Reciprocity relations for scattering from quasi-homogeneous anisotropic media

Valid within the accuracy of the first-order Born approximation, we obtain the analytical expressions of the three-dimensional spatial Fourier transforms, which show the reciprocity relations for the scattering of a polychromatic plane wave incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic scatterer. We find that the spectral degree of coherence of the scattered field is only related with the effective radius of the scatterer and the normalized spectral density of the scattered field is only related with the correlation length of the scatterer.     

Coherence properties of the scattered electromagnetic field generated by anisotropic quasi-homogeneous media

The coherence properties of the scattered field generated by linearly polarized and uniformly unpolarized electromagnetic plane waves incident on anisotropic quasi-homogeneous media are studied. The analytical expressions for the spectral density and the spectral degree of coherence of the three dimensional scattered field are derived. The results of the numerical simulations indicate that not only the properties of the anisotropic media have a great effect on the coherence properties of the scattered field, but also the polarization of the incident wave. And most important, the effect of the polarization of the incident wave on the coherence properties of the scattered field nearly concerns the properties of the anisotropic media. There are also close and interesting relations between the coherence properties of the scattered field that generated by the anisotropic media and by the corresponding isotropic media.     

Scattering of scalar light wave from a Gaussianben Schell model medium

The scattering of scalar light wave from a random medium with a correlation function of Gaussian–Schell model distribution is studied. It is shown that the properties of the scattered field, i.e., the spectral density and the spectral degree of coherence of the scattered field, are closely related to the properties of the scattering medium, including the scaled effective radius and the scaled correlation length of the correlation function.     

Effect of cross-polarization of electromagnetic source on the degree of polarization of generated beam

In this paper we study the degree of cross-polarization of a beam-like field whose cross-spectral density matrix is symmetric with respect to the permutation of its spatial arguments. Formulas were derived expressing the degree of cross-polarization in terms of the generalized Stokes parameters. With the help of an uniformly polarized quasi-homogeneous model source, the effect of degree of cross-polarization of a source on the degree of polarization of the radiated beam was demonstrated, that, two sources with same spectral degrees of coherence and polarization but with different degrees of cross-polarization can generate beams that have different spectral degrees of polarization in the far field.     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media

The correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media was analytically derived. We showed the correlation depends on spatial Fourier transforms of both the intensity and degree of spatial correlation of scattering potentials of the media, while the normalized correlation equals the squared modulus of the degree of spatial coherence of the scattered fields.     

Three-dimensional generalization of the Van Cittert-Zernike theorem to wave and particle scattering

Coherence properties of primary partially coherent radiations (light, X-rays and particles) elastically scattered from a 3D object consisting of a collection of electrons and nuclei are analyzed in the Fresnel diffraction region and in the far field. The behaviour of the cross-spectral density of the scattered radiation transverse and along to the local direction of propagation is shown to be described by respectively the 3D Fourier and Fresnel transform of the generalized radiance function of a scattering secondary source associated with the object. A relativistic correct expression is derived for the mutual coherence function of radiation which takes account of the dispersive propagation of particle beams in vacuum. An effect of the spatial coherence of radiation on the temporal one is found; in the Fresnel diffraction region, in distinction to the field, both the longitudinal spatial coherence and the spectral width of radiation affect the longitudinal coherence. A solution of the 3D inverse scattering problem for partially coherent radiation is presented. It is shown that squared modulus of the scattering potential and its 2D projections can be reconstructed from measurements of the modulus and phase of the degree of transverse spatial coherence of the scattered radiation. The results provide a theoretical basis for new methods of image formation and structure analysis in X-ray, electron, ion, and neutron optics.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves.     

Scattering from Alpha-Stable Non-Gaussian Distributed Surfaces

The scattering problem of alpha-stable non-Gaussian distributed rough surfaces is studied. The alpha-stable non-Gaussian distribution is used to describe the surfaces that exhibit sharp and sparse peaks, not usually seen in Gaussian distributed surfaces. Then a magnetic field integral equation is formulated to calculate the scattered field and the scattering coefficient. Numerical simulations show that the magnitude distribution of the scattered field is affected significantly by the probability distribution of the surface when the height of the surface changes in a random way. In addition, simulation results are presented as bistatic scattering coefficient for alpha-stable distributed surfaces.     

Extension of the van Cittert-Zernike theorem for completely polarized incoherent electromagnetic beam propagating through non-Kolmogorov turbulence

Based on the 2 × 2 cross-spectral density matrix, the van Cittert-Zernike extended theorem is developed for the completely polarized incoherent beams propagation through the paraxial non-Kolmogorov turbulence. On the consequence of the extended theorem and the definition of general spectral degree of cross-polarization of a beam, we found that the spectral degree of cross-polarization of the resultant field is independent of the refractive index structure constant of atmospheric turbulence. We investigated the influences of the propagation distance and the distance of two detection points on the degree of coherence and the spectral degree of cross-polarization.     

Rotationally symmetric scattering from anisotropic media

It is reported that the rotationally symmetric distributions of the spectral density and the spectral degree of coherence of the scattered field in the far zone can be produced by appropriate choices of the effective radius and the correlation length of the scatterer, when a polychromatic plane light wave is incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic medium. The necessary and sufficient conditions are presented. Our results are illustrated by numerical examples.     

Scattering from a Multi-Layered Sphere Located in a High-Order Hermite-Gaussian Beam

Scattering of a high-order Hermite-Gaussian beam by a multi-layered sphere is analyzed. The incident high- order Hermite-Gaussian beam field is expressed by the complex-source-point method and expanded in terms of spherical vector wave functions. The beam shape coefficients of the Hermite-Gaussian beam are obtained. Under electromagnetic field boundary conditions, coefficients in the expressions of scattering fields are derived. Results of the numerical calculation of scattering intensity are presented. The effects of the particle parameters and beam parameters on scattering intensity are discussed in detail.     

Spectral shifts produced by scattering from rotational quasi-homogeneous anisotropic media

The scattering of the polychromatic plane light wave incident upon rotational quasi-homogeneous anisotropic media is investigated. It is different from the light wave scattered by quasi-homogeneous isotropic medium in that the spectral shift can be produced by the rotation of the anisotropic medium. We derive the analytical formula for the spectrum of the scattered field and show some numerical examples.     

Reconstruction of parasitic holograms to characterize photorefractive materials

Photoinduced light scattering is a serious drawback that limits the applicability of thick holographic recording media but provides valuable information on the recording medium. As long as there is no correlation between the scattering centers in the crystal, photoinduced light scattering may be explained to result from the interference pattern of the incident beam and the field scattered from a single point-like scattering center. The hologram of this ellipsoidally scattered wave field will have practically the same structure in the reciprocal space modified by a response function which reflects the anisotropic properties of the recording medium. We studied photoinduced light scattering in LiNbO₃:Fe, a model system for photorefractive materials. The transmitted intensity in the stationary state of the scattering process is investigated as a function of the reconstruction angle at different wavelengths and polarizations of the reconstructing beam. The experimental results are analyzed by a simple phenomenological model based on the Ewald construction and can be used to choose suitable conditions at which holographic scattering can be minimized as well as to extract some physical parameters of the crystal. Received: 27 September 2000 / Revised version: 1 December 2000 / Published online: 21 February 2001     

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.     

Stochastic electromagnetic vortex beam and its propagation

The recent theory formulated in terms of the 2×2 cross-spectral density matrix and the propagation law of cross-spectral density are employed to investigate the stochastic electromagnetic vortex beam and its propagation characterization. Based on these, we derived the general formulae for the intensity distribution, degree of coherence and degree of polarization for stochastic electromagnetic vortex beam while propagating in free space. It is shown that the intensity distribution and the degree of polarization of the stochastic electromagnetic vortex beam propagating in free space depend on the correlation length and the topological charge of the vortex beam.     

Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

Flat-topped spectrum obtained from partially coherent hollow Gaussian Schell-model beams passing through a slit

The anomalous spectral behaviors of partially coherent polychromatic hollow Gaussian Schell-model beams (HGSMBs) diffracted by a slit are investigated. Besides spectral switches, asymmetrical dual-peak spectral split and multi-peak spectral split are observed. In the vicinity of the positions where spectral switches occur, flat-topped spectrum can be obtained, the bandwidth of which is adjustable by changing the transverse coherence width and the observation position. The flat-topped spectrum has potential application for creating probe beams in optical metrology systems and generating broadband optical sources in fiber optic sensor interface systems.