Radiative Transfer in a Layer of Oriented Spheroidal Particles with Oblique Incidence of Light

The results of numerical modeling of diffuse reflection and transmission by layers of oriented spheroidal particles (whose rotation axes are normal to the layer surface) with oblique incidence of a parallel beam of radiation on the layer are presented. To describe the properties of particles in the elementary act of scattering, the Rayleigh-Gans approximation is used. To describe the propagation of radiation in the layer, the radiative transfer equation in which the characteristics of the medium depend on the direction of radiation propagation is used. The influence of Fresnel reflection at the layer boundaries and the influence of the substrate are taken into account. Calculations of the luminance factors at the layer boundaries over a wide range of characteristics of the medium and layer thicknesses have been made.     

Scattering by a plane-parallel layer with high concentration of optically soft particles

A method describing light propagation in a plane-parallel light-scattering layer with large concentration of homogeneous particles is developed. It is based on the radiative transfer equation and the doubling method. The interference approximation is used to take into account collective scattering effects. Spectral dependence of transmitted light for a layer of nonabsorbing optically soft particles with subwavelength-sized particles is investigated. At small volume concentration of the particles the weak spectral dependences of wave exponents for coherently transmitted and diffuse light are observed. It is shown that in a layer with large volume concentration of the subwavelength-sized particles the wave exponent can exceed considerably the value of four, which takes place for the Rayleigh particles. The dependence of wave exponents for coherently transmitted and diffuse light on the refractive index and concentration of particles is investigated in detail. Multiple scattering of light results in the reduction of the exponent. The quantitative results are presented and discussed. It is shown that there is a range of wavelengths where the negative values of the wave exponent at the regime of multiple scattering are implemented.     

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.     

Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.     

The modeling of the radiation and response green's function of a fluid-loaded cylindrical shell with an external compliant layer

Scattering and radiation of acoustic waves from a fluid-loaded cylindrical shell with an external compliant layer are of interest. The compliant layer can be modeled by a normally reacting impedance layer, which has the advantage that complex compliant layer geometries, such as partial compliant layers, can be considered. A question may, however, arise as to the accuracy of this approach. A more rigorous approach is to model the elastic shell and compliant layer using a multilayer shell theory, which has the disadvantage that it cannot be extended to consider partial layers. In this paper scattering results from the normally reacting compliant layer model are compared to those from the multilayer shell model to show that the two approaches produce similar results, except for thickness resonances of the compliant layer. Having established the consistency between the two approaches, results for the far-field acoustic radiation as a function of frequency and radiation angle for a fluid-loaded shell with an external compliant layer excited by an internal ring force are obtained using the normally reacting impedance layer model. These results clearly show the reduction in the far field radiation due to the presence of the compliant layer.     

On the Acceleration of Energetic Cosmic Particles by Electrostatic Double Layers

The capability of electrostatic double layers of accelerating charged particles to high energies is investigated. Starting from a one-dimensional relativistic double-layer model a two-dimensional relativistic double layer in a current filament is studied. It is found that the filamentary double layer has a maximum potential drop that depends both on the magnitude of the filamentary current and on the composition of the layer. The results are applied to two cosmic double layers?one in a solar electric circuit and another in a galactic circuit. If the layers are composed of protons and electrons, these particles may be accelerated to 1011 eV in the solar layer and to 1014 eV in the galactic layer. It is suggested that the solar double layer may account for the acceleration of solar cosmic rays while the galactic layer may contribute to the generation of cosmic radiation.     

Polarized Raman Scattering in Silicon Layers on Sapphire

The intensities of polarized components of Raman light scattering are measured for different crystallographic directions in epitaxial layers of silicon on sapphire. The experiment shows that the scattered radiation has a strong depolarized component, which is directly related to the occurrence of defects in the epitaxial layer. A model of an ensemble of crystallites is proposed to describe a defect crystal silicon layer on sapphire. It is shown that the characteristic value of disordering of crystalline domains in the epitaxial layer can be determined from the ratio between the intensities of the polarized and depolarized components. From measurements of the Raman scattering intensity as a function of the crystallographic direction, the anisotropy of the Raman scattering tensor is determined. Numerical values for two samples are obtained.     

Similarity effects in multiple scattering of coherent radiation: Phenomenology and experiments

Based on phenomenological concepts of statistics of effective optical paths for multiple scattering of coherent radiation, an analysis is carried out of similarity effects observed for the dependences of statistical moments of the scattered field on the relaxation parameters with a dimension of reciprocal length. Within the framework of the diffusion approximation, expressions are obtained that describe the autocorrelation function of fluctuations of the scattered-field amplitude, the degree of polarization, and the normalized intensity of scattered light for media with a finite absorption length in the case of forward scattering of coherent radiation in a plane layer of an isotropic scattering medium. The results of the analysis show the similarity of the dependences of these quantities on the corresponding spatial scales. Experiments with model scattering media (aqueous suspensions of polystyrene spherical particles) supported the existence of similarity effects in multiple scattering. An experimental study was made of the relation between the characteristic depolarization length and the transport length for multiple scattering of coherent radiation in a plane layer. The effective value of the radiation diffusion coefficient providing the best agreement between the experimental and the calculated values of parameters of the scattered field is shown to be independent of the absorption coefficient of a medium.     

Polarization imaging of multiply-scattered radiation based on integral-vector Monte Carlo method

A new integral-vector Monte Carlo method (IVMCM) is developed to analyze the transfer of polarized radiation in 3D multiple scattering particle-laden media. The method is based on a “successive order of scattering series” expression of the integral formulation of the vector radiative transfer equation (VRTE) for application of efficient statistical tools to improve convergence of Monte Carlo calculations of integrals. After validation against reference results in plane-parallel layer backscattering configurations, the model is applied to a cubic container filled with uniformly distributed monodispersed particles and irradiated by a monochromatic narrow collimated beam. 2D lateral images of effective Mueller matrix elements are calculated in the case of spherical and fractal aggregate particles. Detailed analysis of multiple scattering regimes, which are very similar for unpolarized radiation transfer, allows identifying the sensitivity of polarization imaging to size and morphology.     

A continuum model of a multilayer nanosheet

A continuum model for describing the bending and free vibrations of a crystalline graphite sheet consisting of graphene layers is proposed. Graphene is modeled by a two-dimensional layer having a finite rigidity under extension and bending. The interval between graphene layers through which their Van-der-Waals interaction occurs is modeled by a fictitious layer with relatively low rigidity. In the solution, formulas describing the bending of a multilayer sheet with alternating rigid and soft layers are used.     

Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study

A fast Monte Carlo simulation scheme is developed to assess the impact of multiple scattering on space-based lidar backscattering depolarization measurements. The specific application of our methodology is to determine cloud thermodynamic phase from satellite-based lidar depolarization measurements. Model results indicate that multiple scattering significantly depolarizes backscatter return from water clouds. Multiple scattering depolarization is less significant for non-spherical particles. There are sharp contrasts in the depolarization profile between a layer of spherical particles and a layer of non-spherical particles. Although it is not as obvious as ground-based lidar observations, it is likely that we can identify cloud phase not only for a uniform cloud layer, but also for overlapping cloud layers where one layer contains ice and the other water droplets.     

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.     

Multiple monopole scattering of sound waves from spherical particles in liquid and elastic media

A solution to the problem of the mean sound field in liquid and elastic media with spherical particles causing monopole scattering of sound is proposed. The integral equation obtained for the field allows passage to the Helmholtz equation with an effective wave number. The characteristic features of the solution are the absence of radiation loss in the mean field wave and the absence of limitations on the particle concentration. The integral equation is used as the basis for solving the problem of the incidence of a plain sound wave at an arbitrary angle on a plane layer of a medium with particles.     

Coherent X-ray radiation generated by a beam of relativistic electrons in a single crystal under conditions of multiple scattering

The dynamic theory of the coherent X-ray radiation of a divergent beam of relativistic electrons generated in a single-crystal wafer under conditions of the multiple scattering of incident particles is developed. Radiation cross sections are averaged over the divergent beam of rectilinear trajectories of electrons. Expressions describing the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation under conditions of multiple scattering are obtained. Conditions under which the contribution of diffracted brehmsstrahlung can be disregarded are shown, and the spectral-angular characteristics of parametric X-ray radiation and diffracted transition radiation are calculated numerically for such conditions.     

Fullerenes as nuclei of carbon black particles

The existing models for the structure and inception processes of carbon black particles are analyzed taking into account the experimental data on the cluster formation. A new model of the formation of carbon black particles is proposed. The inference is made that single-layer fullerenes being the minimum possible closed carbon black particles serve as nuclei of large-sized carbon black particles. These particles grow via the deposition of carbon layers on the surface of fullerenes with defects. The defects fulfill the role of seeds that give rise to the front of the layer growth. The defect-free fullerenes do not take part in the carbon black formation due to the thermodynamic stability as a result of structural perfection. The primary carbon black particles—globules—are many-layer formations with a hole in the center whose size and configuration match the size and configuration of the initial fullerene nucleus. The layers in the form of concentric spheroids inserted into each other are composed of distorted and defect carbon networks. The flatest parts of several outer layers of carbon black particles are the regions of the coherent X-ray scattering.     

Measurement of sun and heat protecting properties of human skin through addition of titanium dioxide nanoparticles

Based on the developed mathematical model of skin with the addition of titanium dioxide (TiO₂) nanoparticles 62 and 122 nm in diameter, the absorbed energy density distribution in the skin depth is obtained for the skin irradiated by UV radiation at wavelengths of 310 and 400 nm. It is found that high reflective and scattering properties of the corneal layer of the skin treated by photoprotective preparations based on nanoparticles prevent the penetration of the UV radiation into inner skin layers. It is shown that the majority of the radiation energy is captured or reflected in a thin surface skin layer containing nanoparticles. A decrease in the thermal load on the tissue is observed.     

Ultrahigh frequency additional background radiation of the lower ionosphere during strong geomagnetic disturbances

In periods of high solar activity and the formation of geomagnetic storms, additional background incoherent ultrahigh frequency (UHF) radiation with decimeter to millimeter wavelengths in the high E and D layers of the Earth’s ionosphere is generated. This emission is produced by transitions between Rydberg states of atoms and molecules of atmospheric gases, which are excited by electrons and are surrounded by a neutral species of the medium. At present, there is no reliable information on the integrated intensity of UHF radiation in this wavelength range. This problem can be solved on knowledge of the dynamics of collisional and radiative quenching of Rydberg states and of the kinetics of their population in the lower ionosphere. An analysis of the available experimental data shows that the radiation is generated in an atmospheric layer located at altitudes between 50 and 110 km. The current theory is discussed and the ways of its further improvement connected with the development of more rigorous theoretical methods for describing the effect of neutral particles of medium on the collisional and radiative quenching dynamics, including the elementary processes with participation of the nitrogen and oxygen molecules, are suggested. For quantitatively estimates the influence of excited particles on the incoherent UHF radiation of the atmosphere, it is necessary carrying out of the preliminary calculations the potential energy surfaces and dynamics of nonadiabatic transitions between Rydberg states, construction the electronic wave functions, and determination the dipole moments of the allowed transitions and the emission line shapes. Obtained results can be included into the general kinetic scheme which defines of the UHF radiation intensity versus the density and temperature of the atmosphere. Accompanying its infrared (IR) radiation can be used to define of Rydberg states.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Light Reflection and Transmission by layers with oriented spheroidal particles

On the basis of the numerical solution of the radiative transfer equation (RTE), the influence of non-sphericity of oriented spheroidal particles on radiation intensity formation in a layer with a multiple scattering regime is considered. For solving the RTE with characteristics depending on the propagation direction of the radiation beam, an algorithm is developed based on the method of layer doubling. Calculations are presented of angle correlations for intensities of radiation in a layer with Fresnel reflection on the boundaries, and reflection and transmission coefficients.