the thermal behavior of FBGs and provide additional insights into the mechanisms responsible for the photosensitivity in germanosilicate fibers.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.