Coherent effects of multiple scattering for scalar and electromagnetic fields: Monte-Carlo simulation and Milne-like solutions

Based on an expansion of the Bethe-Salpeter equation in scattering orders a semi-analytic approach for simulation of coherent phenomena of multiple scattering in random media has been developed. We found that for scalar field the manifestation of these phenomena, observed as temporal field correlation function and coherent backscattering, are universal and well agreed with the results predicted by diffusion approximation. For the electromagnetic field the temporal correlation function and coherent backscattering are noticeably differ from those found for the scalar field, depending strongly on the scattering anisotropy. The obtained numerical results, for the first time to our knowledge, are compared directly with the known generalizations of the Milne solution.     

Influence of the boundary of a medium on the coherent backscattering of light

The multiple scattering of light from an inhomogeneous medium occupying a half-space is investigated on the basis of the Bethe-Salpeter equation. The latter is integrated over the spatial variables to obtain an identity having the significance of the energy balance of the incident and scattered radiations. This relation is then used to derive a length parameter that plays the role of the Milne interpolation length. The use of this parameter in the method of mirror images for describing the shape of the coherent backscattering peak in isotropic single scattering yields results in almost perfect agreement with the predictions of the Milne theory. The application of the given approach for an anisotropic single-scattering diagram yields quantitative agreement of the theory with experiments on the angular dependence of coherent backscattering. The new approach is generalized to an electromagnetic (vector) field, and backscattering polarization effects are investigated. Zh. éksp. Teor. Fiz. 116, 1912–1928 (December 1999)     

The Milne problem solution for the temporal correlation function of an electromagnetic field

The problem of multiple scattering of light by a medium occupying a half-space is solved in backscattering geometry. The solution obtained in the framework of the Wiener-Hopf method, which is a generalization of the well-known Milne solution for the electromagnetic field, has made it possible for the first time to calculate exactly the initial time dependence of the intensity correlation function as well as the dependence of the backscattering intensity on the scattering angle for different polarizations of the incident and scattered waves.     

Electrooptical properties of aqueous suspensions of nickel hydrosilicate nanotubes

We present the results of our investigations of electrooptical effects that occur as a result of light scattering by an aqueous polydisperse system the disperse phase of which consists of nickel hydrosilicate nanotubes with a chrysotile structure. Multilayer nanotubes were synthesized by the hydrothermal method and had the composition Ni₃Si₂O₅. The dimensions of nanotubes were as follows: the length was 0.1–1 μm or more, the outer diameter was 10–15 nm, and the inner diameter was 3 nm. We have studied relative changes in the intensities of light transmitted and scattered by the suspension that were caused by the orientation of nanotubes in an external electric field. Experiments have been performed at different directions of the linear polarization of the incident and scattered light, different scattering angles, and different degrees of orientation of nanotubes along the field. These measurements allowed us to determine the magnitude of electrooptical effects, such as the conservative dichroism, the light scattering, and the influence of the orientation of nanotubes in the field on the intensity and degree of depolarization of light scattered by them. Curves of free relaxation of electrooptical effects and their field dependences allowed us to determine the distributions of nanotubes and their aggregates in the colloid over lengths and polarizability anisotropy values. The dependences of the degree of depolarization of the scattered radiation on the scattering angle and the relaxation dependences of electrooptical effects allowed us to characterize the aggregation stability of nanotubes in water.     

Study of the time correlation function of scattered light in bounded strongly inhomogeneous media

The time correlation function of the multiply scattered light by a medium comprised of finite-size scatterers is studied theoretically and experimentally. A solution of the Bethe-Salpeter equation for the time correlation function is sought in the P ₂-approximation in the form of a series of terms of the Legendre polynomials. With allowance for the boundedness of the medium, the problem is reduced to a generalized Milne equation, which is solved by the Wiener-Hopf method. The time dependence of the correlation function is studied experimentally in a concentrated latex suspension for particles of different sizes. The results of numerical calculations are in qualitative agreement with the measured dependence of the time correlation function on the scatterer size.     

Measurements of depolarization ratios and polarizability anisotropies of gaseous molecules

Values for the depolarization ratio (?^T_V) of Rayleigh scattered light are reported for a large number of gas molecules. When possible, the results are combined with refractive index data to yield the anisotropy in the optical polarizability.     

Ultimate degree of residual polarization of incoherently backscattered light for multiple scattering of linearly polarized light

By invoking ideas about the distribution of the optical paths of partial components of the scattered field, we obtain an expression for estimating the degree of residual polarization of light that is incoherently backscattered from a disordered multiply scattering semi-infinite medium illuminated by linearly polarized light. In the backscattering regime, the depolarization length of the linearly polarized light in the disordered medium becomes smaller with the passage from the isotropic to anisotropic scattering. Experiments with model media featuring substantially anisotropic scattering (the anisotropy parameter of 0.90 ≤ g ≤ 0.95) demonstrated that for backscattering of linearly polarized light, the depolarization length is close to the transport length of the scattering medium.     

A monostatic inverse scattering model based on polarization utilisation

The solution of the inverse problem of electromagnetic scattering by smooth, convex shaped, perfectly conducting, 3-dimensional scatterers is analysed. Certain geometrical as well as physical-optics approximations were used to incorporate the concepts of the “Minkowski problem” of differential geometry into the space-time integral solution of electromagnetic scattering to yield the formal solution for the recovery of the surface profile of the scatterer from the scattered field data. Although various efficient solutions for target identification are available, still information contained in polarization-depolarization characteristics of the scatterer is not yet exploited to its full extent. Therefore the underlying assumption in this investigation was based on the fact that the “depolarization characteristics” of the scattered field do necessarily contain information regarding the surface profile of the scatterer.     

Stochastic modeling of coherent phenomena in strongly inhomogeneous media

A procedure of numerical simulation for coherent phenomena in multiply scattering media is developed on the basis of the juxtaposition of a Monte Carlo stochastic method with an iterative approach to the solution of the Bethe-Salpeter equation. The time correlation function and the interference component of coherent backscattering are calculated for scalar and electromagnetic fields. The results of simulation are in good agreement with experimental results, as well as with theoretical results obtained by generalizing the Milne solution.     

Five-dimensional geometric electrovacuum problem with a geometric scalar field

A generalized geometric Reissner–Nordstrom problem taking into account a geometric scalar field G ₄₄ (x) is treated in the context of the five-dimensional geometric theory of gravitation and electromagnetism. A general solution is obtained for the corresponding five-dimensional Einstein vacuum equations. The essential contribution of the geometric scalar field, which can give rise to wormholes, is shown.     

Propagation of circularly polarized light in media with large-scale inhomogeneities

Small-angle multiple scattering of circularly polarized waves in disordered systems composed of large (larger than the light wavelength) spherical particles is discussed. The equation for Stokes’s fourth parameter V — the difference between the intensities of the left-and right-hand polarized light — is shown to have the form similar to that of the scalar transport equation for intensity I, the only difference being the presence of an additional “non-small-angle” term responsible for depolarization. In the case of small-angle scattering, depolarizing collisions are relatively rare and, in contrast to the scalar case, the problem contains an additional spatial scale, namely the depolarization depth. The polarization degree and helicity of the scattered light are calculated for the case of purely elastic scattering and in the presence of absorption in the medium. For strong absorption, depolarization is shown to follow the transition to the asymptotic regime of wave propagation. The features appearing in strong (non-Born) single scattering are also discussed. Zh. éksp. Teor. Fiz. 115, 769–790 (March 1999)     

Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media

We study the coherence properties of the field generated by beam radiated from quasi-homogeneous (QH) electromagnetic source scattering on QH media. Formulas for the spectral density and spectral degree of coherence of the three dimensional scattered field are derived. The results show under assumption that the diagonal correlation coefficients of the source are proportional to each other, the far field of the scattered light satisfy two reciprocity relations analogous to that in the scalar case, that, the spectral density is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential; the spectral degree of coherence is proportional to the convolution of the diagonal correlation coefficients and the strength of the scattering potential.     

The effect of strong electric and magnetic fields on the depolarization ratios of gases

The influence of a strong electric field F on the polarization of light scattered elastically by small gaseous molecules is investigated. Two effects are found:

• (i) The field distorts the molecules, thereby changing their polarizabilities. If they are isotropically polarizable when F = 0, and hence capable of scattering only polarized light from a parallel beam, this distortion may lead to depolarization. For inert gas atoms, this depolarization is proportional to F ⁴, and hence normally very small, but for tetrahedral molecules it is proportional to β ² F ², where β is the first hyperpolarizability of the molecule.

• (ii) F tends to orientate anisotropic molecules, thereby affecting the polarization of the scattered light; this effect is related to the anisotropy in the molecular polarizability, and to the dipole moment, but is not likely to lead to information that is not obtainable by simpler means.

The effect of a strong magnetic field, in place of F, is also discussed.     

Kinetic theory of photon density waves

A kinetic equation is obtained for the modulated intensity of multiply scattered light, which generalizes the known Bethe-Salpeter equation. An asymptotic solution is found in the P ₁ approximation, which takes into account the anisotropy of single scattering within the average cosine of the scattering angle. The parameters of the photon density wave are calculated from this solution. It is shown that the relative phase shift and modulation degree calculated for modulation frequencies exceeding several gigahertz noticeably differ from the values predicted by the radiation transfer equation.     

The FKG inequality for the Yukawa2 quantum field theory

We establish the FKG correlation inequality for the Euclidean scalar Yukawa₂ quantum field model and, when the Fermi mass is zero, for pseudoscalar Yukawa₂. To do so we approximate the quantum field model by a lattice spin system and show that the FKG inequality for this system follows from a positivity condition on the fundamental solution of the Euclidean Dirac equation with external field. We prove this positivity condition by applying the Vekua-Bers theory of generalized analytic functions.Research partially supported by the National Research Council of Canada.Alfred P. Sloan Foundation Fellow.     

Measurement of specimen permittivity using a waveguide bridge

The proposed method for measuring the permittivity of the medium in the superhigh frequency band makes use of the depolarizing effect of the electromagnetic field. Upon exposing a dielectric particle to an electromagnetic field having a definitely oriented electric-field intensity vector, E_n, the reflected electric-field intensity vector, E₀, will not, in general, coincide in direction with the incident field (as a result of depolarization). This depolarization depends upon the form and dimensions of the particle, on its permittivity, and on the wavelength.     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

Cylindrically Symmetric Scalar Field and it’s Lyapunov stability in General Relativity

In this paper we found an Exact solution for massless scalar field with cosmological constant. This exact solution generalized the Levi-Civita vacuum solution Levi-Civita (Rend. Acc. Lincei 27:183, 1917) to a massless scalar field, with a cosmological constant term.This solution in the absence of the Cosmological constant recovers the spacetime of a massless scalar field with cylindrical symmetry (Buchdahl metric (Buchdahl in Phys. Rev. 115:1325, 1959)). Also if the scalar field disappears, the spacetime will be a representation of de-Sitter space.We prove that the form of the metric’s function which was purposed in Momeni and Miraghaei (Int. J. Mod. Phys. A 24(31):5991, 2009) is valid even if we assume a general form. Furthermore we show that in which conditions this solution satisfies energy conditions. Finally the credibility of focusing theorem is proved.     

Electromagnetic scattering from a two dimensional perfect electromagnetic conductor (PEMC) strip and PEMC strip grating simulated by circular cylinders

Electromagnetic scattering of an incident plane wave from a rectangular strip and strip grating, are presented semi-analytically. The strip and strip grating are simulated by joining parallel perfect electromagnetic conductor (PEMC) circular cylinders and are illuminated by a TM_z incident plane wave. The PEMC medium does not allow electromagnetic energy to enter. An interface of this medium serves as an ideal boundary to the electromagnetic field. The solution is based on the application of the boundary conditions on the surface of each cylinder in terms of its local coordinate system. The technique is used to predict the scattered field pattern of PEMC strip and PEMC strip grating.     

Effect of electric field on light scattering by aqueous colloids of diamond and graphite

We present the results of our experimental investigation of light scattering by polydisperse colloids of diamond and graphite. The scattering is studied at a random orientation of particles and in an external radiofrequency electric field, which orients particles along the strength. The average dimensions of particles in both colloids are close to each other and comparable with the wavelength of the incident light. The shape of particles and the optical and electrooptical properties of diamond and graphite colloids are significantly different. We analyze the polarization components of scattered light energy when the light incident on the colloids is linearly polarized. We show that the quadrupole light scattering by isotropic diamond particles has the main effect on angular dependences of depolarization of scattered light. For light scattering by anisotropic graphite particles, the depolarization of scattered light is mainly determined by a particular feature of the dipole scattering of particles. It is shown that, in both colloids, the orientational order of particles considerably reduces the depolarization of light scattered by particles. We show that relative changes in the intensity and depolarization of scattered light, which depend on the scattering angle and polarization direction of light, as well as on the parameters of particles, can be used as a measure of electrooptical effects observed in colloids.