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To solve the problems of the repeated scattering of electromagnetic waves at ensembles of dielectric particles taking into account their conductivity, the interaction between collective optical modes of 2D embedded chains of small spherical plasmonic particles, which are characterized by electric dipole coupling, is analytically described on the basis of the quasi-separable T-scattering operator approach. It is assumed that the polarization vector of the electric field of an incident wave is oriented perpendicular to the plane of particle chains. The mutual influence of currents is demonstrated using a regular triangle whose vertices and center of symmetry contain particles and two embedded square chains with eight particles located at their vertices.

Electromagnetic wave (EM) multiple scattering by a plane periodic array of magnetic microelements in free space is considered analytically by natural subdividing of the EM wave into the averaged and fluctuation components. Each magnetic element is characterized by magnetic susceptibility tensor and shape. An exact Dyson integral equation is derived for the magnetic field Floquet-Bloch amplitude in-plane averaged over an array unit cell. The mass operator of the Dyson equation is expressed via the T-scattering operator of the array unit cell that satisfies a type of the Lippmann-Schwinger equation. We showed that magnetic field fluctuations are generated by the Bragg-Laue diffraction of an averaged magnetic field on the periodic array and are described inside the array as waves propagating with the Laue wave vectors equal to the difference between the in-plane wave vector of the incident magnetic field and the reciprocal lattice wave vector. We derived, for the first time, an exact quadrature to calculate magnetic field fluctuations from their averaged value. These general results are illustrated by a simple Born approximation. In particular, we revealed a mechanism of discrete waveguide excitation by an incident plane EM wave via the averaged EM wave Brag-Laue diffraction on the magnetic microelement array in the quasi-static approach when the wavelength of incident EM is much larger than the sizes of magnetic elements and periods of the array. The mode energy excitation coefficient at normal incidence of the plane EM wave on the array is evaluated.

Recent results in magnonics – a topical and rapidly developing branch of spintronics and magnetoelectronics – are presented. The paper describes measurement techniques and theoretical approaches used to explore physical processes associated with the spin-wave propagation in complex nano- and micro-dimensional magnetic structures. The results of the application of magnetic structures in signal processing and transmission systems are discussed. In particular, results on spin wave propagation in distributed magnetic periodic structures, lumped systems, coupled waveguide structures, and controllable magnonic structures are considered. Specific examples of circuitry based on magnonic structures are discussed, and possibilities for further developing this circuitry are explored.

A layer-by-layer method is theoretically developed for reconstructing the temperature distribution inside a biological object from the measured outgoing thermal microwave radiation energy flux. The measurement is carried out along the plane parallel to the heated object surface in the surface’s near-field area. The equation of the inverse problem is obtained. The equation couples the 2D spatial Fourier-component of Poynting’s outgoing radiation vector with the similar Fourier-component of the lateral temperature distribution along elementary inner layers parallel to the object surface. The obtained equation is solved for the case of a 1D periodic or local depth-uniform lateral temperature distribution inside an object. The effective half-width of the spatial-harmonic spectrum for the outgoing thermal radiation energy flux is shown to be estimated by the double wave number inside the object. At the same time, the spatial half-width of a biological object’s thermal-radiation response to a local change in the lateral temperature distribution is estimated as a half of the wavelength inside the object. This result justifies the antenna size conventionally applied in biomedical research.

Two modern problems of the theory of multiple scattering of electromagnetic wave radiation in discrete randomly inhomogeneous media are discussed. One problem is related to the effective magnetic permeability of a statistical assembly of nonmagnetic conducting particles; the other problem is focused on the regard for the near-field effects of scatterers in the radiative transfer theory.

A tunneling mechanism of radiative transfer through a dielectric random medium is revealed applying technique of Dyson and Bethe–Salpeter equations for electromagnetic wave multiple scattering by medium inhomogeneities (scatterers) with near fields effects in scattered fields. The mechanism consists in existing inside of a random inhomogeneity a pair of virtually opposite decaying evanescent waves whose interference results in energy flux.

For the one-dimensional inverse problem of acoustothermography with correlation reception of thermal acoustic radiation, an integral equation is presented and experimentally verified. A method of solving the inverse problem is proposed. The method is based on combining the correlation functions of thermal acoustic radiation that were obtained for different distances between the receivers.

An experiment that models the heating of a biological object is carried out. The model object was a beef liver. The in-depth temperature in the liver was measured in the course of both heating and cooling with the use of a chain of three acoustothermometers. Simultaneously, thermal electromagnetic radiation in the IR range was detected to control the surface temperature of the object. The results of the acoustothermometric measurements and the IR imaging correlate well with the heating-cooling dynamics. A combined application of acoustothermometers and IR imaging enhances the reliability of the temperature measurements.

We consider the problem of distribution of the intensity of diffusely reflected radiation along the surface of semibounded random inhomogeneous medium under the condition that a narrow monodirected light beam impinges upon the surface. Here, the starting point is the transfer equation for the light intensity in diffusing medium. Using a reciprocity to the canonical form of the integral equation for the Green function, the light intensity can be rewritten as the sum of two summands, namely, the contributions made by scatterings of multiplicities from 0 to N (N = 0, 1, 2, …), and the radiation of the efficient generator, in construction of which the radiation with scattering multiplicity N + 1 takes part. Practical realization of the proposed method consists in combining the usage of the diffusive asymptotic for the Green function in the term with the efficient source of radiation and the Monte Carlo method for computing the aforementioned contributions of scattering multiplicities. It is shown that, starting from some critical value of the scattering multiplicity, we have the asymptotic coincidence of computational results obtained by the hybrid method and by the standard Monte Carlo method for solving the problem formulated in its entirety. Moreover, this critical value of the scattering multiplicity depending on the elongation of the indicatrix and the albedo of the elementary act of radiation scattering is estimated.

The higher harmonics of the alternating current in bilayer lipid membranes induced by a sinusoidal voltage applied to the membrane were measured. The bilayer lipid membranes were prepared from diphytanoylphosphatidylcholine in decane and tetradecane; a 16-bit analog-to-digital converter was used for the measurements. A sinusoidal voltage was formed with a 16-bit digital-to-analog converter. The dynamic measurement range reached 90 dB. The coefficients α and β of the expansion of capacitance C in terms of the membrane voltage U—C = C 0(1 + αU 2 + βU 4)—were determined from the measurement results. It was shown within the framework of the electrostriction model that a certain ratio of the coefficients α and β characterizes the inhomogeneity of the membrane with respect to its thickness and Young’s modulus of elasticity.

Phonon transfer in yttrium-oxide (Y2O3) stabilized ZrO2 ceramics is studied experimentally in the range of helium temperatures (1.7–3.8 K). A model of the structure of the intergranular layer in the ceramic is considered, which explains the temperature dependence of the phonon diffusion coefficient, makes it possible to determine the intergranular layer parameters (density, velocity of sound, and thickness), and gives an idea about its structure. Scattering of injected phonons from resonance vibrations of nanoceramic grains is discussed.

An analytic hybrid method is considered for solving the stationary radiation transfer equation in the problem on reflection of a narrow laser beam from biological media such as the 2% aqueous solution of intralipid and erythrocyte suspension with the volume concentration (hematocrit) H = 0.41. The method is based on the reciprocity of the Green function in the radiation transfer theory and on the iteration solution of the integral equation for this function. As a result, the ray intensity is represented as a sum of two terms. The first of them describes the contribution of finite-order scattering to the intensity of a beam diffusely reflected from the medium. The second term contains the explicit analytic expression for a spatially distributed effective source of diffuse radiation emerging from the deep layers of the medium to the surface. This approach substantially improves the diffusion approximation for the problem under study and allows one to obtain the uniform asymptotics of the reflection coefficient at the specified interval of distances between the radiation source and detector on the medium surface with the relative error within +/- 6% for the 2% intralipid emulsion and erythrocyte suspension (H = 0.41).

The transport processes in highly transparent nanocrystalline laser-host ceramics based on C-modification of Y2O3 sesquioxide were investigated by the heat-pulse technique. The propagation kinetics of acoustic phonons was studied in the range of liquid helium temperature (1.7–3.8 K). A structural model for the grain boundary layers is suggested and their thickness is estimated. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present an optical theorem for evanescent (near field) electromagnetic wave scattering by a dielectric structure. The derivation is based on the formalism of angular spectrum wave amplitudes. The optical theorem shows that an energy flux at scattering is emitted in the direction of incident evanescent wave decay.

The phonon transport processes in high-transparency nanocrystalline laser ceramics based on cubic Y3Al5O12 garnet oxide were investigated by the heat-pulse technique. The propagation kinetics of nonequilibrium acoustic phonons was studied in the range of helium temperatures (1.7–3.8 K). The structural model is suggested for the intergrain layers, and their thickness is estimated.

Correlated signals of thermal acoustic radiation from heated sources extending in the transverse direction (a pair of narrow plasticine plates and a wide plasticine strip) are measured. The measurements are performed by multiplying together the signals that are shifted in time with respect to each other and detected by two piezoelectric transducers. The values of the correlated signals of thermal acoustic radiation are determined by the spatial variation of temperature in the medium under study.

An approach is proposed in the theory of multiple scattering of wave fields in two-dimensional inhomogeneous media, which provides a universal description for wave scattering from one-dimensional periodic interfaces between two dielectric media (optical gratings) and from two-dimensional periodic dielectric structures (photonic crystals). The approach is based on the transfer matrix methodology, which involves sub-dividing the scattering medium into elementary layers with gaps; however, in contrast to the transfer matrix method, it leads to invariant imbedding equations for the matrix coefficients of reflection and transmission of an inhomogeneous medium. The developed approach is applied in a quantitative analysis of two optical effects: resonant decrease in the light reflection coefficient from the grating, associated with the profile depth effect, and exponential-power decay of optical radiation in the forbidden band of a 2D photonic crystal upon an increase in the number of its layers starting from one layer. The frequency spectrum for the electromagnetic radiation power transmission through a 2D photonic crystal formed by parallel layers of infinitely long cylinders is interpreted taking into account the spectral dependence of the total cross section of scattering from a single cylinder. Such an interpretation of the frequency spectrum with two forbidden gaps combined with the analysis of layer-by-layer dynamics of its formation makes it possible to reveal the role of microscopic resonant scattering of waves from a single cylinder and of macroscopic Bragg-type resonant scattering from a periodic system of cylinders during the formation of the spectrum of radiation transmission through a photonic crystal. A physical explanation is given for the transparency peaks in one of the forbidden gaps in the spectra of radiation transmission through a perfectly ordered system of cylinders in terms of multipole resonances of scattering from a single cylinder.

The processes of phonon transport in Al 2 O 3 ceramics are studied in the region of helium temperatures. For the ceramic grain size R within two orders of magnitude and more (up to nanosizes), the phonon diffusion coefficient D eff ∝ R and exhibits a decreasing temperature dependence. In nanoceramics with R D eff decreases abruptly by two orders of magnitude, and its temperature dependence changes sign. A model of temperature dependence of the diffusion coefficient is suggested.

Equations have been derived to solve the inverse problem of reconstructing the Fourier expansion coefficients for the temperature of a medium as a function of coordinate along elementary layers. These coefficients are reconstructed from the known similar expansion coefficients for the thermal energy flux at the diffraction grating output as a function of the grating displacement along the medium surface. The grating is in the inhomogeneous wave zone.

The propagation of a quasimonochromatic wave packet of acoustic radiation in a discrete randomly-inhomogeneous medium under the condition that the carrier frequency of the packet is close to the resonance frequency of Mie scattering by an isolated scatterer is studied. The two-frequency Bethe-Salpeter equation in the form of an exact kinetic equation that takes account of the accumulation of the acoustic energy of the radiation inside the scatterers is taken as the initial equation. This kinetic equation is simplified by using the model of resonant point scatterers, the approximation of low scatterer density, and the Fraunhofer approximation in the theory of multiple scattering of waves. This leads to a new transport equation for nonstationary radiation with three Lorentzian delay kernels. In contrast to the well-known Sobolev radiative transfer equation with one Lorentzian delay kernel, the new transfer equation takes account of the accumulation of radiation energy inside the scatterers and is consistent with the Poynting theorem for nonstationary acoustic radiation. The transfer equation obtained with three Lorentzian delay kernels is used to study the Compton-Milne effect—trapping of a pulse of acoustic radiation diffusely reflected from a semi-infinite resonant randomly-inhomogeneous medium, when the pulse can spend most of its propagation time in the medium being “trapped” inside the scatterers. This specific albedo problem for the transfer equation obtained is solved by applying a generalized nonstationary invariance principle. As a result, the function describing the scattering of a diffusely reflected pulse can be expressed in terms of a generalized nonstationary Chandrasekhar H-function, satisfying a nonlinear integral equation. Simple analytical asymptotic expressions are found for the scattering function for the leading and trailing edges of a diffusely reflected δ-pulse as functions of time, the reflection angle, the mean scattering time of the radiation, the elementary delay time, and the parameter describing the accumulation of radiation energy inside the scatterers. These asymptotic expressions demonstrate quantitatively the retardation of the growth of the leading edge and the retardation of the decay of the trailing edge of a diffusely reflected δ-pulse when the conventional radiative transfer regime goes over to a regime of radiation trapping in a resonant randomly-inhomogeneous medium.

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii)...

Pulse propagation of a scalar wave field in discrete random media near resonant scattering is considered on the basis of a modified radiative transfer equation with weak time dispersion in coherent and incoherent scattering. This equation is exactly resolved in terms of the resonant point scatterers model. The numerical evaluation of the obtained solution is applied to the study of a pulse dispersion curve in the time domain. It is shown that the pulse time dispersion curve detected at some distance from the source plane is transformed towards the positive direction of the time axis preserving the integral under the curve with an increase in the specific time delay near resonant scattering.

Diffuse reflection of a narrow collimated light beam from a slab of a dense random medium is considered theoretically and experimentally for the case of the source and the detector fibres dipped into the random medium, as is the case for an endoscopic catheter. By use of the diffusion approximation, a simple and physically clear analytical expression is derived for the distribution of the diffuse reflectance of the light beam along the surface of the random medium slab. We include the effects of reflections from the top and bottom surfaces of the slab. The analytical expression derived predicts that, in the case of small absorption, the relative reflectance is a universal function defined by the geometrical parameters and is independent of specific properties of the random medium. The theoretical prediction is found to show good agreement with the results of measurements.

We present an exact expression for the diffusion constant of vector electromagnetic waves in a random medium of dielectric scatterers in the form of the Green-Kubo relation. The derivation is based on a proper version of the Ward-Takahashi identity for classical waves. The relation between the density of states of the electromagnetic field and the absorption length in the model of weakly absorbing scatterers is discussed.

A new version of nonstationary radiative transfer theory for vector electromagnetic wave multiple scattering in a discrete random medium is presented in which the electromagnetic energy within dielectric scatterers may be large. The starting point is the general two frequency Bethe-Salpeter equation for the coherence tensor-function of the wave electric field. In the two frequency domain it is proved that the Poynting's theorem can be decomposed into (1) a theorem for the spectral component of the electric energy density multiplied by two and (2) a theorem for the difference between the spectral components of the electric and the magnetic energy densities. The Poynting's theorem is closely connected with a generalized two-frequency Ward-Takahashi identity according to which the extinction of a nonsteady radiation is conditioned by the incoherent scattering, the real absorption and changing of the energy accumulation inside scatterers. As result a new radiative transfer equation is obtained for the radianc...

Exact coupled relations have been obtained for the first two statistical moments of an electromagnetic field in a randomly heterogeneous disperse medium. The moments are used to formulate approximate Dyson and Bethe-Salpeter equations that allow for correlations of all orders between the particles of the medium. These approximate equations serve as a basis for the development of methods and instruments for measuring the parameters of disperse media and the exact coupled relations provide an estimate of their accuracy.

A solution to the searchlight problem on back-scattering of a narrow pencil light from a turbid medium with an inhomogeneity is presented for semi-infinite geometry in the framework of the diffusion approximation. The inhomogeneity may be an object with a given reflection coefficient or a variation of mean scattering and absorption properties of a turbid medium. A solution to the diffusion equation for mean diffuse radiant intensity with given boundary conditions is obtained by a perturbation theory method relative to the inhomogeneity effect. The spatially limited inhomogeneity contribution to the back-scattering light intensity is expressed in terms of an inhomogeneity diffuse scattering amplitude and the probability density distribution of photon paths in depth. The theoretical results obtained are applied to the interpretation of the Cui, Kumar and Chance experiment on the change of the back-scattered light beam intensity from turbid biological tissue phantom owing to the existence of small a...

The problem of light extinction in a medium consisting of correlated nonresonant electrical dipoles is considered. The recurrent- scattering correction is calculated for the extinction coefficient. This correction is positive and of the order of the number of scatterers per cubic wavelength. It is shown that only relative two-scatterer arrangements in a thin spherical shell give contributions to this correction. A standing wave is formed between the two scatterers in this arrangement.

The functional Fokker–Planck equation is used to obtain the phenomenological radiative transfer theory in the form of the modified Ambarzumian–Chandrasekhar equation which takes into account the backscattering enhancement effect from the 3D slab of a randomly inhomogeneous medium.

Coherent backscattering of scalar waves from a semi-infinite discrete nonabsorbing random medium of nonisotropic scatterers is considered. The dependence of the line shape of the backscattering peak of the scattering nonisotropy is studied in the frameworks of the diffusion approximation. Various versions of this approximation are applied in which, in particular, the gradiental terms are taken into account, and various forms of boundary conditions are used. It is shown that the peak line shape is almost independent of the form of boundary conditions only in the vicinity of the backscattering direction. The validity of the diffusion approximation is discussed.

The Bethe-Salpeter equation for scalar waves in a random dielectric medium is considered. An eigenfunction expansion and the Ward identity, generalized for the case of an energy dependent potential, are used to find the asymptotic solution. An exact expression for the diffusion constant is obtained in the form of the generalized Green-Kubo formula. Also the accepted point of view on the absence of diffusion in two-dimensional random systems is argued.

Backscattering enhancement is discussed as a universal wave phenomenon inherent to waves of whatever physical nature: electromagnetic, acoustic, spin, etc. This phenomenon arises due to multichannel wave propagation from a source to a scatterer and back and may be observed in the vicinity of the source because of mutual coherence of waves passing in opposite directions along identical (coherent) channels. Backscattering enhancement may be revealed when the wave field is scattered: by a system of chaotically distributed scatterers or by a system of inhomogeneities; by a body embedded in a turbulent medium; by a single body placed near an interface or within a waveguide (randomness of body position is assumed); by a body of complex form or a system of several scatterers randomly oriented in space; by a rough surface; and by many other physical systems. Possible practical applications of these effects are analyzed. >

Some general statements for theory of wave multiple scattering in a three-dimensional inhomogeneous layered dielectric medium are established using the composition rule of the scattering (T-matrix) operators to show that the problem of wave scattering from dielectric interface may be studied similar to the problem of volume wave scattering. The medium is thought as being a stack of n layers, each of them is confined by perpendicular to the z axis planes and consists of a three-dimensional discrete or continuous inhomogeneous medium. The layers do not intersect between them and are embedded into a homogeneous background. A result of the paper is a mixed system of exact operator equations (transfer relations) for the operator wave reflection and transmission coefficients of the medium and the operator wave amplitudes of waves in splits between layers. It is shown that the transfer relations lead to a separate recurrent system of operator equations, which describe the incremental change of the operator wave ...

A theoretical study is presented of transmission spectra formation of perfect two dimensional (2D) photonic crystals (PCs) composed of dielectric cylinders arranged parallel to the electromagnetic wave's electric vector in the square lattice. Layer-by-layer transmission spectra are computed on the basis of a Riccati equation for the matrix wave reflection coefficient from a 2D PC slab and Poynting theorem, regarding 2D PCs as a stack of conservative gratings (layers of non-absorptive rods). The lowest (main) and high-order Mie resonances in a single cylinder and the Bragg-like multiple scattering of electromagnetic waves are determined as three mechanisms of formation and frequency position of two opaque bands, with narrow peaks in one of the bands in the transmission spectra of 2D PCs. It is argued that higher-order Mie resonances are responsible for the transmission peaks within the additional band of a perfect crystal. The possibility of opaque band engineering is discussed. In particular, it is demonstrated that filling fraction of volume occupied by cylinders as small as under half a percent does not destroy the opaque band of 2D PCs.

We present an optical theorem for evanescent (near field) electromagnetic wave scattering by a dielectric structure. The derivation is based on the formalism of angular spectrum wave amplitudes and block scattering matrix. The optical theorem shows that an energy flux is emitted in the direction of the evanescent wave decay upon scattering. The energy emission effect from an evanescent wave is illustrated in two examples of evanescent wave scattering, first, by the electrical dipole and, second, one-dimensional grating with line-like rulings. Within the latter example, we show that an emitted energy flux upon evanescent wave scattering can travel through a dielectric structure even if the structure has a forbidden gap in the transmission spectrum of incident propagating waves.

Recently, in connection with the problem of Anderson localization of light, a new physical mechanism was considered for the decrease of the diffusion coefficient, in which it is supposed that the velocity of energy transport, which appears in the diffusion constant D= @23E l tr /3, may be much smaller than the phase velocity. Using an exact definition of the diffusion coefficient and generalized Ward identity, we, however, show that in the low-density approximation υ E coincides with the phase velocity

Recently Nieh et al. [Phys. Rev. E 57, 1145 (1998)] have considered a version of derivation of the Ward identities for scalar and vector classical wave field propagation in random media and noted that their results are in contradiction with those obtained by Barabanenkov and Ozrin [Phys. Lett. A 154, 38 (1991)]. In this Comment we show that the derivation given by Nieh et al. is based on an incorrect equation for the energy-vertex function where the term that takes into account the contributions of the scatterer polarization to the field energy is lost. Restoring this term removes the above-noted contradiction.

Publisher Summary This chapter describes enhanced backscattering in optics. The chapter considers backscatter enhancement in light scattered from a body embedded in a random medium. A similar phenomenon occurs in multiple scattering of light in a randomly inhomogeneous medium where there are no clear-cut scatterers that stand out against a background. The effects of backscatter enhancement and weak localization are phenomena, in which coherent paths of the Watson-Ruffine type are essential. The chapter describes multiple new manifestations of coherent effects in backscattering. These include the effects of long-distance correlations, the partial reversal of the phase front in a random medium, the magic cap effect, antispecular scattering by very rough random surfaces, and backscattering involving surface waves. The chapter also discusses the opposite case of a small number of scatterers, in which summation cannot be replaced with integration.