Rytov variance equivalence through extended atmospheric turbulence and an arbitrary thickness phase screen in non-Kolmogorov turbulence

An arbitrary thickness phase screen model can describe scintillation index for Gaussian beam propagating through a phase screen more accurate than thin phase screen model. To describing actual scintillation index for Gaussian beam propagating through an extended medium using a phase screen in weak non-Kolmogorov turbulence, the scintillation index and Rytov variance for arbitrary thickness phase screen model are derived. Specially, the ratio of the Rytov variances for a phase screen and extended random media is found under the assumption of equivalence in scintillation index of the two cases. The theoretical results show that the normalized Rytov variance varies with the power law of the turbulence spectrum, the relative thickness of the phase screen, the position of the phase screen, the transmitter beam parameters and the radial position at output plane. The influences of these variables are also simulated. These results will be applied to simulation of adaptive optics and laser communication.     

Statistical characteristics of an intense wave behind a two-dimensional phase screen

An analysis of the parameters of nonlinear waves transmitted through a layer of a randomly inhomogeneous medium is carried out. The layer is modeled by a two-dimensional phase screen. Passing through the screen plane, the wave acquires a random phase shift. The wave front becomes distorted, and randomly located regions of ray convergence and divergence are formed, in which the nonlinear evolution of the wave alters profoundly. The problem is solved in the approximation of geometrical acoustics. The ray pattern of a plane wave transmitted through the regular screen is constructed. The solution that describes the spatial structure of the field and the evolution of an arbitrary temporal wave profile behind the screen is obtained. Statistical characteristics of the discontinuity amplitude are calculated for different distances from the screen. A random modulation is shown to result in a faster (in comparison with the case of a homogeneous medium) nonlinear attenuation of the wave and in the smoothing of the shock profile. The distribution function of the wave field parameters becomes broader because of random focusing effects.     

The mutual coherence function and the backscatter amplification effect for a reflected Gaussian-beam wave in atmospheric turbulence

The influence of a modified spectrum of refractive-index fluctuations (that includes a high wavenumber rise as well as inner- and outer-scale parameters) on the backscatter amplification effect, arising from double passage of an optical wave through statistically dependent inhomogeneities of a random medium, is studied for the case of a Gaussian-beam wave reflected by a mirror of finite size. A formal expression is first developed for the mutual coherence function, which subsequently leads to tractable analytic models for the mean irradiance in the strictly backward direction. When the inner scale and Fresnel zone are of comparable size, the modified spectrum predicts significantly larger values of the enhancement factor than predicted by the Kolmogorov power-law spectrum. It is also shown in this analysis that by varying the focal length of the mirror the enhancement effects can be greater or less than those of a plane mirror, depending on focus adjustment. All calculations are based on weak irradiance fluctuations using complex ABCD ray-matrix representations for the propagation channel and a generalized spectral representation theory for the complex phase perturbations.     

Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.     

Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

Abstract

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Zur Beugung an öffnungen in nichtebenen Schirmen

By means of an approximate method formerly published by this author, diffraction by an aperture in a screen, which is not plane, is discussed. For the special case of a circular aperture in a funnel-shaped screen, the diffraction field on the axis behind the screen is computed for an incident scalar plane wave (different boundary conditions) and for an incident electromagnetic plane wave propagating in the direction of the axis.     

Two-dimensional temporal coherence coding for super resolved imaging

In this paper, we present an approach that can be used for transmission of 2D spatial information through space-limited systems capable of transmitting even only a single spatial pixel. The input 2D object is illuminated with temporally incoherent illumination. The axial coherence length is very short and it equals only a few microns. Attached to the input object spatial random phase mask generates different axial shift for every pixel of the input. The temporal delays of the encoding (axial shifts) of every pixel are longer than the coherence length of the illuminating source. Therefore no temporal correlation exists between the various pixels of the input. A lens combines all spatial pixels into one point at its focal plane. Although the various spatial pixels were mixed together, since the random mask provided axial delay which was larger than the coherence length of the light source, the orthogonality between the spatial content of every pixel is preserved. The decoding system includes a lens that is positioned at the output of the resolution reduction system and it converts the output light into a plane wave containing all the spatial information of the original image mixed together in all of its pixels. By interfering this plane wave with the same plane wave after passing through the same random spatial coding mask, the spatial information of every pixel of the input object is recovered.     

Image encryption based on extended fractional Fourier transform and digital holography technique

We present a new optical image encryption algorithm that is based on extended fractional Fourier transform (FRT) and digital holography technique. We can perform the encryption and decryption with more parameters compared with earlier similar methods in FRT domain. In the extended FRT encryption system, the input data to be encrypted is extended fractional Fourier transformed two times and random phase mask is placed at the output plane of the first extended FRT. By use of an interference with a wave from another random phase mask, the encrypted data is stored as a digital hologram. The data retrieval is operated by all-digital means. Computer simulations are presented to verify its validity and efficiency.     

Plane wave propagation in a uniaxial bianisotropic medium with an application to a polarization transformer

Uniaxial bianisotropic medium is a generalization of the well-studied bi-isotropic and chiral media. It is obtained, for example, when microscopic helices with parallel axes are positioned in a host dielectric in random locations. Plane wave propagation in such a medium is studied and a simple solution for the dispersion equation and for the eigenwaves are found. As a numerical example, polarization properties of a transverse wave propagating in a uniaxial bianisotropic medium is considered. The results give a simple possibility to construct a polarization transformer with a transversely uniaxial chiral medium for changing the polarization of a propagating plane wave.     

Theory of optical scintillation: Gaussian-beam wave model

Abstract

A scintillation model previously developed by the authors is extended in this paper to the case of a propagating Gaussian-beam wave. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. Unlike the previous model, in this paper we include the effect of a finite outer scale in addition to the inner scale. With a finite outer scale, the scintillation index can be substantially lower in strong turbulence than that predicted by a model with an infinite outer scale. This particular behaviour of scintillation in strong turbulence, mostly associated with horizontal paths near the ground, cannot be explained on the basis of previous expressions deduced from the asymptotic theory. Comparisons of the scintillation models with published experimental and simulation data through weak and strong irradiance fluctuations show excellent fits.     

Driven spin wave modes in XY ferromagnet: non-equilibrium phase transition

The dynamical responses of XY ferromagnet driven by linearly polarised propagating and standing magnetic field wave have been studied by Monte Carlo simulation in three dimensions. In the case of propagating magnetic field wave (with specified amplitude, frequency and the wavelength), the low temperature dynamical mode is a propagating spin wave and the system becomes structureless (or random) in the high temperature. A dynamical symmetry breaking phase transition is observed at a finite (non-zero) temperature. This symmetry breaking is confirmed by studying the statistical distribution of the angle of the spin vector. The dynamic non-equilibrium transition temperature was found to decrease as the amplitude of the propagating magnetic field wave increased. A comprehensive phase boundary is drawn in the plane formed by temperature and amplitude of propagating field wave. The phase boundary was observed to shrink (in the low temperature side) for longer wavelength of the propagating magnetic wave. In the case of standing magnetic field wave, the low temperature excitation is a standing spin wave which becomes structureless (or random) in the high temperature. Here also, like the case of propagating magnetic wave, a dynamical symmetry breaking non-equilibrium phase transition was observed. A comprehensive phase boundary was drawn. Unlike the case of propagating magnetic wave, the phase boundary does not show any systematic variation with the wavelength of the standing magnetic field wave. In the limit of vanishingly small amplitude of the field, the phase boundaries approach the recent Monte Carlo estimate of equilibrium transition temperature.     

Reference-wave solutions for the high-frequency fields in inhomogeneous-background random media

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is therefore desirable to have a solution for the high-frequency field propagating along an isolated ray trajectory. A new reference wave is applied to obtain an analytic solution of the parabolic wave equation that describes propagation along the ray trajectory of the deterministic-background medium. The methodology is based on defining a paired-field measure as a product of an unknown field propagating in a disturbed medium and the complex-conjugate component propagating in a medium without random fluctuations. When a solution of the equation for the paired-field measure is obtained, the solution of the deterministic component can be extracted from the paired solution to determine the solution of the unknown field in an explicit form.     

高功率激光系统随机相位屏的特性研究

 高功率激光系统中随机相位屏的统计模型出发,分析了其相位噪声及梯度的一阶和二阶统计性质。研究了完全相干光与部分相干光通过随机相位屏后的传输性质,推导得出部分相干光在经过随机相位屏后,其交叉谱密度的期望等于随机相位屏透过率函数的期望与入射光交叉谱密度的乘积。对该模型下的远场分布进行了数值模拟。结果显示,能量对称分布的完全相干光通过相位干屏后,只有通过随机相位屏透过率函数期望的远场分布是对称的;部分相干光在传输通过随机相位屏后,其谢尔模光束性质不会改变,但光强分布不再具有对称性,且强度明显降低。     

Transverse vibration of a moving strip

Conditions are established for the generation of a wave pattern with stationary nodes by the superposition of plane waves propagating in a uniformly moving medium. These conditions are then used to derive a closed form expression for the natural frequencies and modes of vibration of a thin strip moving between fixed guides with zero tension and to define an algorithm to determine the natural frequencies and modes of vibration for a wide range of problems of a similar type. The thin strip under tension is used as an example.     

Total reflection in a uniaxial crystal–uniaxial crystal interface

Considering an interface between two uniaxial birefringent crystals, four reflected and four refracted waves for each incidence direction are obtained. Along this direction can propagate an ordinary wave and an extraordinary wave. Here, we present the analytic expressions for the four critical angles, from which each refracted wave no more exists as propagating wave. We show the variation in these critical angles for different interfaces varying the orientation of the incidence plane with respect to the optical axes. When both principal refractive indices of the second medium are smaller than those of the first medium, then the four critical angles exist for each incidence plane and for any direction of the optical axes. But, when one of the indices has an intermediate value between the values of the indices of the other crystal, we can chose the optical axes directions in such a way that certain critical angles do not exist. Therefore, we can select the refracted wave that is eliminated by total reflection.     

Two-dimensional wave propagation in a rotating elastic solid with voids

Two-dimensional wave propagation is studied in an isothermal linear isotropic elastic material with voids rotating with constant angular velocity based on a theory of elastic material with voids developed by Ie?an (1986) in the thermoelastic context. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The presence of voids and the rotation of the medium are responsible for this coupling. In the absence of voids, the classical longitudinal and transverse waves are found to be coupled through the rotation of the medium. At very large frequency or when the angular rotation is very small relative to the wave frequency the waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave, (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The first two correspond to the waves of classical elasticity, while the third is new and arises from the presence of the voids. The results are illustrated graphically.     

Fresnel light drag in a coherently driven moving medium

We theoretically study how the phase of a light plane wave propagating in a resonant medium under electromagnetically induced transparency (EIT) is affected by the uniform motion of the medium. For cuprous oxide (Cu2O), where EIT can be implemented through a typical pump-probe configuration, the resonant probe beam experiences a phase shift (Fresnel-Fizeau effect) that may vary over a wide range of values, positive or negative, and even vanishing, due to the combined effects of the strong frequency dispersion and anisotropy both induced by the pump. The use of such a coherently driven dragging medium may improve by at least 1 order of magnitude the sensitivity at low velocity in optical drag experiments.     

Simulation of extended phase screens in problems of optical wave propagation through the atmosphere

Turbulent medium in problems of optical wave propagation through the atmosphere is usually nodeled as a set of statistically independent plane screens with a random two-dimensional field of phase progress. In this paper, we develop methods for the formation of nonperiodic phase screens infinitely extended in a certain direction, which are required in problems of dynamic simulation of wave propagation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 21–34, January 2006.