Light scattering by a coated sphere illuminated with a Gaussian beam

The intensity of light scattered by a coated sphere illuminated with an off-axis Gaussian beam is calculated. Results are shown for different beam positions with respect to the sphere. As the beam is shifted further away from the surface of the sphere, the higher-Q morphology-dependent resonances become increasingly important in the backscatter spectra, and the angular scattering intensity becomes smoother.

The scattered intensity depends on the beam position, the refractive indices of the core and coat, the radius of the core, and the thickness of the coat. As the beam is moved further away from the sphere, the effect of the core on the scattering intensity decreases. When the incident Gaussian beam is focused outside of a particle with a relatively small core, the scattering spectra and angular scattering patterns become similar to those of a homogeneous sphere having the refractive index of the coat. These calculated results suggest that measurements of spectral scattering and angular scattering patterns for several Gaussian beam positions could be useful for the characterization of coated spheres.

     

Rainbow scattering by a coated sphere

We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core a(12) and the thickness of the coating δ are varied. As the ratio δ/a(12) increases from 10(-4) to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For δ/a(12) ? 10(-3), the rainbow intensity is an oscillatory function of the coating thickness, for δ/a(12) ≈ 10(-2), the first-order rainbow breaks into a pair of twin rainbows, and for δ/a(12) ≈ 0.33, various rainbow-extinction transitions occur. Each of these effects is analyzed, and their physical interpretations are given. A Debye series decomposition of coated-sphere partial-wave scattering amplitudes is also performed and aids in the analysis.     

Light scattering from an optically active sphere into a circular aperture

To show how apertures affect measurements of the circularly polarized components of light scattered to a detector, we develop two methods of averaging the V and I Stokes parameters over a circular aperture that collects light scattered from an optically active sphere. One method uses a two-dimensional numerical integration that is appropriate for small apertures, and the other gives analytical expressions for scattering into a solid angle of any size. We identify the aperture locations that, independent of aperture size, give an average V (and an effective degree of circular polarization) of zero for scattering from an optically inactive sphere and of nonzero for scattering from an optically active sphere.     

Light scattering losses of high reflection dielectric multilayer optical devices

Light scattering losses from dielectric multilayer are becoming increasingly important for designing high precision performance optical devices. In this paper, we applied the bi-directional reflectance distribution function of optical multilayer and analyzed the total reflectance scattering losses based on both the completely correlated and non-correlated interface models to compare with a high reflection 17-layer optical multilayer deposited on roughness of 2.8 nm substrates. The experimental result supports the completely correlated interface model as firstly the wavelength dependence is in good agreement with the phase change of the calculated result and secondly the calculated scattering intensity of the completely correlated interface scattering model is approximately the same as that of the measured scattering spectrum, while the intensity using the non-correlated interface scattering model is significantly higher than the measured result in the high transmission ranges and lower in the main band of the high reflection range.     

Forward scattering of a Gaussian beam by a nonabsorbing sphere

The forward scattering of a Gaussian laser beam by a spherical particle located along the beam axis is analyzed with the generalized Lorenz-Mie theory (GLMT) and with diffraction theory. Forwardscattering and near-forward-scattering profiles from electrodynamically levitated droplets, 51.6 μm in diameter, are also presented and compared with GLMT-based predictions. The total intensity in the forward direction, formed by the superposition of the incident and the scattered fields, is found to correlate with the particle-extinction cross section, the particle diameter, and the beam width. Based on comparison with the GLMT, the diffraction solution is accurate when beam widths that are approximately greater than or equal to the particle diameter are considered and when large particles that have an extinction efficiency near the asymptotic value of 2 are considered. However, diffraction fails to describe the forward intensity for more tightly focused beams. The experimental observations, which are in good agreement with GLMT-based predictions, reveal that the total intensity profile about the forward direction is quite sensitive to particle axial position within a Gaussian beam. These finite beam effects are significant when the ratio of the beam to the particle diameter is less than approximately 5:1. For larger beam-to-particle-diameter ratios, the total field in the forward direction is dominated by the incident beam.     

Debye series for light scattering by a multilayered sphere

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.     

Electromagnetic-wave scattering by a sphere with multiple spherical inclusions

An exact solution to the problem of electromagnetic-wave scattering from a sphere with an arbitrary number of nonoverlapping spherical inclusions is obtained by use of the indirect mode-matching technique. A set of linear equations for the wave amplitudes of the electric field intensity throughout the inhomogeneous sphere and in the surrounding empty space is determined. Numerical results are calculated by truncation and matrix inversion of that set of equations. Specific information about the truncation number pertaining to the multipole expansions of the electric field intensity is given. The theory and the accompanying computer code successfully reproduce the results of other pertinent papers. Some numerical results [Borghese et al., Appl. Opt. 33, 484 (1994)] were not reproduced well, and that discrepancy is discussed. Our numerical investigation is focused on an acrylic sphere with up to four spherical inclusions. This is the first time that numerical results are presented for a sphere with more than two spherical inclusions. Interesting remarks are made about the effect that the look direction and the structure of the inhomogeneity have on backscattering by the acrylic host sphere.     

Light scattering by a multilayered spheroidal particle

The light scattering problem for a confocal multilayered spheroid has been solved by the extended boundary condition method with a corresponding spheroidal basis. The solution preserves the advantages of the approach applied previously to homogeneous and core-mantle spheroids, i.e., the separation of the radiation fields into two parts and a special choice of scalar potentials for each of the parts. The method is known to be useful in a wide range of the particle parameters. It is particularly efficient for strongly prolate and oblate spheroids. Numerical tests are described. Illustrative calculations have shown that the extinction factors converge to average values with a growing number of layers and how the extinction varies with a growth of particle porosity.     

Light scattering by a core-mantle spheroidal particle

A solution of the electromagnetic scattering problem for confocal coated spheroids has been obtained by the method of separation of variables in a spheroidal coordinate system. The main features of the solution are (i) the incident, scattered, and internal radiation fields are divided into two parts: an axisymmetric part independent of the azimuthal angle ? and a nonaxisymmetric part that with integration over ? gives zero; the diffraction problems for each part are solved separately; (ii) the scalar potentials of the solution are chosen in a special way: Abraham's potentials (for the axisymmetric part) and a superposition of the potentials used for spheres and infinitely long cylinders (for the nonaxisymmetric part). Such a procedure has been applied to homogeneous spheroids [Differential Equations 19, 1765 (1983); Astrophys. Space Sci. 204, 19, (1993)] and allows us to solve the light scattering problem for confocal spheroids with an arbitrary refractive index, size, and shape of the core or mantle. Numerical tests are described in detail. The efficiency factors have been calculated for prolate and oblate spheroids with refractive indices of 1.5 + 0.0 i, 1.5 + 0.05 i for the core and refractive indices of 1.3 + 0.0 i, 1.3 + 0.05i for the mantle. The effects of the core size and particle shape as well as those of absorption in the core or mantle are examined. It is found that the efficiency factors of the coated and homogeneous spheroids with the volume-averaged refractive index are similar to first maximum.     

Off-axis scattering of an ultrasound bessel beam by a sphere

In this paper, the scattering of an ultrasound zero-order Bessel beam by a rigid sphere in the off-axis configuration is studied. The beam is described through the partial wave expansion. The beam-shape coefficients which represent the amplitude of each multipole mode of the partial wave expansion are computed by numerical quadrature. Calculations are presented for both near- and far-field off-axis scattering. The far-field scattering is examined in both Rayleigh and geometrical acoustic limits. Results demonstrate that the scattered pressure in the off-axis case may significantly deviate from that in the on-axis configuration. In addition, the directive pattern of the scattered pressure is highly dependent on the relative position of the beam to the sphere.     

Debye series for Gaussian beam scattering by a multilayered sphere

The Debye series has been a key tool for the understanding of light scattering features, and it is also a convenient method for understanding and improving the design of optical instruments aimed at optical particle sizing. Gouesbet has derived the Debye series formulation for generalized Lorenz-Mie theory (GLMT). However, the scattering object is a homogeneous sphere, and no numerical result is provided. The Debye series formula for plane-wave scattering by multilayered spheres has been derived before. We have devoted our work to the Debye series of Gaussian beam scattering by multilayered spheres. The integral localized approximation is employed in the calculation of beam-shape coefficients (BSCs) and allows the study of the scattering characteristics of particles illuminated by the strongly focused beams. The formula and code are verified by the comparison with the results produced by GLMT and also by the comparison with the result for the case of plane-wave incidence. The formula is also employed in the simulation of the first rainbow by illuminating the particle with one or several narrow beams.     

Improved recursive algorithm for light scattering by a multilayered sphere

An improved recurrence algorithm to calculate the scattering field of a multilayered sphere is developed. The internal and external electromagnetic fields are expressed as a superposition of inward and outward waves. The alternative yet equivalent expansions of fields are proposed by use of the first kind of Bessel function and the first kind of Hankel function instead of the first and the second kinds of Bessel function. The final recursive expressions are similar in form to those of Mie theory for a homogeneous sphere and are proved to be more concise and convenient than earlier forms. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by previous methods, especially for large, highly absorbing thin shells. Various calculations and tests show that this algorithm is efficient, numerically stable, and accurate for a large range of size parameters andrefractive indices.     

Low frequency electromagnetic scattering by a perfectly conducting moving sphere

The paper investigates the propagation of a plane electromagnetic waves in the exterior of a moving obstacle. Under the assumption that the obstacle moves with uniform velocity and more slowly than the incident field, we apply the Lorentz transformation. In the object’s frame, where the scatterer is stationary, we introduce the low-frequency approximation technique. For the near electromagnetic field we obtain the Rayleigh low-frequency coefficients while in the far field we derive the leading non-vanishing terms for the scattering amplitude and scattering cross-section. Finally, using the inverse transformation we express the same quantities in the observer’s frame.     

Light scattering by wood fibers

We consider the scattering of light by single wood fibers both theoretically and experimentally. We describe the size and the shape distributions and the internal structure and chemical composition of the wood fibers. We have modeled the random shape of the hollow, cylindrical wood fiber by using multivariate lognormal statistics. We have computed wood-fiber absorption and scattering cross sections, asymmetry parameters, and scattering phase matrices in the ray-optics approximation. Finally, we have provided experimental results from angular scattering measurements for wood fibers and present what we believe is the first comparison between these measurements and ray-optics computations for Gaussian random wood-fiber models. In spite of the complicated internal structure of the wood fiber, our model together with the ray-optics treatment explains the scattering measurements surprisingly well.     

The elastic theory dynamic problem for a transtropic multilayer sphere

The analytical solution is obtained in quadratures of the elastic theory dynamic centrally-symmetric boundary problems of the same class for multilayer transtropic spheres, the sonic speed in the radial direction of which tends to infinity. Convergence and accuracy of the derived solutions are analyzed. It is shown that the analytical solutions obtained can be used as the first approximation for the cases where the sonic speed in materials is finite.     

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.     

Light scattering by microscopic spheres behind a glass-air interface

Scattering of light from single spheres placed behind a glass-air interface with light incident through the glass is examined. This scattering is investigated for both p- and s-polarized light incident at angles below the glass-air critical angle. The intensity of light scattered into the air half-space from each sphere is measured as a function of scattering angle, and this response is compared in situ with the background scatter produced by the planar substrate. A detailed comparison between data and established theory are thereby obtained. This system is of interest in the field of optical biosensing.