Long-distance propagation of pseudo-partially coherent Gaussian Schell-model beams in atmospheric turbulence

Propagation properties of spatially pseudo-partially coherent Gaussian Schell-model beams through the atmo- spheric turbulence over a long-distance uplink path are studied by numerical simulation. A linear coordination trans-formation is introduced to overcome the window effect and the loss-of-resolution problem. The beam spreading, beam wandering, and intensity scintillation as functions of turbulence strength, source correlation length, and change frequency of random phase that models the partial coherence of the source are analyzed. It is found that the beam spreading and the intensity scintillation of the partially coherent beam are less affected by the turbulence than those of the coherent one, but it suffers from a more severe diffractive effect, and the change frequency of random phase has no evident influence on it. The beam wandering is insensitive to the variation of source correlation length, and decreases firstly then goes to a fixed value as the change frequency increases.     

用零相关相位板匀滑散斑的理论研究

对零相关相位板匀滑散斑的特性进行了理论分析和散值计算,结果表明尽管零相关相位板是针对入射场为平面波面而设计的,但在入射场的振幅和相位有一定起伏的情况下,其远场光斑的散斑对比度明显低于采用随机相位板的情形.因而用零盯关相位板匀滑散斑是一种更为有效的方法.     

Energy loss of a fast-electron beam due to the excitation of collective oscillation in hot plasma

Energy loss due to a fast-electron beam interacting with the hot plasma at a high density is analysed theoretically. By splitting the particle density fluctuations into the individual part due to the random thermal motion of the individual electrons and the collective part due to plasma－wave excitation, we are concerned with the collective interaction of the relativistic plasma electrons resulting from the Coulomb interactions. Consequently, we derive the frequency of the hot plasma and the "Debye length" with the modification of the relativistic effect. And finally we calculate the energy loss of a fast-electron beam due to the excitation of collective oscillation in the hot plasma.     

Microscopic Theory of the Two-Dimensional Quantum Antiferromagnet in a Paramagnetic Phase

We have developed a consistent theory of the Heisenberg quantum antiferromagnet in the disordered phase with a short range antiferromagnetic order on the basis of the path integral for spin coherent states. In the framework of our approach we have obtained the response function for the spin fluctuations for all values of the frequency ω and the wave vector k and have calculated the free energy of the system. We have also reproduced the known results for the spin correlation length in the lowest order in 1/N. We have presented the Lagrangian of the theory in a form which is explicitly invariant under rotations and found natural variables in terms of which one can construct a natural perturbation theory. The short wave spin fluctuations are similar to those in the spin wave theory and they are on the order of the smallness parameter 1/2s where s is the spin magnitude. The long-wave spin fluctuations are governed by the nonlinear sigma model and are on the order of the smallness parameter 1/N, where N is the number of field components. We also have shown that the short wave spin fluctuations must be evaluated accurately and the continuum limit in time of the path integral must be performed after the summation over the frequencies ω.     

Interferometric study of phase fluctuations of laser radiation

An interferometric method is proposed for studying the phase fluctuations of laser radiation during propagation in media with random inhomogeneities. It differs from other methods in that the beam is split into two by the first mirror of a Jamin interferometer before the beam enters the medium. The visibility of the intereference pattern is related functionally to the correlation coefficient of the amplitude fluctuations and the structure function of the phase fluctuations. Results found in an experimental study of phase fluctuations by this method are reported.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 103–108, November, 1970.     

Wave beam tremble within an absorbing random medium with lens properties

The present paper investigates the joint influence of fluctuations of the complex dielectric constant, ε, of a medium and its lens properties on random displacements of a radiation beam. Based on a non-traditional approach, an expression is obtained for the variance of the beam energy centre tremble, σ²_ρ, taking into account the contribution of fluctuations of the real and imaginary parts of ε, as well as that of their correlations. It was shown that the influence of fluctuations of the imaginary part of ε is particularly pronounced in the initial section of the path, as well as in paths of great length. Due to regular refraction, a considerable enhancement of the dependence of σ²_ρ upon the path length occurs, with the greatest contribution being made by fluctuations of the imaginary part of the dielectric constant. A positive correlation of random changes of the real and imaginary parts of ε was shown to result in a partial compensation of the beam tremble.     

Collinear interaction of optical waveguide modes with an increasing space-charge wave

Collinear interaction of optical modes in a thin-film semiconductor waveguide with a space-charge wave increasing along its propagation direction has been investigated. Analytical solutions to the equations of coupled unidirectional and counterpropagating waveguide modes at their phase matching are obtained for the first time, and the dependence of the mode conversion efficiency on the space-charge wave amplification level, the coupling coefficient, and the length of the interaction region of optical modes is analyzed.     

Suppressing amplitude fluctuations of the wave propagating in a randomly inhomogeneous medium

We suggest using spatial processing of the wave field with the aid of the double (in source and observer coordinates) weighted Fourier transform (DWFT) to suppress amplitude fluctuations (amplitude scintillations) during wave propagation in a randomly inhomogeneous medium. We examine the influence of sizes of receiving and transmitting antenna systems on the efficiency of the spatial processing in suppressing scintillations for both weak and strong intensity fluctuations. We demonstrate that the efficiency of the suppression of amplitude fluctuations by the inverse DWFT depends on the excess of sizes of fan beam projections of receiving and transmitting antenna systems over the Fresnel radius in a region with irregularities.     

Propagation of a Gaussian-beam wave through a random phase screen

Tractable analytic expressions are developed for a variety of basic statistical quantities involving a Gaussian-beam wave propagating through a random medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, it is well known that the statistics in the receiver plane are in close agreement with those associated with a plane wave propagating through an extended random medium between input and output planes. For a similar comparison between a phase screen and extended turbulence in the case of a Gaussian-beam wave at the input plane, the present analysis reveals that the phase screen must be positioned between input and output planes differently from the plane-wave case, the position being dependent upon the Fresnel ratio of the Gaussian beam. The analytic results developed in this paper for the thin phase screen model are based on the Kolmogorov power-law spectrum for refractive-index fluctuations and the Rytov approximation. Extension of these results to multiple phase screens is also discussed.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Measurement of the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame by means of a laser-based interferometer technique

With a view to measuring the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame, a thin laser beam is sent into the flame perpendicular to the flow direction. The laser beam generally undergoes fluctuations of direction, phase, and amplitude. Only the random deflections of the laser beam may be taken into account. After having traversed the flame, the perturbed laser beam enters into an interferometric system. Materials and experimental procedure are described. In the unperturbed interference pattern, the zones only sensitive to fluctuations of the angle-of-arrival of the laser beam are detected. From the random displacements of the central bright fringe, the structure coefficient of refractive index fluctuations in the flame is measured. To prove that the method of measurement is satisfactory, the result obtained is applied for computing the power spectral density of the angle-of-arrival of the laser beam from the formula of correlations of the laser beam deflection angles which we have demonstrated in previous works. This computed power spectral density is compared to that measured from the effective position of the detector. A good agreement is observed between the two results.     

快波模式转换效率的理论分析和数值模拟

利用相位积分法, 在传统的布登模型基础上, 考虑了高场侧截止层的影响, 构建了三体模型, 求出了快波通过单一衰减层的传输系数、反射系数和模式转换系数. 在双离子情况下, 模拟的结果与Kazakov等人的结果相符合. 针对EAST实验, 将双离子模型推广至三离子模型, 分析了不同相位、少子浓度、频率和纵场强度对快波模式转换效率的影响, 为未来离子回旋加热实验提供参考. 关键词： 模式转换加热 离子回旋波加热 相位积分     

Scattering losses from planar waveguides with material inhomogeneity

We consider the propagation of guided waves in a planar waveguide that has a finite-length segment of inhomogeneous media. Except for the inhomogeneous segment, which varies in length from 0 to 160λ, the waveguide is piecewise homogeneous everywhere. The inhomogeneity is modelled by two-dimensional random permittivity fluctuations that are numerically generated from an assumed Gaussian correlation function.

In 2D, the Maxwell equations are solved in the frequency domain for both TE and TM polarization by using modal expansion methods, perfectly matched absorbing boundary layers and the R-matrix transfer matrix algorithm. The guided waves are excited by a Gaussian beam incident on the waveguide aperture. For various waveguide design parameters, numerical results are given for waveguide power loss per unit length of waveguide inhomogeneity. The power loss curves are calculated as the average from numerous realizations of the random permittivity and the coefficient of variation is also given.     

Disorder and pseudogap in strongly correlated systems: Phase diagram in the DMFT + Σ approach

The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.     

Aharonov-Bohm effect in normal metal quantum coherence and transport

We review some of the recent surprising theoretical and experimental results obtained on the transport properties of small disordered metal samples. Even in the presence of disorder, the quantum mechanical interference of electron wavefunctions can still be observed. The Aharonov-Bohm effect is a particularly clear demonstration of this. In doubly connected structures (such as loops of wire) threaded by a magnetic flux, the electrical conductance oscillates because of the Aharonov-Bohm effect. In fact, because the electron trajectories are diffusive (i.e. random walks), even a lone wire (a singly connected structure) will exhibit a random pattern of conductance fluctuations as a function of the magnetic field because of the same interference effects. All that is required for the observation of these interferences is that the electrons retain ‘phase memory’ duing the period of transit through the sample. The length over which memory is maintained (the phase coherence length) can be much larger than the random walk step length (the mean free path). We focus mainly on effects observed in the limit where the phase coherence length of the electrons is comparable to or larger than the sample size. We explain how the interferences are averaged as the system size grows larger than the phase coherence length. We also remark on surprising aspects of the fluctuations such as those resulting from the non-local character of the wavefunction; some of the results are forbidden classically.     

Polarization fluctuations in the radiation from cosmic sources due to scattering in a random inhomogeneous magnetoactive plasma

We use Feynman integrals along the trajectories to obtain expressions for the fourth-order statistical moments of polarized radiation propagating through a random inhomogeneous plasma. We write down the correlation functions and dispersion of the fluctuations in the Stokes parameters for the case of small fluctuations in the wave filed. We analyze the correlation functions of the Stokes parameters as a function of the polarization of the radiation from the source and the characteristics of the inhomogeneous plasma. We show that for each of the normal waves, the amplitudes and the phases experience different amounts of decorrelation in a random inhomogeneous magnetoactive plasma. As a result, fluctuations occur in the circular polarization.Radio Astronomical Institute, Academy of Sciences of the Ukrainian SSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 738–747, July, 1991     

Scattering losses from planar waveguides with material inhomogeneity

Abstract

We consider the propagation of guided waves in a planar waveguide that has a finite-length segment of inhomogeneous media. Except for the inhomogeneous segment, which varies in length from 0 to 160λ, the waveguide is piecewise homogeneous everywhere. The inhomogeneity is modelled by two-dimensional random permittivity fluctuations that are numerically generated from an assumed Gaussian correlation function.

In 2D, the Maxwell equations are solved in the frequency domain for both TE and TM polarization by using modal expansion methods, perfectly matched absorbing boundary layers and the R -matrix transfer matrix algorithm. The guided waves are excited by a Gaussian beam incident on the waveguide aperture. For various waveguide design parameters, numerical results are given for waveguide power loss per unit length of waveguide inhomogeneity. The power loss curves are calculated as the average from numerous realizations of the random permittivity and the coefficient of variation is also given.     

Theoretical Study of Two Dimensional Evolution of a Weak Gaussian Wave in a F Region Ionosphere Modified by a Strong Gaussian Wave

A high power electromagnetic Gaussian beam is assumed to be incident on the F region ionosphere, which causes modification in the plasma temperature and density. Subsequently the evolution of a second Gaussian em beam in such modified F region inosphere has been studied numerically. The numerical calculations are carried out in a two dimensional grid space which covers a region of 80 km horizontally and 100 km vertically. It is seen that the second wave propagating through the modified plasma gets focused in the axial regions and gets filamented near its peak intensity point. Consequently the plasma gets irregularly structured and the resulting fluctuations in plasma temperature and density give rise to a pressure gradient force. This force inturn causes the formation of more number of filamentary structures about the axis in wave intensity and also amplifies the initially formed ones.     

Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: Random phase approximation

We consider the propagation of p-polarized electromagnetic waves obliquely incident on stratified random dielectric media. Using the invariant imbedding method generalized to random media and applying the random phase approximation, we derive a simple analytical expression of the localization length and calculate the disorder-averaged reflectance and transmittance and the fluctuations of the localization length and the reflectance as functions of the incident angle. We also calculate the disorder-averaged intensity profile of the magnetic field inside the random medium. We find that within the random phase approximation, the p wave can be delocalized and transmitted completely at a certain critical incident angle, which is bigger than the Brewster angle in the uniform case.