Low-frequency sound propagation modeling over a locally-reacting boundary using the parabolic approximation

There is substantial interest in the analytical and numerical modeling of low-frequency, long-range atmospheric acoustic propagation. Ray-based models, because of frequency limitations, do not always give an adequate prediction of quantities such as sound pressure or intensity levels. However, the parabolic approximation method, widely used in ocean acoustics, and often more accurate than ray models for lower frequencies of interest, can be applied to acoustic propagation in the atmosphere. Modifications of an existing implicit finite-difference implementation for computing solutions to the parabolic approximation are discussed. A locally-reacting boundary is used together with a one-parameter impedance model. Intensity calculations are performed for a number of flow resistivity values in both quiescent and windy atmospheres. Variations in the value of this parameter are shown to have substantial effects on the spatial variation of the acoustic signal

Geometric phases in astigmatic optical modes of arbitrary order

The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different order, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of non-astigmatic optical modes with orbital angular momentum states in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights in the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schr\"odinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.Comment: final versio

Mechanism of Catch Force: Tethering of Thick and Thin Filaments by Twitchin

Catch is a mechanical state occurring in some invertebrate smooth muscles characterized by high force maintenance and resistance to stretch during extremely slow relaxation. During catch, intracellular calcium is near basal concentration and myosin crossbridge cyctng rate is extremely slow. Catch force is relaxed by a protein kinase A-mediated phosphorylation of sites near the N- and C- temini of the minititin twitchin (~526 kDa). Some catch force maintenance car also occur together with cycling myosin crossbridges at submaximal calcium concentrations, but not when the muscle is maximally activated. Additionally, the link responsible for catch can adjust during shortening of submaximally activated muscles and maintain catch force at the new shorter length. Twitchin binds to both thick and thin filaments, and the thin filament binding shown by both the N- and Cterminal portions of twitchin is decreased by phosphorylation of the sites that regulate catch. The data suggest that the twitchin molecule itself is the catch force beanng tether between thick and thin filaments. We present a model for the regulation of catch in which the twitchin tether can be displaced from thin filaments by both (a) the phosphorylation of twitchin and (b) the attachment of high force myosin crossbridges

Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity

We present, to the best of our knowledge, the first exact dark spatial solitons of a nonlinear Helmholtz equation with a self-defocusing saturable refractive-index model. These solutions capture oblique (arbitrary-angle) propagation in both the forward and backward directions, and they can also exhibit a bistability characteristic. A detailed derivation is presented, obtained by combining coordinate transformations and direct-integration methods, and the corresponding solutions of paraxial theory are recovered asymptotically as a subset. Simulations examine the robustness of the new Helmholtz solitons, with stationary states emerging from a range of perturbed input beams

Discrete diffraction and shape-invariant beams in optical waveguide arrays

General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws describing beam spreading, beam decay and discrete far-field patterns in homogeneous arrays are derived using the method of moments and the steepest descend method. In curved arrays, the method of moments is extended to describe evolution of global beam parameters. A family of beams which propagate in curved arrays maintaining their functional shape -referred to as discrete Bessel beams- is also introduced. Propagation of discrete Bessel beams in waveguide arrays is simply described by the evolution of a complex $q$ parameter similar to the complex $q$ parameter used for Gaussian beams in continuous lensguide media. A few applications of the $q$ parameter formalism are discussed, including beam collimation and polygonal optical Bloch oscillations. \Comment: 14 pages, 5 figure

Verifying continuous variable entanglement of intense light pulses

Three different methods have been discussed to verify continuous variable entanglement of intense light beams. We demonstrate all three methods using the same set--up to facilitate the comparison. The non--linearity used to generate entanglement is the Kerr--effect in optical fibres. Due to the brightness of the entangled pulses, standard homodyne detection is not an appropriate tool for the verification. However, we show that by using large asymmetric interferometers on each beam individually, two non-commuting variables can be accessed and the presence of entanglement verified via joint measurements on the two beams. Alternatively, we witness entanglement by combining the two beams on a beam splitter that yields certain linear combinations of quadrature amplitudes which suffice to prove the presence of entanglement.Comment: 11 pages, 7 figures, to appear in Phys. Rev.

Rotationally induced vortices in optical cavity modes

We show that vortices appear in the modes of an astigmatic optical cavity when it is put into rotation about its optical axis. We study the properties of these vortices and discuss numerical results for a specific realization of such a set-up. Our method is exact up to first order in the time-dependent paraxial approximation and involves bosonic ladder operators in the spirit of the quantum-mechanical harmonic oscillator.Comment: 8 pages, 5 figures. Accepted for publication in a special issue (singular optics 2008) of Journal of Optics A: Pure and Applied Optic

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Orbital angular momentum exchange in an optical parametric oscillator

We present a study of orbital angular momentum transfer from pump to down-converted beams in a type-II Optical Parametric Oscillator. Cavity and anisotropy effects are investigated and demostrated to play a central role in the transverse mode dynamics. While the idler beam can oscillate in a Laguerre-Gauss mode, the crystal birefringence induces an astigmatic effect in the signal beam that prevents the resonance of such mode.Comment: 10 pages, 8 figures, regular articl

Coherent Diffusion of Polaritons in Atomic Media

Coherent diffusion pertains to the motion of atomic dipoles experiencing frequent collisions in vapor while maintaining their coherence. Recent theoretical and experimental studies on the effect of coherent diffusion on key Raman processes, namely Raman spectroscopy, slow polariton propagation, and stored light, are reviewed in this Colloquium.Comment: Submitted to Review of Modern Physic