Diffuse reflectance of TiO2 pigmented paints: Spectral dependence of the average pathlength parameter and the forward scattering ratio

Diffuse reflectance spectra of paint coatings with different pigment concentrations, normally illuminated with unpolarized radiation, have been measured. A four-flux radiative transfer approach is used to model the diffuse reflectance of TiO₂ (rutile) pigmented coatings through the solar spectral range. The spectral dependence of the average pathlength parameter and of the forward scattering ratio for diffuse radiation, are explicitly incorporated into this four-flux model from two novel approximations. The size distribution of the pigments has been taken into account to obtain the averages of the four-flux parameters: scattering and absorption cross sections, forward scattering ratios for collimated and isotropic diffuse radiation, and coefficients involved in the expansion of the single particle phase function in terms of Legendre polynomials.     

Angularly resolved light scattering from aerosolized spores: observations and calculations

Angularly resolved elastic light scattering patterns from individual aerosolized Bacillus subtilis spores were qualitatively compared with simulations. Two-dimensional angular optical scattering patterns of the spores were collected for polar scattering angles varying from approximately 77 degrees to 130 degrees and azimuthal angles varying from 0 degrees to 360 degrees . Computations were performed with single T-matrix formalism by simulating a spore with three different particle shapes: (1) a finite-length cylinder with spherical end caps, (2) a spheroid, and (3) two spheres in contact. Excellent agreement between computation and measurement was found for the finite-length cylinder with spherical end caps, poorer agreement was found for the spheroids, and the poorest agreement was for the two spheres in contact.     

Derivatives of light scattering properties of a nonspherical particle computed with the T-matrix method

Based on the T-matrix formalism, we analytically calculate derivatives of light scattering quantities by a nonspherical particle with respect to its microphysical parameters. Illustrative computations are performed for a spheroid, and the results agree with those obtained by finite differencing. The proposed formalism also predicts correctly derivatives for a sphere obtained by linearized Lorenz-Mie theory.     

A General T-Matrix Approach Applied to Two-Body and Three-Body Problems in Cold Atomic Gases

We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states, describing external center-of-mass motions of pairs of interacting particles; while each matrix element is guaranteed to be finite by a proper renormalization for internal relative motions. This approach is able to incorporate various scattering problems and the calculations of related physical quantities in a single framework, and also provides a physically transparent way to understand the mechanism of resonance scattering. For applications, we study two-body effective scattering in 2D–3D mixed dimensions, where the resonance position and width are determined with high precision from only a few number of matrix elements. We also study three fermions in a (rotating) harmonic trap, where exotic scattering properties in terms of mass ratios and angular momenta are uniquely identified in the framework of T-matrix.     

Scattering properties of rutile pigments located eccentrically within microvoids

We study the optical properties of opaque polymer pigmented coatings. The system consists of spherical rutile particles encapsulated in spherical microvoids embedded in a transparent polymer resin. The single-scattering properties of this system have been analyzed already, in case the rutile particle is located at the center of the microvoid . Here, we use a T-matrix approach to generalize and extend this analysis to the more realistic case when the rutile particles is located off-center within the microvoid. We also consider the multiple-scattering effects of a cluster composed by a collection of air bubbles with off-center rutile inclusions. Our calculations take into account the multiple scattering and the dependent-scattering processes of each pigment particle of the aggregate, using a new recursive T-matrix algorithm.     

Morphological characterization of cells in concentrated suspensions using multispectral diffuse optical tomography

Based on a non-spherical model of particle scattering, we investigate the capabilities and limitations of a T-matrix based inverse algorithm to morphologically characterize cells in concentrated suspensions. Here the cells are modeled as randomly orientated spheroidal particles with homogenous dielectric properties and suspended in turbid media. The inverse algorithm retrieves the geometrical parameters and the concentration of cells simultaneously by inverting the reduced scattering coefficient spectra obtained from multispectral diffuse optical tomography (MS-DOT). Both round and spheroidal cells are tested and the role of multiple and higher order scattering of particles on the performance of the algorithm is evaluated using different concentrations of cells.     

USING THE MULTIPLE SCATTERING THEORY FOR CALCULATION OF THE RADIATION FLUXES FROM EXPERIMENTAL AEROSOL DATA

The ground-based measurements of the spectral direct solar radiation fluxes and spectral sky radiances were basis for obtaining the aerosol characteristics such as columnar distribution function and effective refractive index, respectively. These characteristics were retrieved by a numerical solution of the inverse problem. The particle columnar size distribution function was chosen in the form of modified gamma distribution. The obtained aerosol parameters were utilized as input data for the multiple radiation scattering model (MRSM) to calculate the radiation fluxes. The dependence of calculation error of individual radiation characteristics (sky radiance, global and diffuse radiation) on a given number of terms NT (scattering orders) in the MRSM is studied. The NT necessary for successful calculation of radiation characteristics (for chosen accuracy) for actual atmospheric conditions is shown (aerosol optical properties were characterized, e.g., by spectral optical thickness). The approximate formulae for calculating the total sky radiances and total radiation fluxes, are find. Applying these formulae the value NT′ smaller than NT can be used for calculating radiation characteristics with the same accuracy. The scattering orders higher than NT′ are calculated on the basis of a known structure of previous scattering orders (1→NT′).     

Temperature and field dependent scattering in noble metal alloys

The scattering formalism of Blaker and Harris which is appropriate to potential scattering in dilute cubic alloys is modified to include the spin-dependent scattering. An expression for the total T-matrix which describes the ordinary and exchange scattering by magnetic impurities is obtained. The new formalism is compared with other work in the area and is used to discuss the dHvA data for Kondo alloys based on Cu and Au.     

Temperature and field dependent scattering in noble metal alloys

The scattering formalism of Blaker and Harris which is appropriate to potential scattering in dilute cubic alloys is modified to include the spin-dependent scattering. An expression for the total T-matrix which describes the ordinary and exchange scattering by magnetic impurities is obtained. The new formalism is compared with other work in the area and is used to discuss the dHvA data for Kondo alloys based on Cu and Au.Supported by the National Research Council of Canada.     

Scattering and Transmission by a Monolayer of Spheres: A Study on the Monolayer Structure

The angular distribution of scattered light and the transmission of radiation through a monolayer of monodisperse spherical particles at variable particle concentration are studied. The scattering of light by a single particle is calculated with the classical Lorentz‐Mie theory. For a monolayer of mono‐dispersed spherical particles, if the monolayer density is less than 0.5 and the particle size parameter is larger than 5, effects from multiple scattering and dependent scattering can be excluded so that only steric interactions are considered. It is found that the scattering pattern, especially in the forward and backward directions, and the transmission are strongly dependent on the monolayer density.     

Calculations of acoustic scattering from ellipsoidal voids: bends, krill and fish

The T-matrix approach is used to calculate the scattering of sound waves by an ellipsoidal void in a fluid. Results are presented for the total cross-section of a sphere as a function of frequency; this is related to the detection of the onset of bends in divers. Results are also presented for the angular variation in scattered amplitude when a plane wave is incident on an ellipsoidal cavity in water; this is related to the target strength of euphausiids and teleostean. It is concluded that the model is a useful representation of the scattering from such marine organisms.     

Manipulation of Particles with Counter-Propagating Evanescent Waves

Two counter-propagating evanescent beams are used to align and manipulate polystyrene particles on a prism surface. Since the radiation pressure transferred laterally from the evanescent wave is negated on both sides, particles can be stably aligned. By projecting a circular and a linear beam spot onto the interface, both multiple and single arrays of particles are achieved. Arrays of particles trapped on the interface can be easily moved adjusting the intensity of incident beams on either side. We also simulate electromagnetic distribution of scattering light that is converted from the evanescent wave using the FDTD method. The results show that scattering light converts from an evanescent wave propagating through a particle array and has a distance longer than that propagating from a normal evanescent wave.     

The multiple scattering theory of phonons in mass disordered lattices

A version of the multiple scattering theory previously applied to the electronic problem of substitutional alloys is completed and modified in order to handle the problem of vibrations of general mass-disordered crystal lattices. The Born series is expressed in terms describing the scattering corrections to the appropriate effective medium. A new physical interpretation of the effective medium condition is given and the total partial summation of the Born series for the full scattering T-matrix is completed to the infinite order. The T-matrix is thus re-expressed in terms corresponding to resonant “ping-pong” scattering of renormalized phonons on all possible clusters of scattering centres. Confining to clusters of only limited number of scattering centres yields a set of successive approximations. The one-centre approximation for cubic crystals complies with the Taylor's selfconsistent procedure. A simple illustrative example in the two-centre approximation is solved and discussed.     

Directional far-field response of a spherical nanoantenna

We study the directional far-field response of a spherical nanoantenna via engineering the plasmonic nanosphere's distance, size, and material. A unified pattern synthesis approach based on the T-matrix method and the particle swarm optimization is proposed for the directional beamforming of the nanoantenna. The angular response of the directional nanoantenna is very sensitive to the material change but is immunized to the random error of the spatial position of each particle. The physical origin of the high directionality is attributed to the coherent near-field distribution with large correlation length. This work provides the fundamental theory and physics for future nanoantenna design.     

Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

Aggregation and composition effects on absorption and scattering properties of dye-sensitized anatase TiO2 particle clusters

A transition matrix approach is used to compute the scattering and absorption cross sections, as well as phase functions, asymmetry factors and forward scattering ratios, of clusters of spherical particles. In order to approach the local structure and composition of the nanosized active layer of photoelectrochemical solar cells, some clusters consist of homogeneous non-absorbing anatase spherical pigments, others have anatase particles coated with a monolayer of absorbing dye molecules, and others can consist of both uncoated and dye-coated anatase particles. Orientation average values of the volumetric scattering and absorption cross sections are computed in terms of the size of the spherical particles in the clusters and their number. The degree of scattering and absorption when considering dye-coated anatase particles in the clusters is characterized. The effect of dependent scattering on the average angular distribution of the scattered radiation is also considered.     

The use of the galerkin method for radiation transfer in an anisotropically scattering slab with reflecting boundaries

Radiation transfer in an absorbing, emitting, anisotropically scattering, plane-parallel medium with diffusely reflecting boundaries is solved by application of the Galerkin method. With this approach, the radiation heat flux, angular distribution of radiation intensity, and the divergence of the radiation heat flux anywhere in the medium can be determined highly accurately. For optical thicknesses up to about 10, exact results are also readily obtainable if sufficient number of terms are considered in the expansion. Numerical results are presented for representative cases.     

Scattering of Electromagnetic Radiation by Linear Small-Particle Aggregates of Finite Dielectric Cylinders

Journal of Applied Spectroscopy - A volume integral equation formalism is used for numerical simulation of the normalized functions of the angular scattering intensity distribution for dimers and...     

Effect of anomalous photoabsorption on parametric X-ray radiation from relativistic electrons

Parametric x-ray radiation from relativistic electrons moving in a crystal is theoretically investigated in Bragg geometry. It is shown that the effect of anomalous photoabsorption can manifest itself within this geometry of the scattering of the pseudophoton field of a fast particle. In this case, the angular distribution of the radiation changes significantly, while the total radiation yield can increase by a factor of 3.