Polarization visualization of scattering media with CW laser radiation

The method of polarization visualization of a multiply scattering medium containing macroinhomogeneities based on analysis of polarization spatial distribution of a scattered linearly polarized light is discussed. The treatment is based on statistical properties of the effective optical path distribution of scattered field components. The influence of media scattering properties and the geometry of the experiment on the inhomogeneity image contrast obtained with use of polarization degree and of normalized scattered intensity of radiation as visualization parameters are discussed, as well as spatial resolution achieved in these both cases. Using the results of theoretical analysis and of the experimental model, the relationship between the shapes of spatial distributions of polarization degree and the intensity of the scattered light is considered as a function of the position of the visualized object (an absorbing half-plane immersed in a plane layer of the scattering medium). The opportunities for enhancing the quality of the images formed in this way are also discussed.     

Effect of absorption of multiply scattering media on the degree of residual polarization of backscattered light

The effect of absorption in a scattering medium on the degree of residual polarization of backscattered radiation is studied in the case of probing of multiply scattering media by a linearly polarized light. An approximate expression describing the dependence of the degree of residual linear polarization of the backscattered radiation on the optical characteristics of a multiply scattering medium is derived within the framework of the phenomenological approach, based on the concept of the distribution of the optical paths of partial components of the scattered optical field under the conditions of multiple scattering, and with the use of the ideas about the similarity of statistical moments of the multiply scattered optical fields. The cut-off of the partial components, characterized by a large value of the optical path, because of their absorption, results in a substantial increase of the degree of residual polarization for the bands of the selective absorption caused by the presence of chromophores in the scattering medium. The results of experiments with model scattering media (whole milk) and biological tissues (human skin in vivo) are presented.     

Monte Carlo simulation for millimeter wave propagation and scattering in rain medium

As the operating frequencies of communications systems more higher into the millimeter wave range, the effects of multiple scattering in precipitation media become more significant. This paper treats the problems of electromagnetic multiple scattering in rain medium by the Monte Carlo method. The em wave is regarded as a Markov chain of photon collisions in a medium in which it is scattered and absorbed. For the sake of simplicity, the polarization is not taken into account, the above mentioned problems are described by the scale integro-diffierential equation of transfer. When the plane wave through a random medium with particle size distribution, the technique of weighted average is used to characterize the radiation intensity, including average scattering, absorption coefficients and phase function. The Monte Carlo simulation algorithms are done for the rain attenuation and reflectance at millimeter wavelength region. Our computational results are in good agreement with experimental data of rain attenuation.     

Diffraction phenomena in a dichroic medium

Diffraction phenomena accompanying the propagation of narrow directed beams of coherent radiation in a medium with anisotropy of absorption and gain are theoretically analyzed. A quasi-optical equation is obtained, which differs from the traditional equation by the complexity of the diffraction coefficient, and this leads to effective diffusion of radiation in anisotropically absorbing media. Because of this, the intensity of minima observed in the far-field region in the case of diffraction of coherent radiation by a slit does not vanish, but has a finite value. The solution for Gaussian beams is constructed. It is shown that the beam width increases as the square root of the path length in an anisotropic medium, whereas the angular divergence varies in inverse proportion to the square root of the path length.     

Speckle polarization diagnostics of scattering media using partially coherent radiation

The paper discusses a method for probing a randomly inhomogeneous medium using partially coherent radiation and polarization filtering of the radiation scattered by the medium. The method is based on the analysis of the contrast of speckle-modulated images of the object under study as a function of the coherence length of the probe radiation. A theoretical justification of the method is given as applied to systems of discrete scatterers with the subsequent modification of the results obtained for continuously distributed scattering systems. The results of experimental testing of the developed method for scattering media characterized by nondiffusion conditions of propagation of the probe radiation are presented and compared with the results of the theoretical analysis.     

Speckle diagnostics of multiple scattering media with the use of frequency-modulated laser radiation

A method for probing randomly inhomogeneous multiple scattering media with the use of frequency-modulated laser radiation is considered. The method is based on analysis of the dependence of the blinking index of time-averaged speckles formed upon scattering of the probing radiation in a medium on the frequency modulation depth of the probing radiation. In the case of a binary frequency modulation, the blinking index of the detected speckle-modulated radiation is determined by the cosine Fourier transform of the probability density of the optical path-length difference of partial components of the scattered field in the probed medium. The values of the probability density of the optical path-length difference reconstructed with the use of the proposed method from the measured blinking index of speckles for model scattering media (fluoroplastic layer and layer of TiO₂ particles on a glass substrate) are in a good agreement with the results of statistical simulation of the probing radiation transfer in multiple scattering media.     

Concept of formation length in radiation theory

The features of electromagnetic processes are considered which connected with finite size of space region in which final particles (photon, electron–positron pair) are formed. The longitudinal dimension of the region is known as the formation length. If some external agent is acting on an electron while traveling this distance the emission process can be disrupted. There are different agents: multiple scattering of projectile, polarization of a medium, action of external fields, etc. The theory of radiation under influence of the multiple scattering, the Landau–Pomeranchuk–Migdal (LPM) effect, is presented. The probability of radiation is calculated with an accuracy up to “next to leading logarithm” and with the Coulomb corrections taken into account. The integral characteristics of bremsstrahlung are given, it is shown that the effective radiation length increases due to the LPM effect at high energy. The LPM effect for pair creation is also presented. The multiple scattering influences also on radiative corrections in a medium (and an external field too) including the anomalous magnetic moment of an electron and the polarization tensor as well as coherent scattering of a photon in a Coulomb field. The polarization of a medium alters the radiation probability in soft part of spectrum. Specific features of radiation from a target of finite thickness include: the boundary photon emission, interference effects for thin target, multi-photon radiation. The theory predictions are compared with experimental data obtained at SLAC and CERN SPS. For electron–positron colliding beams following items are discussed: the separation of coherent and incoherent mechanisms of radiation, the beam-size effect in bremsstrahlung, coherent radiation and mechanisms of electron–positron creation.     

Combined spectroscopic method for determining the fluorophore concentration in highly scattering media

The spectroscopic analysis of composition of highly scattering media, in particular, biological tissues, is associated with difficult interpretation of the spectrum of radiation subjected to both absorption and multiple scattering in a medium. The proposed technique of the combined analysis of spectra of laser radiation fluorescence and diffuse reflection by highly scattering biological media allows quantitative determination of concentrations of basic chromophores and fluorophores in tissues with simultaneous estimation of structural changes in objects under study. To determine the effect of structural parameters on the intensity of backscattered laser and fluorescent radiation, numerical simulation and physical modeling of the interaction of exciting and fluorescent radiation with highly scattering media are performed. The dependences of the measured signal on the concentrations of scatterers and fluorophore (protoporphyrin IX) under study are measured.     

Rain induced attenuation for 3mm wave band and its measurement system

In this paper, the effect of rain induced attenuation for millimeter wave is discussed. The theory of multiple scattering is used to obtain the solution for the plane wave propagation through a plane parallel medium of thickness L containing randomly distributed nonspherial particles. The coherent field and the total field are studied, respectively. The numerical results are good agreement with experimental data and the multiple scattering effects must be included. A 3mm wave propagation measurement system was made on a 0.8km terrestrial link.     

Coherent transverse speckle dynamics in the case of probing of stationary bulk scattering media by a laser with frequency deviation

A coherent transverse dynamics of scattered speckle fields that arises upon propagation of tunable laser radiation through stationary optically inhomogeneous bulk media has been discovered. The dynamic photochromic speckle effect can be observed experimentally if the deviation of the laser radiation frequency is comparable with or greater than the effective phase delays arising upon scattering of waves in a random or partly organized medium. It was found experimentally that, with an increase in the frequency tuning range of a probing laser diode (λ = 650 nm) or a compact YAG:Nd laser (λ = 532 μm), which can reach hundreds of gigahertz for multiply scattering bulk media from several millimeters to two centimeters thick (fluoroplastic phantoms), the two-dimensional correlation coefficient of speckle structures decreased monotonically, and the characteristic drop for thicker structures was observed at smaller frequency detunings.     

Investigation of nonstationary models of laser pulse propagation through a homogeneous scattering layer

Using three nonstationary models of radiation transfer in two versions (diffusion-based and axial), the absorption and scattering coefficients of homogeneous scattering media are found from experimental temporal distributions of an ultrashort laser pulse transmitted through the scattering layer of different thickness. These optical characteristics are found to be dependent on the scattering layer thickness, which contradicts physical considerations. The reason for the discovered effect is related to incomplete taking into account of the properties of the scattering indicatrix in the used approximate models. The validity of this interpretation is supported by a Monte Carlo simulation, which yielded similar dependences. Recommendations on the correct use of the approximate radiation transfer models are given.     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

Nuclear resonant scattering using synchrotron radiation

A one-dimensional quantum model for nuclear resonant scattering using synchrotron radiation has been developed. This model gives a clear physical interpretation of the most prominent features of the coherent forward scattering process namely, the “speed-up” and “dynamical beat” effects. The form of the solution, for the time-dependent forward scattered intensity of the resonant radiation from the resonant medium after synchrotron radiation excitation, is a finite series. This unique solution can be interpreted in terms of a summation over all multiple forward scattering paths the radiation takes in reaching the detector. The resonant medium is represented by a linear chain of N effective resonant nuclei. The analysis starts from a coupled set of quantum mechanical equations for the relevant amplitudes in frequency space. Transformation to the time domain gives an analytical expression for the forward scattered intensity. The contribution of every order of the multiple scattering processes from the N effective nuclei appears naturally. The expression gives a clear physical understanding of all relevant aspects of resonant forward nuclear scattering. Furthermore, the present formalism allows the consideration of incoherent processes. This permits the study of processes in which there is gamma emission with recoil or emission of internal-conversion electrons. This revised version was published online in August 2006 with corrections to the Cover Date.     

Reflection of waves from a strong scatterer buried in a random medium

Reflection of waves from a mirror covered by a random layer of isotropic, absorbing scatterers is studied and the angular distribution of the scattered intensity is calculated both analytically and numerically. It is shown that backscattering enhancement as well as an enhancement of the incoherent signal in the specular direction take place even in the singly scattered random field. The dependence of the retroreflected intensity is shown to be a non-monotonic function of the depth of the mirror, with a maximum at a depth of the order of the scattering mean free path. Possibilities for employing the results obtained to detect buried strong scatterers and to retrieve parameters of the random media are discussed. In particular, it is shown that in the case of strong absorption the reflecting plane manifests itself by the presence of a peak in the retroreflected intensity which is missing from the scattering diagram of a free-standing or an infinitely thick random layer.     

Enhanced backscattering of vortex waves from volume scattering media

The effect of phase vortices on the enhanced coherent backscattering from volume scattering media is studied theoretically and experimentally. The experimental results are well described by a theoretical model based on the diffusion approximation corrected for small path lengths contributions. Based on this approach, a self-referencing method for measuring the optical characteristics of a multiple scattering medium can be developed.     

Method for Describing the Angular Distribution of Optical Radiation Scattered by a Monolayer of Ordered Spherical Particles (Normal Illumination)

We have developed a method for describing the angular distribution of intensity of radiation scattered by a monolayer of homogeneous spatially ordered monodisperse spherical particles normally illuminated by a plane circularly polarized electromagnetic wave. The method is based on the quasicrystalline approximation (QCA) of the theory of multiple scattering of waves (TMSW) using the multipole expansion of fields and the tensor Green function in vectorial spherical wavefunctions. The method is applied for analyzing the characteristics of radiation scattered by a partially ordered monolayer and a monolayer with a nonideal lattice. The results of calculations are compared with the available experimental data on the position of the first-order diffraction peak on the angular and spectral dependences of the intensity of radiation scattered by a closely packed monolayer with a nonideal triangular lattice of SiO₂ particles. Good conformity of the results has been established.     

Influence of Electric and Magnetic Fields on Interference Effects upon Multiple Light Scattering in Cold Atomic Ensembles

The correlation functions of the electromagnetic radiation scattered by an ensemble of atoms cooled to sub-Doppler temperatures and placed in an external static electric or magnetic field have been calculated by the diagram technique. Based on the derived relations, we have studied in detail the effect of coherent backscattering (CBS) of light. We have calculated the enhancement factor for CBS and analyzed its polarization and spectral dependences. We show that external fields affect the nature of multiple light scattering in an atomic ensemble, in particular, the character of interference upon such scattering, by leading to its optical anisotropy and related birefringence and dichroism. This, in turn, affects all of the observed CBS characteristics.     

Bremsstrahlung of nonrelativistic electrons in metals with allowance made for the polarization channel

We theoretically investigate the bremsstrahlung that appears when nonrelativistic electrons are scattered in a metal target with allowance made for the polarization contribution. We take into account the interference of ordinary and polarization bremsstrahlung, the absorption of radiation in the target material, the energy losses and elastic scattering of an electron by atoms of the medium, and the coherent effects when the radiating electron interacts with the target. We analyze the influence of the target thickness on the process and the contribution of polarization bremsstrahlung to the total yield of bremsstrahlung photons as a function of the problem parameters.     

Visualization of scattering media upon backscattering of a linearly polarized nonmonochromatic light

The method of polarization visualization of multiply scattering macroinhomogeneous media, based on analysis of the spatial distributions of polarization characteristics of a linearly polarized radiation backscattered from a medium, is discussed. The effect of optical characteristics of the medium and the scattering geometry on the quality of the images obtained in the case of visualization of an absorbing heterogeneity immersed into a multiply scattering medium is considered. The comparative analysis of the quality of formed images was performed with the use of different polarization characteristics of the backscattered radiation as a visualization parameter. The theoretical interpretation of the obtained experimental results is given within the framework of the phenomenological approach based on the concept of the distribution of the effective optical paths of partial components of the scattered optical field. To calculate the probability density of the effective optical paths, the statistical simulation method was used.     

Multiple scattering and intensity fluctuations in optical coherent tomography of randomly inhomogeneous media

An expression for signal intensity fluctuations in optical coherent tomography has been obtained for the first time in the framework of the theory of the multiple scattering of low-coherent optical radiation in a random medium. The contribution of the multiple scattering of low-coherent radiation backscattered from a randomly inhomogeneous layer, as well as the speckles of the interference component in optical coherent tomography, has been calculated.