Resonant absorption of alfvén waves near a neutral point

It is shown that, although the mathematical analysis of the Alfven-wave equation does not show any variation at non-zero or zero singular points, the role of surface waves in the physical mechanism of resonant absorption of Alfven waves is very different at these points. This difference becomes even greater when resistivity is taken into account. At the neutral point the zero-frequency surface waves that are symmetric surface modes of the structured neutral layer couple to the tearing mode instability of the layer. The importance of this study for the energy balance in tearing modes and the association of surface waves with driven magnetic reconnection is also pointed out.

Entanglement and nonclassicality for multimode radiation-field states

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multimode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beam splitters, in a transparent manner. For single-mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beam splitter, these conditions turn exactly into signatures of negativity under partial transpose (NPT) entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beam-splitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three-mode beam-splitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.

Boson Inverse Operators and a New Family of Two-photon Annihilation Operators

We introduce the inverse of the Hermitian operator (acircacirc†) and express the Boson inverse operators acirc-1 and acirc†-1 in terms of the operators acirc, acirc† and (acircacirc†)-1. We show that these Boson inverse operators may be realized by Susskind-Glogower phase operators. In this way, we find a new two-photon annihilation operator and denote it as acirc2(acircacirc†)-1. We show that the eigenstates of this operator have interesting non-classical properties. We find that the eigenstates of the operators (acircacirc†)-1 acirc2, acirc(acircacirc†)-1 acirc and acirc2(acircacirc†)-1 have many similar properties and thus they constitute a family of two-photon annihilation operators.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

Optical phase conjugation by two-wave mixing in iron-doped lithium niobate

A novel technique to generate forward phase conjugate wave by two-wave mixing (TWM) in photorefractive iron-doped lithium niobate crystal has been demonstrated. An optical beam from a positive transparency was forward phase conjugated by TWM technique. The experimental scheme was then extended to a specific interferometric application.

Some Algorithms for Eigensubspace Estimation

An important tool in signal processing is the use of eigenvalue and singular value decompositions for extracting information from time-series/sensor array data. These tools are used in the so-called subspace methods that underlie solutions to the harmonic retrieval problem in time series and the directions-of-arrival (DOA) estimation problem in array processing. The subspace methods require the knowledge of eigenvectors of the underlying covariance matrix to estimate the parameters of interest. Eigenstructure estimation in signal processing has two important classes: (i) estimating the eigenstructure of the given covariance matrix and (ii) updating the eigenstructure estimates given the current estimate and new data. In this paper, we survey some algorithms for both these classes useful for harmonic retrieval and DOA estimation problems. We begin by surveying key results in the literature and then describe, in some detail, energy function minimization approaches that underlie a class of feedback neural networks. Our approaches estimate some or all of the eigenvectors corresponding to the repeated minimum eigenvalue and also multiple orthogonal eigenvectors corresponding to the ordered eigenvalues of the covariance matrix. Our presentation includes some supporting analysis and simulation results. We may point out here that eigensubspace estimation is a vast area and all aspects of this cannot be fully covered in a single paper. (C) 1995 Academic Press, Inc.

Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

MIMO Precoding With X- and Y- Codes

We consider a slow fading multiple-input multiple-output (MIMO) system with channel state information at both the transmitter and receiver. A well-known precoding scheme is based upon the singular value decomposition (SVD) of the channel matrix, which transforms the MIMO channel into parallel subchannels. Despite having low maximum likelihood decoding (MLD) complexity, this SVD precoding scheme provides a diversity gain which is limited by the diversity gain of the weakest subchannel. We therefore propose X- and Y-Codes, which improve the diversity gain of the SVD precoding scheme but maintain the low MLD complexity, by jointly coding information across a pair of subchannels. In particular, subchannels with high diversity gain are paired with those having low diversity gain. A pair of subchannels is jointly encoded using a 2 2 real matrix, which is fixed a priori and does not change with each channel realization. For X-Codes, these rotation matrices are parameterized by a single angle, while for Y-Codes, these matrices are left triangular matrices. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but with encoding matrices adapted to each channel realization. We observed that X-Codes/Precoders are good for well-conditioned channels, while Y-Codes/Precoders are good for ill-conditioned channels.

Lasing in active, sub-mean-free path-sized systems with dense, random, weak scatterers

We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent: with experimentally observed features. (C) 1997 Optical Society of America.

Exact complex-wave reconstruction in digital holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique. (C) 2011 Optical Society of America

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Non-interferometric methods of phase estimation for application in optical tomography

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.

Wavelet based compression and denoising of optical tomography data

Two methods based on wavelet/wavelet packet expansion to denoise and compress optical tomography data containing scattered noise are presented, In the first, the wavelet expansion coefficients of noisy data are shrunk using a soft threshold. In the second, the data are expanded into a wavelet packet tree upon which a best basis search is done. The resulting coefficients are truncated on the basis of energy content. It can be seen that the first method results in efficient denoising of experimental data when scattering particle density in the medium surrounding the object was up to 12.0 x 10(6) per cm(3). This method achieves a compression ratio of approximate to 8:1. The wavelet packet based method resulted in a compression of up to 11:1 and also exhibited reasonable noise reduction capability. Tomographic reconstructions obtained from denoised data are presented. (C) 1999 Published by Elsevier Science B.V. All rights reserved,

Precoding with X-codes to increase capacity with discrete input alphabets

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on X-Codes in to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and the 2 × 2 real rotation matrices for each pair (parameterized with a single angle). This precoding structure enables to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is equivalent to i) optimizing the rotation angle and the power allocation within each pair and ii) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz et al., and significantly better than mercury/waterfilling strategy by Lozano et al.. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.