On the strength distribution of a field created by randomly distributed dipoles

The probability distribution of the strength of a field created by parallel dipoles arranged randomly, on average, uniformly is considered. The problem of divergence at small distances is analyzed. It is shown that, for any, including an arbitrarily small, number of dipoles ε in the cutoff sphere, the average field value is zero. In the case ε ? 1, the field distribution consists of a central part, whose half-width is of an order of the average polarization of a medium, and a very wide and structured background. An interpolation formula for the Fourier image of the field distribution applicable for arbitrary values of ε is proposed. An analogy with the theory of spectral line broadening is established. The connection with the problems of molecular optics and inhomogeneous Stark broadening of spectral lines is discussed.     

Polarization mode dispersion properties of constantly spun randomly birefringent fibers

We calculate the asymptotic first-order polarization mode dispersion statistics of constantly spun fibers. We show that in the long length regime the mean differential group delay of constantly spun fibers grows linearly with distance at the same rate as for unspun fibers. Conversely, the short length regime of constantly spun fibers may be much longer, even for limited spin rates.     

Polarization fluctuations in a dipolar medium in an electrostatic field

Radio Engineering and Electronics Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1113–1124, September, 1989.     

Polarization fluctuations in regions bounded by equi-potentials

It is shown that the integral of <{P(rτ), P(r')}>· n? as a function of r over a volume V_e bounded by an equi-potential is independent of r' and of V_e and is determined solely by [?(ω)?1] · n? provided the dielectric constant is local and that V_e is of macroscopic dimensions.     

Polarization properties of vectorial nonparaxial Gaussian beams in the far field

The polarization properties of vectorial coherent nonparaxial Gaussian beams are studied. It is shown that, when the source of a nonparaxial Gaussian beam is completely polarized, the degree of polarization of the propagation field maintains a constant value of 1. However, when the source is completely unpolarized, the degree of polarization does not maintain a constant value of 0. In the far field, vectorial nonparaxial Gaussian beams can become partially polarized, except on the propagation axis, and are spatially nonuniform across a typical cross section of the beam even though the source field is completely unpolarized.     

Polarization and modal field properties of quinquangular-core photonic crystal fibers

A kind of highly birefringent quinquangular-core photonic crystal fiber(Q-PCF) structure is proposed and analyzed by full-vector finite element method(FEM) . The modal field,effective index,and birefringence properties are investigated. From the numerical results,it is found that the birefringence of the new polarization-maintaining PCFs is at least five times larger than that of the standard highly birefringent hexagonal PCFs(H-PCFs) with the same hole pitch,hole diameter,and whole hole area as that of the new PCFs at 1 550 nm. Moreover,the modal field of the new PCFs could be better restricted than that of the standard highly birefringent H-PCFs;hence,the loss of fibers could be reduced.     

Large-scale magnetic field generation by randomly forced shearing waves

A rigorous theory for the generation of a large-scale magnetic field by random nonhelically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low magnetic Reynolds number (Rm) and weak shear. The dynamo is kinematic and due to fluctuations in the net (volume-averaged) electromotive force. This is a minimal proof-of-concept quasilinear calculation aiming to put the shear dynamo, a new effect recently found in numerical experiments, on a firm theoretical footing. Numerically observed scalings of the wave number and growth rate of the fastest-growing mode, previously not understood, are derived analytically. The simplicity of the model suggests that shear dynamo action may be a generic property of sheared magnetohydrodynamic turbulence.     

Polarization mode dispersion of spun fibers with randomly varying birefringence

We show analytically how periodic spinning affects the polarization mode dispersion of a fiber in three different practical regimes that are determined by the values of three length scales: the beat length, the birefringence correlation length, and the spin period. We determine in which limits the spin is effective in reducing the mean differential group delay.     

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.     

Intensity fluctuations of randomly scattered waves considered as local time

The concept of local time of a stochastic process is available for the study of intensity fluctuations in randomly scattered waves. A result of Jakeman on rays scattered by a corrugated surface of brownian slope is deduced from the Ray-Knight theorem on brownian local time.     

Equilibrium and passing properties of dislocation dipoles

Static and dynamic properties of dislocation dipoles are investigated under isotropic and anisotropic elasticity. In elastically isotropic systems for a dislocation character between 35 and 40°, a dipole assumes the same stress-free equilibrium angle of 90° as the screw dipole. This can be affected by elastic anisotropy, as in Cu where the equilibrium angle assumed by a screw dipole (≈59°) is unchanged up to a dislocation character of 22°. In contrast, the static properties of near-edge dislocation dipoles are little influenced by elastic anisotropy. Certain dipole passing properties, not the passing stress however, are also modified by elastic anisotropy. For large heights and/or in the case of undissociated dislocations, the minimum passing stress corresponds to a dipole character of ～60° and it exhibits a sharp maximum in screw orientation. Reasonably moderate dislocation reorientations should facilitate the passing of near-screw dislocations in fatigue channels. Within a certain range of applied stresses, the passing of dipoles, comprised of unlike attractive dislocations, is accompanied by the sweeping of one dislocation by the other over a limited distance. Dissociation plays a prominent role in determining both static and dynamic properties for dipole heights less than a few times the dissociation distance of an isolated dislocation.     

Calculation of the field of a lattice of point magnetic dipoles

The magnetic field H produced by a spatially periodic distribution of point magnetic dipoles is expanded in a Fourier series. Because of a rapid (exponential) falloff of its harmonic amplitudes, the field H at an arbitrary point is the sum of the fields of only several nearest layers (or chains) of dipoles. The method is applied to calculate the magnetic fields at interstitial sites of Sm in different antiferromagnetic states.     

均匀带电薄圆盘的电场

通过解拉普拉斯方程导出均匀带电薄圆盘的电势和电场的级数表达式,进而讨论均匀带电薄圆盘平面内、中心轴线上和远区的电场。     

Model of the light-beam fluctuations in a turbid medium with randomly nonuniform absorption

We study theoretically the light-field fluctuations in a turbid medium with strongly anisotropic scattering and randomly nonuniform distribution of an absorbing material. Analytical models of the correlation functions of the relative fluctuations of brightness and irradiation in the wide and narrow light beams are developed. Dependences of the variance and the correlation scales of the relative fluctuations of brightness and irradiation on the scattering characteristics and the absorption-index fluctuations are analyzed. Distinctive features of the correlation characteristics of the narrow and wide light beams are revealed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 9, pp. 799–815, September 2006.     

Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces

The stress propagation in a concentrated attractive colloidal suspension under shear is studied using numerical simulations. The spatial correlations of the intercolloidal stress field are studied and an inertia-like tensor is defined in order to characterize the anisotropic nature of the stress field. It is shown that the colloids remain in a liquid order, the intercolloidal stress is strongly anisotropic. A transition under flow is observed: during a transient regime at low deformation, the stress propagates along the compression direction of the shear, whereas at larger deformations, the stress is organized into layers parallel to the (flow, vorticity) plane.