Propagation of light through a monolayer of particles: Analysis of phase and coherent transmittance

Phase variations of a wave transmitted through a monolayer of spherical scatterers are studied as functions of size, optical constants, and particle concentration for light incident normally to the surface of the layer. The analysis is performed in the quasi-crystal approximation of the theory of multiple scattering of waves and in the single scattering approximation. The results obtained allow one to estimate the limits of applicability of the single scattering approximation to layers with partial ordering of scatterers in analysis of the transmitted wave phase. The variations of the phase of the wave in the range of the parameters where the coherent component of the transmitted beam exhibits quenching are studied. It is shown that small variations in the refractive index of the particles may give rise to strong variations of the phase. This effect can be used for phase modulation of light beams, e.g., in liquid crystal films controlled by an electric (or magnetic) field.     

Light scattering by Gaussian particles with internal inclusions and roughened surfaces using ray optics

We study light scattering by Gaussian-random-sphere particles that are large compared to the wavelength of the incident light using ray optics that, in addition to Fresnellian reflection and refraction, accounts for diffuse scattering. We consider two types of diffusely scattering media. One type of media constitutes a uniform medium inside the particle, i.e. a diffuse internal medium. The second type of media constitutes a layer on the surface of the particle that is thin compared to the particle dimensions and acts as a diffuse external medium mimicking the particle surface roughness. We illustrate the effects of the diffuse media on the scattering characteristics for both cases and show that incorporating diffuse scatterers allows us to explain the scattering matrices measured experimentally for Saharan sand particles large compared to the wavelength.     

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.     

Electromagnetic energy transport via linear chains of silver nanoparticles

We propose the idea of a subwavelength-sized light guide represented by a linear chain of spherical metal nanoparticles in which light is transmitted by electrodynamic interparticle coupling. The light-transport properties of this system are investigated by use of model calculations based on generalized Mie theory. Considering Ag particles of 50-nm diameter, we find optimum guiding conditions for an interparticle spacing of 25 nm, and a corresponding 1/e signal-damping length of 900 nm is evaluated. The proposed principle of optical energy transport may be useful for subwavelength transmission lines within integrated optics circuits and for near-field optical microscopy.     

Thermocapillary mechanism of convection in nanofluids due to the absorption of spatially periodic laser radiation

The problem of origination of regular convection in the layer of nanofluid with one free surface by the absorption of light waves with spatially periodic intensity distribution in the plane of the layer caused by the temperature dependence of the surface tension coefficient is studied. The profiles of velocity and temperature in the volume of medium are determined. It is shown that the response of the system on the influence of a light wave is maximal other conditions being equal, when the period of interference pattern is about twice as large as the layer thickness.     

Effect of the “inversion” of a scattering medium in layers of close-packed titanium dioxide nanoparticles

The features of the behavior of the diffuse transmission of layers of close-packed titanium dioxide nanoparticles in the visible and near infrared spectral ranges with an increase in the volume fraction f of the particles in a layer have been analyzed. It has been found that an increase in f for layers of small particles (about 25 nm) with a relatively low volume fraction (0.20–0.25) is accompanied by the expected decrease in diffuse transmission. At the same time, an increase in f for layers of large particles (about 100 nm) with a volume fraction of 0.45–0.50 results in a strong increase in transmission. The described phenomenon has been interpreted in terms of the concepts of inverse scattering systems, where the main scattering centers are air nanocavities in a TiO₂ matrix rather than TiO₂ particles in an air matrix.     

Diffraction of light by an acoustic wave with three frequency components

Collinear light diffraction by three-frequency sound is investigated theoretically. The amplitude distributions of transmitted and diffracted light waves along the cell are calculated for different amplitudes of sound signals. The dependence of the intensity of principal diffraction peaks on the frequency difference between acoustic signal components is studied for different amplitude ratios of these components. It is shown that the character of this dependence for a wave being in synchronism differs substantially from that for two other waves characterized by detuning. The dependence of the amplitudes of principal and parasitic diffraction peaks on the efficiency of acoustooptical interaction is investigated. It is demonstrated that parasitic sideband components in diffracted light can play a considerable role if the diffraction efficiency is sufficiently high and exceeds 80%.     

低噪音光折变体全息存储

光折变全息存储中,透过晶体的散射光会影响再现象的信噪比,本文基于两波耦合理论,对光折变存储中的散射噪音随光斑尺寸的变化作了简化计算和分析,结果表明减小辐照在晶体上的光斑尺寸能降低散射噪音,提高衍射效率和信噪比,采用球面参考波小光斑尺寸入射,在KNSBN光折变晶体中存储了傅里叶全息图,并得到了低噪音的再现象.     

New regions of diffraction reflection in apodized one-dimensional photonic crystals with a large modulation depth

The specific features of light transmission in a cholesteric liquid crystal (LC) cell with a director rotated by 90° have been investigated. In this structure, where a light wave is incident at a large angle with respect to the LC surface, the light is reflected (refracted) in the LC layer near the opposite boundary. It is shown that the application of an electric field changes the character of extraordinary wave refraction, as a result of which light starts passing through a cell. The transmission threshold voltage is determined, and its dependence on the angle of incidence of light is obtained. The dependence of the transmitted-light intensity on the voltage across the cell is obtained as well. The same dependences are also derived by numerical calculations with allowance for the turning points and extinction.     

On the theory of brownian motion. VIII. A Brownian particle in a dilute gas with inelastic collisions

The Fokker-Planck equation for a heavy particle in a dilute gas of light particles is derived from a Boltzmann equation. Inelastic collisions between the heavy and light particles are considered, and explicit quadratures for the frictional coefficients are given in terms of the scattering kernels. It is shown that the general formulation reduces properly to known results in the cases of pure elastic and pure diffuse scattering, respectively.     

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.     

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.     

Investigation of roughness cross correlation in a Ni/C multilayer mirror by X-ray diffuse scattering method

The possibility of applying X-ray diffuse scattering for studying roughness in multilayer X-ray mirrors, including the correlation of roughnesses of neighboring interfaces (roughness cross-correlation) is considered. It is shown that the reliability and informativeness of this method can be improved by rejecting the classical experimental schemes and using alternative schemes in which not only the intensity of diffuse scattering itself, but also its dependence on certain experimental parameters (conditions), vary. Such parameters can be the spatial coherence of incident radiation, the direction of the momentum transfer relative to the specular diffraction plane, or the X-ray wavelength. In the framework of this approach, the results of comparative measurements of diffuse scattering from a Ni/C multilayer X-ray mirror prepared by laser ablation are considered for two close values of photon energy: below (8.325 keV) and above (8.350 keV) the K absorption edge for nickel. It is shown that, in view of effective screening of deep layers in the hard photoabsorption mode, this method provides more reliable (as compared to the standard diffuse scattering method) information on the evolution of interfaces between the layers. It is found that the smoothing of roughness in the experimental sample occurs over large spatial scales such as the micrometer scale. Only large-scale defects with a size exceeding 10 µm are replicated well from layer to layer. Possible physical reasons for the observed effect are considered. It is shown that effective smoothing on the micrometer and submicrometer spatial scales is of fundamental importance for preparing multilayer X-ray mirrors with high reflectances.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

Squeezing alcohols into sonoluminescing bubbles: the universal role of surfactants

We conduct an experimental study of the dependence of single bubble sonoluminescence intensity on the concentration of various alcohols. The light intensity is reduced by one-half at a molar fraction of ethanol of approximately 2.5x10(-5); butanol achieves the same reduction at a concentration 10 times smaller. We account for the results by a theoretical model in which the alcohols are assumed to be mechanically forced into the bubble at collapse, modifying the adiabatic exponent of the gas. The increasing hydrophobicities of the alcohols lead to decreasing effective adiabatic exponents, and thus to less heating and therefore less light. Support for this model is obtained by replotting the experimental light intensity values vs the calculated exponents, yielding a collapse of all data onto a universal curve.     

Local field effects in magneto-optics of two-dimensional arrays of ferromagnetic nanoparticles

A theory of the polar magneto-optical Kerr effect in a layer of small ferromagnetic particles has been developed in the framework of the Green’s function method of electrodynamics. The manifestation in magneto-optics of the local field effect, which is initiated by the contribution to the effective field of dipole moments induced in particles, has been studied in terms of the model of a square lattice of ferromagnetic ellipsoids. The magneto-optical Kerr effect stimulated under normal incidence of a linearly polarized electromagnetic wave on a layer of particles magnetized perpendicular to the layer plane has been analyzed. The dependence of the Kerr rotation angle in an array of ellipsoidal Co particles embedded in the transparent dielectric CaF₂ on the light frequency, the parameters of the ellipsoidal particles, and the lattice period (concentration of the magnet in the layer) has been studied numerically. It has been shown that, within a broad (2.0–4.5 eV) spectral range, the local field effect studied as a function of increasing concentration of Co particles in the layer manifests itself in the reversal of the sign of the Kerr rotation compared to that observed in a single ellipsoid or a solid Co film.     

Equivalence of MTF of a turbid medium and radiative transfer field

The equivalence of the modulation transfer function (MTF) of a turbid medium and the transmitted radiance from the medium under isotropic diffuse illumination is demonstrated. MTF of a turbid medium can be fully evaluated by numerically solving a radiative transfer problem in a plane parallel medium. MTF for a homogenous single layer turbid medium is investigated as illustration. General features of the MTF in the low and high spatial frequency domains are provided through their dependence on optical thickness, single scattering albedo, asymmetrical factor, and phase function type.     

Morphology and decay kinetics of Co-Ni-Ti alloys

The effects of small-angle diffuse modulated-structure electron scattering in Co-Ni-Ti alloys are studied. It is shown that elastic atomic-plane displacement plays a determining role in satellite formation on electron-diffraction patterns. It is also shown that in the early disintegration stages in Co-Ni-Ti alloys, the new-phase particles are equiaxial and randomly disposed. At later stages, a transition to one-dimensionally periodic modulated structure is observed. The time dependence of modulation period and particle size is described by the Lifshits-Slezov-Vagner equation. The coagulation-activation energy determined from kinetics curves is Q=64 kcal/mole. It is concluded that volume diffusion controls particle coarsening.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 123–130, December, 1972.The authors consider it their pleasant duty to express appreciation to L. S. Bushnev for discussion of the present work.     

The influence of the characteristics of a collection of particles on the scattered spectral density and its applications

The far-zone scattered spectral density of a light wave on the scattering from a collection of particles is investigated, and the relationship between the character of the collection and the distribution of the scattered spectral density is discussed. It is shown that both the number of particles and their locations in the collection play roles in the distribution of the far-zone scattered spectral density. This phenomenon may provide a potential method to reconstruct the structure character of a collection of particles from measurements of the far-zone scattered spectral density.     

Birefringence and scattering of light in colloidal solutions of magnetite in kerosene

The birefringence and dynamic and static scattering of light in colloidal solutions of magnetite nanoparticles in kerosene with different concentrations of the solid phase have been investigated. It is shown that these solutions contain both individual colloidal particles about 12 nm in diameter and their aggregates up to 100?600 nm in diameter. The largest aggregates are formed in solutions with the lowest concentration (on the order of 0.001 vol % or lower). The presence of relatively large aggregates makes it possible to observe specific features of optical anisotropy relaxation in these solutions, which are related to the non-Rayleigh character of light scattering from magnetite-particle aggregates.