Charles Acquista

Light scattering by tenuous particles - A generalization of the Rayleigh-Gans-Rocard approach

We consider scattering by arbitrarily shaped particles that satisfy two conditions: (1) that the polarizability of the particle relative to the ambient medium be small compared to 1 and (2) that the phase shift introduced by the particle be less than 2. We solve the integro-differential equation proposed by Shifrin by using the method of successive iterations and then applying a Fourier transform. For the second iteration, results are presented that accurately describe scattering by a broad class of particles. The phase function and other elements of the scattering matrix are shown to be in excellent agreement with Mie theory for spherical scatterers.

Scattering of light from arbitrarily oriented finite cylinders

An iterative approach to the scattering of light from a finite dielectric cylinder first developed by Shifrin and extended by Acquista is applied to cases where the phase shift is <2, and the cylinder is arbitrarily oriented. It is found that the first 2 orders of the iteration converge to within 1% when the aspect ratio (length/diameter) of the cylinder is as small as 20. The results are compared to the exact theory for infinite cylinders, and the effects of finite size are calculated and discussed.

Asymptotic behavior of the efficiencies in Mie scattering

We prove that a previous derivation of the scattering and extinction efficiencies for infinitely large absorbing spheres is incorrect, and leads to an erroneous limit for the scattering efficiency. We then derive an expression for the scattering efficiency limit from geometrical optics and that is valid when the refractive index has a small imaginary part.

Validity of modifying Mie theory to describe scattering by nonspherical particles

A calculation procedure has been developed (Chylek et al., 1976) for determining the scattering properties of irregularly shaped, randomly oriented particles. The procedure uses a modified form of the Mie theory for spheres with equivalent cross-sectional areas. The validity of the procedure is examined with reference to the work of Welch and Cox (1978). Particular consideration is given to: (1) the assumption that surface waves constitute the only major difference between scattering by spherical and nonspherical particles, (2) the identification of certain properties of the Mie coefficients with surface waves, and (3) the technique of removing surface waves from the Mie theory. It is concluded that the idea of determining the scattering properties of random orientations of irregular particles by eliminating surface waves from the Mie expansion is valid. It is also found that the technique for removing the resonances leads to the introduction of substantial fictitious absorption.

Light scattering from dielectric targets composed of a continuous assembly of circular disks

A technique for computing the electromagnetic fields scattered by spheres, cylinders, spheroids, spirals, toroids, and other targets which can be subdivided into circular disks is given. First-order calculations are performed for targets the size and refractive index of which preclude the creation of standing waves within the target. It is found that the scattering signatures of these various shapes are distinguishable for wavelengths larger than the target, but the differences rapidly diminish, as expected, with increasing wavelength. Finite cylinders are compared to prolate spheroids of equal volume, toroids are compared with oblate spheroids of equal volume, and calculations of the CIDS ratio for a spiral target are made for various wavelengths. It is found, on comparing these spiral calculations to other work on essentially 1-D spirals, that giving the spiral wire even a very small radius significantly affects the CIDS pattern for backscattering.

Light scattering by tilted cylinders: properties of partial wave coefficients

We investigate relations among the partial-wave coefficients that describe scattering by infinite cylinders in terms of the parameters governing this process: the refractive index m, the size parameter x, and the tilting angle ϕ. We present a complete set of relations for nonabsorbing cylinders, and we discuss their physical significance in terms of the principles of reciprocity and energy conservation. In particular, we find that energy conservation for this nonspherical shape leads to additional constraints not present in the case of scattering by spheres.

Shifrin’s Method Applied to Scattering by Tenuous Non-Spherical Particles

Shifrin constructed an integro-differential equation to describe the scattering characteristics of an irregular particle and developed an iterative procedure for solving the equation. This procedure is fast enough to handle many physical problems that involve scattering by a cloud of particles with different sizes, shapes and orientations. In particular, the case of tenuous particles (small size or weakly refracting) will be considered, and Shifrin’s procedure will be shown to be a generalization of the Rayleigh-Gans approximation.

Apparatus for continuous, fast, and precise measurements of position and velocity of a small spherical particle

The position and velocity of optically levitated glass spheres (radii 10–20 μm) moving in a gas are measured accurately, rapidly, and continuously using a high‐speed rotating polygon mirror. The experimental technique developed here has repeatable position accuracies better than 20 μm. Each measurement takes less than 1 μs and can be repeated every 100 μs. The position of the levitated glass spheres can be manipulated accurately by modulating the laser power with an acoustic optic modulator. The technique provides a fast and accurate method to study general particle dynamics in a fluid.

Energy conservation - A test for scattering approximations

We explore the roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations. We show that the Rayleigh, Rayleigh-Gans, Anomalous Diffraction, Geometrical Optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the Modified Mie approximation does not. Further examination of the Modified Mie approximation for the ensembles of non-spherical particles reveals additional problems with that method.