Sound scattering by random fractal inhomogeneities in the ocean

Sound scattering by random volume inhomogeneities (fluctuations of the refraction index in a medium) with an arbitrary anisotropy is considered using the small perturbation method (Born’s approximation). Surfaces (boundaries) of the inhomogeneities are deemed to be fractal ones: the energy spectra of the refraction index fluctuations follow the power law with a nonintegral exponent. Formulas are obtained for the volume scattering coefficient. Frequency and angular dependences of the scattering coefficient and their relations to the fractal dimension of inhomogeneities with different kinds of anisotropy and different sizes (on the sound wavelength scale) are presented. The fractal dimension of the inhomogeneities is estimated.     

Role of light-induced scattering in the optical limitation of laser radiation on the basis of fullerene-containing media

A theoretical and experimental study of the contribution of light-induced scattering to nonlinear optical limitation is made. It is shown that light-induced scattering makes a considerable contribution to the optical limitation of radiation by fullerene-containing solutions. Radiation is scattered by small-scale (1–10 μm) inhomogeneities of density, and the corresponding increments are rather large. Because of this, scattering can be initiated by small-scale inhomogeneities of the input beam. Numerical simulation of nonlinear scattering is made, and the angular distribution and limitation of radiation in optical limiters are calculated. The calculation results are compared with the experiment.     

Boundary diffraction waves and the effective size of the inhomogeneities of the scattering object

A method for measuring the angular size of the halo from boundary diffraction waves without using two-position schemes is proposed. The relationship between the angular distortions of the beam and the size distribution of inhomogeneities is derived for a random transmitting screen. The effective size of inhomogeneities is expressed in terms of the ratio between the fourth-order and second-order moments of the distribution function. A method for estimating the correspondence between the effective size of the inhomogeneities and the parameters of the real screen is substantiated. The key relation for the estimation is the equality of the angular sizes of the halo for the simulated and real scattering objects.     

Angular scattering pattern of waves in the ocean in the presence of anisotropic inhomogeneities

Closed integrodifferential equations are derived for the coherence function and the ray intensity in the ocean. Random inhomogeneities of the medium are assumed to be large-scale and statistically anisotropic. The influence of anisotropy on the angular scattering pattern is analyzed.     

Investigation of multiple ultrasmall-angle neutron scattering with the aid of a double-crystal diffractometer

A method of multiple small-angle neutron scattering (MSANS), used to obtain information about inhomogeneities of substances, is considered. Experimental schemes and theory of a double-crystal diffractometer intended for measuring multiple small-angle neutron scattering are described. Methods used to approximate MSANS angular distributions at a low concentration of inhomogeneities and based on Moliére’s theory are reviewed. Their applicability is demonstrated for the examples ofMSANS spectra of samples from ferromagnetic iron-nickel alloys, aluminum powders, and high-T _c superconductor ceramic materials. Theoretical and experimental investigations of interference effects that manifest themselves in multiple small-angle neutron scattering on systems containing high concentrations of scatterers are reported.     

Computer modeling of sound propagation in the ocean with fractal inhomogeneities

The wave-field computer code based on the wide-angle parabolic equation is modified and adapted to the problems of sound scattering in a medium with anisotropic inhomogeneities of fractal type. To verify the computer code, a model numerical experiment on determining the angular dependence of the scattered sound field is performed for different anisotropy coefficients of the sound speed inhomogeneities. The comparison of the computed data with the theoretical dependences shows their rather good agreement and indicates that the computer code can be applied to calculations of sound propagation in the ocean with fine-structure inhomogeneities possessing fractal properties.     

Multiple scattering of electromagnetic waves by the internal surfaces of turbulent bodies of revolution

Using the method of statistical modeling, we have solved the problem of multiple scattering of electromagnetic waves by THE internal surfaceS of bodies of revolution: a cone and paraboloids of the second and fourth orderS along whose generatrices turbulent inhomogeneities move. The angular and frequency spectra of the scattered signal are obtained and their dependence on the shape of the scattering surface, on the reradiation pattern of turbulent inhomogeneities, and on the variance of their travel velocity is analyzed.Siberian Physical and Technical Institute, State University, Tomsk. Translated from izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 9, pp. 906–912, September, 1995.     

Correlation effects in multiple small-angle neutron scattering at the surface layers of inhomogeneities

The influence of spatial correlations on the angular distribution of multiple small-angle neutron scattering (MSANS) at the surface layers of inhomogeneities is studied. Calculations are carried out by taking instrumental distortions into account when observing multiple small-angle neutron scattering by means of methods of a double-crystal diffractometer and a small-angle diffractometer with a position-sensitive detector. Within the framework of the eikonal approximation, the MSANS line is calculated, and the influence of the surface-layer thickness and the inhomogeneity concentration on its width is studied.     

Illumination of the shadow zone in a two-channel oceanic waveguide with a fine structure of sound speed inhomogeneities

The experimental data on the sound field structure, which were obtained by emitting a continuous pseudonoise signal (a midfrequency of 3.2 kHz) in a two-channel oceanic waveguide, are compared with the calculations performed by the wave program with allowance for the fine structure of the sound speed inhomogeneities. A considerable increase in the intensity of the sound field with a definite angular spectrum is observed in the upper channel in the first shadow zone, and, in the experiment, the increase begins nearer to the sound source than predicted by the wave and ray calculations for a smooth sound speed profile. These features of the field structure are explained by the illumination of the shadow zone by the regular scattering of signals from highly anisotropic fine-structure inhomogeneities of the sound speed profile, which are clearly pronounced in the region of the given oceanic experiment.     

Electromagnetic wave scattering by large-scale inhomogeneities in a bragg cavity

We study the single scattering of a plane electromagnetic wave by random inhomogeneities in a plane periodically nonuniform layer with a reflecting rear boundary. It is shown that when the incident wave satisfies the condition of excitation of the fundamental Bragg cavity mode and its field is large in the layer depth, the average angular spectrum of the backscattered wave field at the cavity output has a narrow maximum proportional to the exponent of the quadruple optical thickness of the periodic structure. This maximum corresponds to the condition of excitation of the fundamental Bragg cavity mode by the scattered field. The other spectral maxima have small amplitudes and intensities. Such scattering takes place if the characteristic size of random inhomogeneities in the direction perpendicular to the layer boundary exceeds the scale of multiple scattering on a periodic structure. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 11, pp. 1342–1354, November, 1997.     

Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories

It is common practice to use effective medium theories (EMT) to estimate average, “effective” optical constants of inhomogeneous materials. A variety of EMTs were developed for different internal structures of the medium and for a variety of shapes, size distributions and physical properties of the inhomogeneities. The most popular EMTs (Maxwell Garnett, Bruggeman, Looyenga, etc.) consider inhomogeneities that are much smaller than the wavelength. The so-called extended EMTs were developed to find effective optical constants in the case of inhomogeneities comparable and slightly larger than the wavelength. This paper compares angular distribution and wavelength dependence of intensity and polarization of scattered light obtained from calculations using the most popular EMTs and extended EMTs with the results of microwave analog measurements at the microwave facilities of the University of Florida. We simulated the light scattering by organic grains with silicate inclusions of size parameter x=0.075 (≈0.01 μm), 0.60 (≈0.1 μm), and 1.24 (≈0.2 μm). The conclusion is that for inclusions of a small size and for a small volume fraction of them in the mixture all EMTs yield similar results and show reasonable agreement with experimental results. The accuracy is better for the angular dependencies of the intensity and of the polarization of the scattered light than for their wavelength dependencies. For inhomogeneities comparable and larger than the wavelength extended EMTs work better but for smaller inclusions non-extended EMTs show more accurate results. Large volume fractions of the inclusions in the mixture (>10%) essentially reduce the accuracy of the results obtained with EMTs. Based on our study we do not recommend to use EMTs in the back-scattering domain and at the scattering angles 30°<θ<70°.     

Interference of speckle fields in the diffraction zone of a focused spatially modulated laser beam by a random phase screen

The processes of formation of average-intensity interference fringes upon diffraction by a random-phase object of a laser beam having interference fringes and focused on the surface of the object are considered. The dependences of the fringe contrast on the parameters of scattering inhomogeneities of the object and the parameters of the focused laser beam are established in analytical form for various diffraction regimes. Practical possibilities of a method of probing of scattering objects in problems of measuring the parameters of inhomogeneities and problems of interference-pattern formation in optical systems with scattering media are discussed.     

Multiple small-angle scattering—A review

Small-angle scattering (SAS) is a powerful experimental technique in condensed matter physics for studying structural features of inhomogeneities of colloidal dimensions. So far the technique has been largely exploited to study thin samples for which the single scattering approximation, for the radiation-matrix interaction, holds good. The single scattering approximation is invalid when the thickness of the sample exceeds the scattering mean free path. This situation calls for a guideline to analyse the scattering data having significant contribution from multiple scattering. Since multiple scattering broadens the scattering profile, the beam broadening nature of multiple scattering can also be exploited, by making the sample suitably thick, to study large size inhomogeneities which are otherwise inaccessible to a small-angle scattering set up because of its resolution constraints. The present article presents a review and extension of the theoretical basis for analysing multiple scattering data from the point of view of a recent formalism on multiple small-angle scattering. The formalism is valid for both monodisperse and polydisperse scattering media characterized by the presence of large size inhomogeneities in the matrix. It is shown that multiple scattering from a polydisperse sample can be described by a system of coupled integrodifferential equation. However, multiple scattering from a monodisperse sample can be described by a Fokker-Planck type of equation. These equations have been analysed with an emphasis laid on the nature of the structural information pertaining to the inhomogeneities which is extractable from the multiple scattering profile. When the linear dimension of inhomogeneities becomes comparable to the scattering mean free path of the radiation in the sample, the statistical nature of the medium becomes pronounced. The statistical nature of the medium modulates the scattering profile. The modulation effect could be broadening or narrowing of the profile depending upon the nature of the inhomogeneities and their population distribution. The limiting regimes of validity and the implications of various approximations, frequently used to analyse the scattering data, have been indicated.     

Sounding of an artificially perturbed ionosphere by means of an ionosonde/position finder with chirp modulation of the signal

We describe the operation of an ionosonde/position finder with chirp modulation of the signal. The first results of measuring the characteristics of short-wave radio signals scattered by artificial small-scale inhomogeneities, which were obtained by means of an ionosonde/position finder on the IZMIRAN—“SURA”—Rostov-on-Don path are presented. It was found that under certain ionospheric conditions, the angular and frequency selection of the scattered signals take place, in which case the signals are observed simultaneously in several frequency intervals (mainly, in three, namely, 6–9.5 MHz, 10–12 MHz, and 15–18 MHz) with different angles of incidence of radio waves in the vertical plane. In this case, the incidence angles were 20◦–35◦, 18◦–32◦, and 10◦–20◦ from the horizon for the first, second, and third frequency interval, respectively. Ionograms of oblique sounding were modeled allowing for the scattering of radio waves by artificial small-scale inhomogeneities. It is shown that at frequencies from 10 to 12 MHz, aspect conditions are fulfilled for the signals ducting along the high-angle beam (Pedersen mode). At frequencies 15–18 MHz (higher than the maximum observable frequency of the forward signal on the path IZMIRAN—Rostov-on-Don), aspect scattering conditions are fulfilled for the signals incident on a scattering area in the ascending part of the trajectory. At low frequencies 6–9.5 MHz (below the maximum observed frequency of the forward signal on the IZMIRAN—Rostov-on-Don path), the observable additional signals are caused by the scattering of radio waves by artificial inhomogeneities with subsequent relfection of the scattered signal from the Earth on the “SURA”—Rostov-on-Don path. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 4, pp. 267–278, April 2009.     

Laser excitation of flexural waves and their scattering by fractal inhomogeneities in a thin plate

The excitation of flexural waves in a thin plate (film) by harmonically modulated laser radiation and their scattering by small fractal inhomogeneities are considered. An expression for the mean fluctuation intensity for the scattered wave field is obtained. A relationship between the intensity, parameters of the laser radiation and the plate, and the fractal dimension of inhomogeneities is found. The expected frequency dependence of the flexural wave attenuation in the plate due to their scattering by fractal inhomogeneities is discussed.     

Single scattering of waves by random strong anisotropic inhomogeneities

Research is carried out into scattering of waves by random strong anisotropic inhomogeneities when the inhomogeneities are in the distant zone according to one (transverse) scale and at the same time they are in the near zone according to another (longitudinal) scale. To analyse the formulas of the single scattering the stationary phase method in the longitudinal coordinate integral is used. It is shown that the angle sensitivity of strong anisotropic scattering, unlike weak anisotropic scattering, strongly depends on the longitudinal statistical homogeneity of the medium.     

Detection of inhomogeneities in biological tissues by the methods of confocal microscopy

The model of detection of local inhomogeneities of scattering and absorbing types in biological tissues by the methods of reflection and transmission confocal microscopy has been developed on the basis of the theory of vision in scattering media. General equations for calculation of the image contrast of an inhomogeneity against the background of a scattering medium are derived. The influence of the object characteristics and observation-system parameters on the maximum detection depth of inhomogeneities is analyzed. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 5, pp. 625–639, May, 1998.     

On the scintillations of radiation from an extended source in a randomly inhomogeneous medium

Using the method of refractive scattering of radio waves (RSRW), we solve the problem of space correlation of scintillations of radiation from an extended source in a randomly inhomogeneous medium. General expressions are obtained for the index and radius of the space correlation of fluctuations of intensity of radiation from a source with finite angular dimensions as it propagates though a multilayered medium with refractive index fluctuations. The RSRW method is similar to the diffraction calculation of space correlation of scintillations of an extended source in a thick layer with inhomogeneities. We note that under certain conditions an increase in the number of inhomogeneous layers on the radio wave propagation path leads to a pronounced decrease in the scintillation index and an increase in the space correlation of fluctuations of intensity of received radiation from an extended source. The results obtained have a simple geometric-optical interpretation. We indicate a specific feature in determining the angular dimensions of extended radio sources using the known method of scintillations. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 5, pp. 586–593, May, 1997.     

The scattering of flexural waves by random fractal inhomogeneities in a thin plate

The scattering of flexural waves by small statistical fractal inhomogeneities in a thin plate is considered. An expression for the average intensity of the fluctuations of the scattered wave field is obtained. A relation of the intensity to the plate parameters and to the fractal dimension of the inhomogeneities is determined. An expected frequency dependence of the attenuation of flexural waves in a plate due to the scattering by fractal inhomogeneities is discussed.     

Relativistic scattering of electromagnetic radiation by inhomogeneities of the velocity of motion of the medium

Analysis of the relativistic scattering of electromagnetic radiation by inhomogeneities of the velocity of the motion of a medium is carried out. The characteristics of the scattering of a plane monochromatic wave by a rotating dielectric cylinder surrounded by an immobile medium with a refractive index the same as that of the cylinder are calculated. The differential scattering cross section is found. It is shown that the rotation of particles with actual parameters may yield a significant contribution to the scattering, of the same order of magnitude or larger than the contribution made by Rayleigh and Raman scattering.