Streuung elektromagnetischer Oberflächen- und Volumenwellen an rauhen Oberflächen. Teil I. Allgemeine Grundlagen

Scattering of Electromagnetic Surface and Bulk Waves from Rough Surfaces. Part I. General Theory A classical theory of scattering of electromagnetic surface and bulk waves on rough surfaces (dielectrics or conductors) is given. The primary wave creates a surface polarization on the rough boundary presenting the source for the radiation of scattering. These roughness-caused polarization must be considered in the wave equations and in the boundary conditions of the fields, too. General expressions for the spectral power density of surface and bulk scattering waves will be given. The excitation of surface polarization can result from primary waves homogenously or inhomogenously.     

Streuung elektromagnetischer Wellen an rauhen Oberflächen mit anisotroper Autokorrelationsfunktion

Scattering of Electromagnetic Bulk Waves from Rough Surfaces with Anisotropic Autocorrelation Function Starting with the theory of light scattering given in [1]. a general theory of scattering of electromagnetic waves from a rough surface is deduced. In the general case of arbitrary anisotropic autocorrelation functions (acf) the spectral power densities for all different possibilities of polarisation variants of excitation and scattered light will be presented. In the special case of an elliptically anisotropic acf of surface roughness the measurement of the position of the acf-main axes will be described and the strategy of analyse of the measured indicatrix of scattered light for determining the acf will be given.     

Eine neue Methode zur Bestimmung der Rauhigkeitsautokorrelationsfunktion von optischen Oberflächen

A New Method of Determining the Autocorrelation Function of Polished Optical Surfaces Starting with a general theory of light scattering a measuring procedure for determining the autocorrelation function of surface roughness of well polished substrates is deduced. In this method light intensity scattered into a fixed direction has to be measured in dependence on the dimensions of the scattering area. The results are tested for a glass surface polished by different methods.     

Dispersionsgleichungen für Oberflächenwellen und verallgemeinerte Brewster-Fälle an der Grenze zu optisch einachsigen Medien

Dispersion Relations for Surface Waves and Generalized Brewster Cases at the Interface to Optic Uniaxial Media The dispersion relation für surface waves and for generalized Brewster cases at the interface between isotropic and optic uniaxial media with arbitrary orientation of the optic axis is derived by means of invariant methods. This is an equation of 4-th degree with respect to the squares of the tangential components of the wave vectors relative to the interface. The amplitude relations for the electric fields of the participating waves are calculated. Special cases concerning the orientation of the optic axis and of the plane of incidence and also the transition to isotropic media are discussed.     

Light scattering from colloids

This paper presents a review of light scattering results on static and dynamic properties of ordered colloidal suspensions of charged polystyrene particles and fractal colloidal aggregates. Our studies on static structure factor,S(Q), of ordered monodisperse colloidal suspensions and binary mixtures of particles with different particle diameters, measured by angle-resolved Rayleigh scattering will be discussed. This will include determination of bulk modulus using gravitational compression and observation of colloidal glass (inferred from splitting of the second peak inS(Q)). Dynamic light scattering, with real time analysis of scattered intensity fluctuations, is used to get information about Brownian dynamics of the particles. Recent advances in the field of light scattering from colloidal aggregates which show fractal geometry will also be discussed.     

Multiple scattering of plasmons at rough surfaces

We investigated the polarization and angle dependence of the scattered light intensity of surface plasma oscillations (SPO) propagating along rough silver surfaces. The rough silver films were prepared using the methods of pre-evaporating CaF₂ and silver on heated substrates. The scattered light intensity of both systems is explained by surface scattering effects. Differences of the light intensities between the rough silver films prepared by the two methods mainly were observed in “restlight intensities”, which cannot be described by first-order scattering theories. We explain these differences by higher order scattering effects.     

Direct observation of p,p′‐dimercaptoazobenzene produced from p‐aminothiophenol and p‐nitrothiophenol on Cu2O nanoparticles by surface‐enhanced Raman spectroscopy

Surface‐enhanced Raman scattering of p‐aminothiophenol and p‐nitrothiophenol were obtained on the surface of Cu₂O nanoparticles, showing novel spectral changes with morphology‐dependent and time‐dependent characteristics. The measured Raman signals were believed to partly originate from the newly produced surface species p,p′‐dimercaptoazobenzene. The nature of surface chemisorption status during Raman measurement was investigated experimentally and theoretically via combined surface‐enhanced Raman scattering and density functional theory study, indicating that surface catalytic reaction of p‐aminothiophenol and p‐nitrothiophenol could take place on the surface of oxide nanostructures as well as coinage metal material. Copyright © 2013 John Wiley & Sons, Ltd.     

Scattering of Rayleigh waves by a statistical inhomogeneity of the mass density

The problem of the scattering of a Rayleigh wave by a surface inhomogeneity of the mass density of an isotropic solid is solved in the Born approximation of perturbation theory. The inhomogeneity is statistical with a Gaussian correlation function in the plane parallel to the surface and is deterministic with an exponentially decaying dependence on the coordinate perpendicular to the surface. Expressions are derived for the displacement fields in the scattered longitudinal (P), transverse (SV and SH), and Rayleigh (R) waves at large distances from the inhomogeneity. The Rayleigh wave energy scattering coefficients are calculated as functions of the wavelength λ, the correlation length a of the inhomogeneity, the depth d of the defective layer, and the Poisson ratio of the medium, σ. The angular distribution of the scattered Rayleigh wave energy is determined. Asymptotic expressions are obtained for the scattering coefficient in various limiting cases with respect to the parameters a/λ and λ/d. The relation between the energies in the scattered P, SV, SH, and R waves is established. The resulting equations are used to calculate the scattering coefficients numerically over a wide range of variation of the parameters a/λ, λ/d, and σ; the results are presented in the form of graphs and a table. A physical pattern of the scattering process is constructed and used as a basis for interpreting the results of the study. Fiz. Tverd. Tela (St. Petersburg) 39, 267–274 (February 1997)     

Diffractive production of dijets at HERA

We investigate the production of a quark-antiquark pair in diffractive photon-proton scattering, approximating soft pomeron exchange by the exchange of two nonperturbative gluons. In deep inelastic scattering at HERA, events with two jets and the scattered proton in the final state are predicted to be observable, with an important contribution from charm production. For photoproduction of light quark jets with high transverse momentum we find that both exchanged gluons must have a large invariant mass, so that the cross section is very small, whereas for charm quarks it is quite appreciable. From our calculation we also extract the quark structure function of the pomeron for the scaling variablez no too close to 0 or 1, finding a strong flavour dependence and a behaviour somewhat harder thanz(1?z) for light quarks.     

Effect of turning of rays on scattering of light in a layered medium

The problem of the scattering of light by random inhomogeneities in a layered medium whose characteristic scale is large compared to the wavelength of light is considered. The attention is mainly focused on the effect that the turning of incident and scattered waves has on light scattering in such a medium. In the mixed (q _⊥, z) Fourier representation, expressions for normal waves, and Green’s function are found, which can be used both far from the turning point, where the fields are described in the WKB approximation, and near this point, where the fields are described using the Airy function. Based on these expressions and using the Kirchhoff method, a general expression for the scattering intensity in the far field of the sample is obtained, which takes into account the turning of the incident and scattered waves in the fluctuating medium. Physical consequences of the calculation results are analyzed. In particular, it is shown that even a comparatively small gradient of the refractive index in the layer leads to a rather appreciable redistribution of the scattering intensity between the forward and backward hemispheres. In this case, the shape of the scattering indicatrix is rather exotic with sharp discontinuities, peaks, and dips whose amplitude is on the order of the intensity itself. Original Russian Text ? A.Yu. Val’kov, A.A. Zhukov, V.P. Romanov, 2008, published in Optika i Spektroskopiya, 2008, Vol. 105, No. 4, pp. 647–666.     

A stable ‘sandwich’ system of Surface‐Enhanced Resonance Raman Scattering for the analysis of β‐carotenes in a photosynthetic pigment‐protein complex

In plants, Photosystem I (PSI) is composed of a core complex and a membrane‐associated antenna complex light‐harvesting complex I that captures light and funnels its energy to the core complex. To obtain Raman structural information on β‐carotenes embedded in the PSI core complex, a ‘sandwich’ system of roughened silver slice: target protein complexes: single silver nanoparticles was fabricated for Surface‐Enhanced Resonance Raman Scattering (SERRS) measurements. This study provided a method to overcome spectral irreproducibility, which is the main drawback of Surface‐Enhanced Raman Scattering/SERRS‐based studies. The Raman spectra of β‐carotenes embedded in the PSI core complex can be obtained at very low sample concentrations (1–5 µg Chl/ml) and high signal/noise ratios. The β‐carotenes in the spinach PSI core complex were predominantly all‐trans configuration. The membrane protein‐mediated adsorption of silver nanoparticles induced the uniform distribution of a large number of single nanoparticles, which contributed to achieving highly reproducible SERRS spectra. This study is the first to apply single silver nanoparticle‐based SERRS analysis in membrane proteins. Copyright © 2013 John Wiley & Sons, Ltd.     

Scattering of F atoms and anions on a TiO2(1 1 0) surface

Results of a study of energy losses and electron transfer processes for grazing scattering of fluorine atoms and anions scattering along different azimuthal orientations of the TiO₂ crystal are presented. We observe strong variations in the overall intensity of scattered particles which are due to channelling effects. The energy losses do not show strong variations as a function of crystal azimuth except for the case of scattering along the (0 0 1) direction between the bridging oxygen atom rows, where we also observe differences in the energy losses of scattered ions and neutrals. We attribute this to the fact that larger F⁻ survival occurs for trajectories staying farther from the surface, when also the energy losses remain small. The overall characteristics of energy losses are attributed mainly to trajectory effects due to scattering in regions of different electron density. Measurements of the ratio of scattered ions to the total scattered flux, i.e. the ion fractions which reflect electron capture and loss processes, show that these are not the same for incident anions and atoms. A strong difference for scattering along the (0 0 1) direction is observed, where at low incident energies a strong survival of incident ions occurs. These results are tentatively discussed in terms of non resonant electron capture at lattice O⁻ sites and electron loss into the conduction band or by collisional detachment with bridging O atoms.     

Dynamic light scattering at the ice water interface during freezing

The 488 nm radiation of an argon laser is scattered quasi-elastically at the [0001]-face (basal plane) of a growing ice crystal. The scattering plane is the basal plane. The Rayleigh-linewidth is proportional to the square of the scattering vector. One measures about 2 krad/s at a scattering angle of 90°. The linewidth does not depend on the growth rate. Scattering is only observed once a critical growth rate ν_crit = 1,5 μ m?s has been exceeded. Then the scattering intensity depends linearly on the growth rate in the range between 0,03 μ m?s and 2,5 μ m?s. Once the surface is molten scattering vanishes and does not reappear until the growth rate has again exceeded the threshold ν_crit. The coherence properties of the scattered light indicate that the thickness of the scattering layer is less than 6 μ m. The observations are interpreted in terms of a fluctuating interface. The decay time of the fluctuations has been calculated. Satisfactory agreement with the observed Rayleigh linewidth is obtained.     

Search for a spin glass phase in Mn0.22Zn0.78F2

No spin glass behaviour has been found in Mn_0.22Zn_0.78F₂ which is close to the antiferromagnetic critical concentration. Bulk magnetic measurements show no cusp above 1.7 K, no remanent moment after cooling in a field, and no difference between field cooled and zero field cooled susceptibilities. The infinite time susceptibility derived from diffuse neutron scattering measurements is also in good agreement with the bulk measurement, indicating no frozen component of the bulk susceptibility. The temperature dependence of the susceptibility is explained with a simple paramagnetic model.     

Zur O2-Dissoziation in der Gleichstromglimmentladung. Teil I Bestimmung des Dissoziationsgrades mittels der O3-Bildung an gekühlten Oberflächen

The synthesis of ozone on the surface S cooled with liquid nitrogen O + O₂·S→O₃·S[1] was used to measure the concentration of atoms in a flow tube downstream of a d.c. discharge. The flow tube was constructed in the form of a U-tube. The ozone was deposited as a blue liquid film in the neighbourhood of the surface of the liquid nitrogen on the walls of the part of the U-tube, which was connected with the discharge tube. The oxygen atom decay in the U-tube was observed by measuring the production of ozone as the distance between the discharge tube (diameter: 5,2 cm) and the surface of the liquid nitrogen was varied. The decay is first order in atom concentration for the pressures p > 1 torr. But for the pressures below p = 1 torr near by the discharge tube we observed deviations from the law of decay In [O]₀/[O] = k·t for the currents of about i = 100 mA. This effect was attributed to the process From the extrapolation of an ozone production curve atom concentrations in the discharge have been obtained. The transition from the ?H”? form to the ?T”? form (striated, low average electric field) of the discharge [2] caused the dissociation to decrease rapidly. The highest dissociation (10%) was obtained in the ?H”? form at high currents (i = 120 mA) and low pressures (p = 0,60 torr). The yield of atomic oxygen per kilowatt hour of energy was measured as functions of pressure and gas flow rate for i = 100 mA and i = 50 mA.     

Transport and relaxation properties of isotopomeric hydrogen–helium binary mixtures. I. H2–He mixtures

An extensive comparison has been carried out between calculated and measured bulk properties of H₂–helium mixtures. Detailed comparisons are presented for the interaction second virial coefficient, binary diffusion, mixture shear viscosity and thermal conductivity, rotational relaxation, thermal diffusion field-effects, collision broadening of the depolarized Rayleigh light scattering spectrum, and flow birefringence. Scattering calculations have been carried out for the ab initio potential energy surfaces obtained by Tao (1994, J. chem. Phys., 100, 4947) and Schaefer and Köhler (1985, Physica A, 129, 469). The values for the various bulk gas properties calculated from these two potential surfaces are generally found to lie within or near the experimental uncertainties.     

Equations for the description of wave scattering by multi-valued random surfaces

We consider a scattering theory for multi-valued rough surfaces which cannot be described by the conventional equation of the type z = ζ(x,y). Both Dirichlet and Neumann problems are analyzed. Starting with Green's theorem we obtain a representation of the scattered field, the surface integral equation, and the extinction theorem for such surfaces. In contrast to conventional theory, these equations contain three random functions x = x(u ₁,u ₂), y = y(u ₁,u ₂), and z = z(u ₁,u ₂), where u ₁ and u ₂ are the parameters describing the surface. We introduce two scattering amplitudes S _± for describing the scattered wave above and below the surface. The extinction theorem, if formulated in terms of S _?, allows us to determine S _? for an arbitrary multi-valued surface and after this it becomes possible to derive a simple integral equation for surface sources. Knowledge of the surface sources allows us to find S ₊ by integration.     

Singularities in forward scattering through random media

Abstract

We consider a random medium in which scattering is exclusively in the forward direction. Waves are emitted by an object in the medium and Fourier components of the intensity are shown to propagate independently. At small wavevectors the intensity propagates very simply through increasing thickness, z, of medium, as λ ^z , and Fourier components of the object can easily be reconstructed. For wavevectors greater than a critical value, q _c , the intensity changes with z in a more complex fashion making it very difficult to reconstruct the object. They develop a simple model for the singularity and apply it to the reconstruction of an object degraded by passage through a random medium.     

Integration method for directly analyzing interface statistics of periodic multilayers from X‐ray scattering

An integration method is demonstrated for directly determining the average interface statistics of periodic multilayers from the X‐ray scattering diagram. By measuring the X‐ray scattering diagram in the out‐of‐plane geometry and integrating the scattered intensity along the vertical momentum transfer q_z in an interval, which is decided by the thickness ratio Γ (ratio of sublayer's thickness to periodic thickness), the cross‐correlations between different interfaces are canceled and only the autocorrelations are reserved. Then the multilayer can be treated as a `single interface' and the average power spectral density can be obtained without assuming any vertical correlation model. This method has been employed to study the interface morphology of sputter‐deposited W/Si multilayers grown at an Ar pressure of 1–7 mTorr. The results show an increase in vertical correlation length and a decrease in lateral correlation length with increased Ar pressure. The static roughness exponent α = 0 and dynamic growth exponent z = 2 indicate the Edwards–Wilkinson growth model at an Ar pressure of 1–5 mTorr. At an Ar pressure of 7 mTorr, α = 0.35 and z = 1.65 indicate the Kardar–Parisi–Zhang growth model.