Transverse spectra of waves in random media

Abstract

We consider the statistics of the transverse spectra of forward-propagating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the long-range evolution of the ensemble-averaged transverse wave spectrum and coherence. The conditions under which these equations may be approximated by differential and integro-differential equations are given, and it is shown that the approximation is valid for the treatment of beam propagation provided that the transverse dimension of the beam is sufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenable to numerical solution by marching techniques. We use the equation that governs the spectral density of the total energy flux, and also the propagation of waves which are statistically homogeneous in transverse planes, to show the conditions under which previously studied approximations derive from the present formulation, and to illustrate the numerical solution of the problem.     

非相干空间孤子的自陷行为

用相干密度法研究了一维非相干光束在饱和对数型光折变介质中的自陷行为,发现在传输过程中孤子的形态可具有稳态和周期性振荡的特点,具体取决于入射光束的初始宽度、相干特性和材料的非线性响应;研究了构成非相干光束的相干组份的传播行为,发现各相干组份的强度和光束宽度沿纵向发生周期性变化,峰值位置沿横向发生周期性变化.另外,利用横向相干宽度研究了非相干光束在各种传输状态下相干特性的变化,从而进一步解释了非相干光束在不同传播状态下的演化特性.     

Transverse Wave Propagation in Relativistic Two-Fluid Plasmas around Schwarzschild-de Sitter Black Hole

We investigate transverse electromagnetic waves propagating in a plasma influenced by the gravitational field of the Schwarzschild-de Sitter black hole. Applying 3+1 spacetime split we derive the relativistic two-fluid equations to take account of gravitational effects due to the event horizon and describe the set of simultaneous linear equations for the perturbations. We use a local approximation to investigate the one-dimensional radial propagation of Alfvén and high frequency electromagnetic waves. We derive the dispersion relation for these waves and solve it for the wave number k numerically.     

Transverse wave propagation in relativistic two-fluid plasmas in de Sitter space

We investigate transverse electromagnetic waves propagating in a plasma near the horizon of the de Sitter space. Using the 3+1 formalism we derive the relativistic two-fluid equations to take account of the effects due to the horizon and describe the set of simultaneous linear equations for the perturbations. We use a local approximation to investigate the one-dimensional radial propagation of Alfvén and high frequency electromagnetic waves and solve the dispersion relation for these waves numerically.     

Transverse Wave Propagation in Relativistic Two-Fluid Plasmas around Reissner–Nordström Black Hole

We investigate transverse electromagnetic waves propagating in a plasma influenced by the gravitational field of the Reissner–Nordström black hole. Applying 3+1 spacetime split we reformulate the relativistic two-fluid equations to take account of gravitational effects due to the event horizon and describe the set of simultaneous linear equations for the perturbations. Using a local approximation we investigate the one-dimensional radial propagation of Alfvén and high frequency electromagnetic waves. We derive the dispersion relation for these waves and solve it for the wave number k numerically.     

A criterion for the existence of spin waves in polarized gases in a wide temperature range

We derive a kinetic equation for a polarized paramagnetic gas that is exact in the Boltzmann (binary) approximation. The equation is written in a compact form and applies to both Fermi and Bose gases in a wide temperature range as long as the Boltzmann approximation remains applicable. The derived equation is used to analyze the conditions for the propagation of spin waves in polarized Fermi and Bose gases. We deduce a universal criterion for the propagation of weakly damped spin waves in a wide temperature range. The criterion is reduced to the condition that the real parts of the particle zero-angle scattering amplitudes (or T matrices) be much larger than their imaginary parts. We derive dispersion equations for spin waves at high and low gas temperatures and show that spin waves can propagate in both these limiting cases.     

Propagation of a twisted anisotropic Gaussian Schell-model beam beyond the paraxial approximation

With the help of a tensor method, an analytical nonparaxial propagation formula for a twisted anisotropic Gaussian Schell-model (GSM) beam in free space is derived based on the generalized Raleigh-Sommerfeld diffraction integral. The far-field nonparaxial propagation expression for a twisted anisotropic GSM beam is also derived. The paraxial approximation is dealt with as a special case of our general result. Our numerical results show that the nonparaxial propagation properties of a twisted anisotropic GSM beam are closely related to the initial beam parameters (i.e., twist factor, transverse spot width matrix, coherence width matrix and wavelength) and the propagation distance. Our formulae provide a convenient and powerful way for studying the paraxial and nonparaxial propagation of an isotropic or anisotropic GSM beam with or without twist phase in free space.     

The coherence of low-frequency sound in shallow water in the presence of internal waves

The coherence time and transverse coherence length of a low-frequency (100–300 Hz) sound field that is formed by an omnidirectional point source at a distance of 10–30 km in a shallow-water acoustic waveguide, which is characteristic of an open ocean shelf, were estimated analytically and in a numerical experiment. An anisotropic field of background internal waves is considered as a source of spatiotemporal fluctuations. It is shown that the coherence time decreases as the frequency increases, and strongly depends on the perturbation-movement direction. The transverse coherence length is primarily determined by phase incursions that are related to the cylindrical shape of the acoustic-wave front. In the case of transverse propagation, background internal waves may lead to significant variations in this length. The introduction of compensating phase corrections during processing provides a considerable increase in the average transverse coherence length.     

Transverse envelope solutions in an atomic chain

We derive a set of discrete nonlinear equations for transverse waves in an atomic chain under longitudinal stress. Circularly and linearly polarized envelope solitons are obtained, numerical simulations are used to check the stability and the collisions.     

Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.     

相干与非相干激光成丝不稳定性的数值模拟研究

利用二维三温磁流体力学激光靶程序（ＣＡＳＴＯＲ）数值模拟了相干光和诱导空间非相干（ｉｎｄｕｃｅｄ ｓｐａｔｉａｌ ｉｎｃｏｈｅｒｅｎｃｅ ＩＳＩ）光的成丝不稳定性．用求解激光传播方程和简化流体模型的方法研究了随机相位板（ｒａｎｄｏｍ ｐｈａｓｅ ｐｌａｔｅ ＲＰＰ）光滑化技术对成丝不稳定性的影响，结果表明ＩＳＩ和ＲＰＰ去相干方法可以有条件地减弱或抑制成丝不稳定性． 关键词：     

Volume Fresnel reflection of electromagnetic waves in three-dimensionally inhomogeneous media

Eikonal approximation is used to derive equations describing propagation of monochromatic electromagnetic waves in a three-dimensionally inhomogeneous medium, including volume Fresnel reflection from inhomogeneities. The analysis is based on a locality principle. Separation into reflection and transmission effects is performed. The former effects are found to be isotropic, whereas the latter are anisotropic and depend on interference phenomena. Interference effects lead to violation of the Rytov law of polarization rotation. Brewster phenomena in layered and three-dimensionally inhomogeneous media are shown to occur under different conditions.     

Spatial optical solitons in inhomogeneous elliptic core saturating nonlinear fiber

We have investigated the propagation characteristics of spatial optical solitons in saturating nonlinear waveguide employing JWKB and paraxial ray approximation. We have obtained two second-order coupled nonlinear differential equations for transverse soliton widths of solitons. Threshold power for stable propagation of the beam has been calculated from these coupled equations. We have undertaken stability analysis, which predicts robustness of these solitons. Both guiding as well as antiguiding cases have been considered and shown that stable spatial soliton propagation is possible in both cases.     

Bragg-induced oscillations in non-PT complex photonic lattices

We investigate Bragg-induced oscillations in complex non-PT periodic structures, that is, a periodic medium with gain and loss and not necessarily symmetric under the combined action of parity and time reversal operations. We compare our analytic results based on the expansion of the optical field in Bragg-resonant plane waves with a direct numerical integration of the paraxial wave equation beyond the shallow potential approximation and using a wide Gaussian beam as initial condition. In particular, we study under which conditions a mode trapping phenomenon may still be observed and to inspect how the energy exchange between the spectral modes takes place during propagation in this more general class of asymmetric complex potentials.     

Longitudinal Wave Propagation in Relativistic Two-Fluid Plasmas Around Reissner-Nordström Black Hole

The 3+1 spacetime formulation of general relativity is used to investigate the transverse waves propagating in a plasma influenced by the gravitational field of Reissner-Nordström black hole, as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here, a local approximation is used to investigate the one-dimensional radial propagation of longitudinal waves. We derive the dispersion relation for these waves and solve it numerically for the wave number k.     

Pulse propagation of acoustic waves scattered in a channel

When acoustic waves are scattered by random sound-speed fluctuations in a two-dimensional channel the energy is continually transferred between the propagating modes. In the multiple- scattering region the energy flux assumes an asymptotic form in which there is equal energy flux propagating in each mode. Here we shall make use of this well known result to show how to obtain an asymptotic form for a pulse of acoustic energy propagating in the channel. In the multiple-scattering region the speed of the acoustic waves in the pulse continually changes as the energy is transferred between the modes. The process is basically a diffusion process around the mean speed of propagation. We shall first show, using physical arguments, that the diffusion coefficient is proportional to the square root of the propagation distance times the mean free path of scattering. The theory governing the acoustic propagation in the channel is formulated in terms of modal coherence equations and we shall next give a brief review of the definitions of the coherence functions and a discussion of how the equations governing the propagation of the modal coherence functions are derived. We shall then show how the pulse shape and the relevant parameters may be obtained by solving the basic modal coherence equations at large propagation distances.     

非傍轴高斯光束传输方程解的探讨

由洛伦兹规范下光场满足的矢势和标势方程出发, 探讨了初始光场具有任意对称性的一般非傍轴光束在空间的传输情况。利用角频谱并结合傅里叶变换处理得到了非傍轴光束的传输方程。利用扰动方法并结合新近似取法得到了非傍轴横向光场的扰动形式解, 该解对于近场弱非傍轴情况下的效果比强非傍轴条件下要好。给出了光束非傍轴传输高阶(八阶)修正解。对于零阶情况, 非傍轴光束退化为傍轴光束, 传输方程也相应退化为傍轴传输的模型方程。高斯解为扰动参量的零阶修正解。     

Application of the Green functions to the problem of the thermally induced vibration of a beam

This paper considers the problem of the transverse vibrations of a beam induced by a mobile heat source. The formulation of the problem is based on the differential equations of heat conduction and transverse vibrations of the beam, which are complemented by suitable initial and boundary conditions. The effect of internal and external damping on the vibrations of the beam is considered. The solution to the problem in analytical form is obtained by using the properties of the Green functions. A time partitioning method has been used to avoid the difficulties associated with the slow convergence of the series occurring in the solution to the heat conduction problem. The numerical results of the thermally induced vibration of the beam are presented.     

Transverse instability of optical spatiotemporal solitons in quadratic media

We present experimental and numerical observations of transverse instability in quadratic media under conditions that emphasize the inherently spatiotemporal and multidimensional nature of the wave propagation. Intensity-dependent beam filamentation is shown to be closely connected to the periodic evolution of quadratic solitons, and implications for the generation of three-dimensional spatiotemporal solitons are discussed.