Geometrical optics model of Mie resonances

The geometrical optics model of Mie resonances is presented. The ray path geometry is given and the resonance condition is discussed with special emphasis on the phase shift that the rays undergo at the surface of the dielectric sphere. On the basis of this model, approximate expressions for the positions of first-order resonances are given. Formulas for the cavity mode spacing are rederived in a simple manner. It is shown that the resonance linewidth can be calculated regarding the cavity losses. Formulas for the mode density of Mie resonances are given that account for the different width of resonances and thus may be adapted to specific experimental situations.     

Light scattering by optically soft large particles of arbitrary shape

Light scattering by chaotically oriented optically soft large particles of arbitrary shape is considered within the framework of the Rayleigh-Gans approximation. It has been shown that outside the forward direction, the scattering pattern has the dependence of Δk??(1+cos2θ), where is an average particle surface area, Δk is the difference between scattered and initial wave vectors, θ is the scattering angle, and this pattern is independent of particle shape. A simple approximating formula is suggested, which correctly describes the scattering pattern in the entire range of scattering angles. This formula is compared to the particular case of size-distributed spherical particles and is shown to have high accuracy. Also, it is shown that the inherent optical properties, as total, transport, and backward scattering coefficients, are determined by the specific particle surface area and the effective particle size.     

Reciprocity theorem for the calculation of average scattering properties of agglomerated particles

The reciprocity theorem in light scattering is a general theorem that is verified theoretically and experimentally. However, violation of the reciprocity theorem has been encountered in previous investigations for simulation of light scattering from agglomerates. We demonstrate that the violations of the reciprocity theorem are due to inappropriate orientation averaging or the incorrect formulation of light-scattering quantities. In situ optical diagnostics of aggregated aerosols requires the calculation of the orientation averages of scattering quantities. Thus it is imperative to establish a criterion that can be used to determine a sufficient number of orientations for the reliable calculation of averages for the scattering quantities. It is demonstrated that the reciprocity theorem may serve as such a criterion for typical sizes of agglomerates such as flame soot with fractal dimensions D(f) = 1.8, primary particle size parameter x 相似文献   

Energy relaxation during inelastic electron scattering on localized states

A mechanism which can be responsible for the phase relaxation in polycrystalline semiconductors and metals is proposed. This mechanism is related to the inelastic scattering of electrons on localized states with energies near the Fermi level.     

Inelastic scattering on particles with inclusions

The investigation of particles with inclusions is of high interest in many parts of scientific research. Raman scattering is very good at yielding information on the internal composition of the particle. We use a geometrical-optics-based technique to determine the angle dependence of the inelastic scattering on particles with several spherical inclusions.     

Analytical solution to the optical transfer function of a scattering medium with large particles

A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas.     

Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices

The finite-difference time-domain (FDTD) technique is examined for its suitability for studying light scattering by highly refractive dielectric particles. It is found that, for particles with large complex refractive indices, the FDTD solution of light scattering is sensitive to the numerical treatments associated with the particle boundaries. Herein, appropriate treatments of the particle boundaries and related electric fields in the frequency domain are introduced and examined to improve the accuracy of the FDTD solutions. As a result, it is shown that, for a large complex refractive index of 7.1499 + 2.914i for particles with size parameters smaller than 6, the errors in extinction and absorption efficiencies from the FDTD method are generally less than ~4%. The errors in the scattering phase function are less than ~5%. We conclude that the present FDTD scheme with appropriate boundary treatments can provide a reliable solution for light scattering by nonspherical particles with large complex refractive indices.     

Dynamics in liquids studied by inelastic X-ray scattering

Inelastic X-ray scattering with an energy resolution of the order of milli-electron volts is a relatively new tool to investigate collective excitations in condensed matter. A high energy resolution can be achieved by extreme backreflection (Bragg angle close to 90°) from perfect crystals. This technique is used with the spectrometer INELAX for inelastic scattering experiments at DESY, Hamburg. Energy transfers from a few milli-electron volts up to 5 eV at any wavevector between 0.3 and 14 Å^–1 are accessible. One of the successful applications of this method is the investigation of the dynamical structure factor of liquids. Results on liquid lithium are presented and compared with neutron data and molecular dynamics.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Spin dynamics by inelastic neutron scattering in YBCO

Key features of Inelastic neutron scattering experiments in YBCO-based cuprates are discussed. We underline the importance of precise oxygen content determination in samples having similar T_C as well as the resolution configuration used. This may explain the apparent contradictory results recently obtained by different groups.     

Elastic and inelastic scattering of 59.54 keV gamma rays

Cross sections for the elastic scattering of 59.54 keV gamma rays through 141° by Al, Cu, Mo, Yb, Ta, Au and Pb have been accurately determined using a Si(Li) detector. The values of the cross sections have been obtained by a normalization technique based on a comparison with the Compton scattering from the essentially free electrons from an Al scatterer. For the lower-Z elements Al, Cu and Mo the experimental cross sections are more or less in agreement with the form-factor predictions as well as the S-matrix calculations. For the heavier elements Ta, Au and Pb the experimental results deviate strongly from the form-factor values but agree favourably with the S-matrix values. As a by-product, incoherent scattering functions have been evaluated for Cu, Mo and Yb. Also, a clear indication has been obtained for resonant Raman scattering in the case of Yb.     

Effect of near-field coupling on far-field inelastic scattering imaging of gold nanoparticles

The optical near-field enhancement induced by coupling between noble nanoparticles and the substrate has been studied by a far-field imaging method. The longitudinal mode of the incident laser is revealed to contribute to the coupling. The far-field images of individual gold nanoparticles exhibit a peanut-shaped pattern; these were constructed by the intensity of inelastically scattered light. The coupling between gold nanoparticles and the silicon substrate leads to the patterned image. By tuning the separation between the gold nanoparticles and substrate using SiO(2) layers of different thickness, the coupling efficiency decreases with the thickness of the SiO(2) layer.     

Collective motion of inelastic particles between two oscillating walls

This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles’ average energy increases abruptly at certain critical filling fractions, wherein the system changes into a solid-like phase with particles clustered in their compact form. Molecular dynamics simulations of the system show that the critical filling fraction is a decreasing function of vibration amplitude independent of vibration frequency, which is consistent with previous experimental results. This study considers the entire group of particles as a giant pseudo-particle with an effective size and an effective coefficient of restitution. The N-particles system is then analytically treated as a one-particle problem. The critical filling fraction’s dependence on vibration amplitude can be explained as a necessary condition for a stable resonant solution. The fluctuation to the system’s mean flow energy is also studied to show the relation between the granular temperature and the system phase.     

Electromagnetic scattering of high-permittivity particles on a substrate

We contribute to the study of the optical properties of high-permittivity nanostructures deposited on surfaces. We present what we believe is a new computational technique derived from the coupled-dipole approximation (CDA), which can accommodate high-permittivity scatterers. The discretized CDA equations are reformulated by use of the sampling theory to overcome different sources of inaccuracy that arise for high-permittivity scatterers. We first give the nonretarded filtered surface Green's tensor used in the new scheme. We then assess the accuracy of the technique by comparing it with the standard CDA approach and show that it can accurately handle scatterers with a large permittivity.     

Light scattering on Chebyshev particles of higher order

We present what we believe to be the first results of a light-scattering analysis on several Chebyshev particles characterized by higher orders. Chebyshev particles of comparatively lower orders were used in the past to study the effects of nonspherical but concave geometries in remote sensing applications. We will show that, based on the developed methodology, accurate results can also be obtained for particles of higher orders exhibiting a more pronounced surface waviness. The achieved results demonstrate that higher-order Chebyshev particles can be used to estimate the influence of a weak surface roughness on the light-scattering behavior of the underlying smooth scatterer. The effects obtained correspond with the results of other approaches and with the theoretical expectations of a weak surface roughness. In contrast to what is known for regular particles, there can be observed an essential difference between the phase functions of the underlying spherical scatterer and the corresponding higher-order Chebyshev particle if a higher absorptivity of the scattering medium is considered. This paper demonstrates additionally that Chebyshev polynomials can be simply combined with smooth geometries other than spheres.     

Light scattering by ellipsoids in a physical optics approximation

A physical optics approximation based on Presnel's laws is developed to calculate the intensity of light scattered by a three-axis ellipsoid of any orientation and any refractive index. Some results concerning totally reflecting spheres and dielectric spheroids are presented. An approach suitable for large scatterers is particularly good for small scattering angles. The angular intensities, i(1) and i(2), are then plotted versus θ for large axially oriented ellipsoids of various thicknesses. Theoretical small-angle light-scattering patterns are also presented and discussed. The data from one of them correspond to red cells in a shear flow.     

Hydrodynamics of rapid granular flow of inelastic particles into vacuum

The problem of expansion of a dilute granular gas consisting of smooth, inelastic hard spheres into vacuum was investigated by three different methods: both (1) analytical and (2) computational (CFD) treatments of a hydrodynamic model, and (3) by Discrete Element Method (DEM) simulation. Furthermore, the systems were followed for long times, over which the granular kinetic energy decreases by several hundredfold. The hydrodynamic model assumes that the particles are uniformly distributed in space, yet, in the DEM simulations, the particles are free to cluster. Thus the comparison allows us to evaluate the effects of cluster formation on the system. All three methods give quantitatively similar results for the escape momentum, energy evolution, and for the hydrodynamic velocity distribution, even for restitution coefficients as small as e=0.8. The maximum deviation between the escape momentum computed from the hydrodynamic model and from DEM is shown to be no more than 4%. This means that cluster formation exerts only a relatively minor effect on the hydrodynamic quantities, suggesting to us that the hydrodynamic model in combination with the CFD algorithm may provide an efficient tool in other related problems. In addition, it is one of few cases where hydrodynamic theory and DEM agree quantitatively. Received: 17 June 2002