Scattering from arbitrarily shaped particles: theory and experiment

Discrete dipole approximation method for electromagnetic scattering by particles in an absorbing host medium

Electromagnetic (EM) scattering by particles in an absorbing host medium is frequently encountered in practical applications, which makes the conventional EM scattering theory controversial and most of the theoretical methods for EM scattering inapplicable. Most of the relevant works in literature are confined to spherical particles. In this work, we develop the discrete dipole approximation (DDA) method for EM scattering by an arbitrary particle immersed in an absorbing host medium. We elaborate how the near- and far-field scattering quantities can be calculated by DDA. The accuracy of DDA is validated by comparison with the apparent and inherent scattering quantities of spherical particles computed by exact Mie theory. Then EM extinction by non-absorbing spheroids in absorbing host medium is studied by DDA. We find that particles that are prolonged in the incident direction are more likely to produce a negative apparent extinction, which is also supported by the near-field electric field distribution. The DDA method we develop will be useful and flexible in the study of EM scattering by particles in absorbing host medium.

Cross-sectional particle measurement in the resonance domain on the substrate through scatterometry

We developed a versatile method for three-dimensional shape measurement where a specific particle can be selected on the substrate and its cross-sectional shape and size can be measured. A non-contact fast measurement is possible for the particle in the resonance domain. We applied rigorous coupled-wave analysis to the particle and calculated the diffraction patterns, comparing the patterns with the experimental results to obtain the size and shape. The shape and position of the focusing spot on the scattering particle was controlled precisely. With this method, the category of the analyzable object is extended to more shapes, such as rectangles and triangles, in addition to a conventional ellipsoid.

Computational study of the surface-enhanced Raman scattering from silica-coated silver nanowires

Surface-enhanced Raman scattering (SERS) is a popular vibrational spectroscopic technique that can have several applications in chemical and biological sensing. Within the last decade or so, our ability to chemically synthesize nanostructures has improved to the point that the rational design of a variety of SERS substrates is now viable. In this report, we describe a computational study using the finite element method (FEM) to investigate the effects of patchy silica coatings on silver nanowires. We found that varying the degree of silica coating on silver nanowires impacts the enhancement and may be explained through two processes. The first process is a consequence of changes in the dielectric environment surrounding the nanowire due to the silica. As additional layers of silica coat the nanowire, the localized surface plasmon resonance of the nanowire redshifts. The second process is a result of silica distorting the local electric field around the nanowire surface. Anisotropic silica coating can influence anticipated enhancement depending on its spatial localization with respect to excited plasmon modes in the nanowire. We propose that the design of nanostructures with patchy silica coatings can be a viable tool for increasing surface enhancement.

Convergence of the discrete dipole approximation. I. Theoretical analysis

We perform a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear term and a quadratic term in the size of a dipole d when the latter is in the range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for noncubically shaped scatterers. Therefore, for small d, errors for cubically shaped particles are much smaller than for noncubically shaped ones. The relative importance of the linear term decreases with increasing size; hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations are carried out for a wide range of d. Finally, we discuss a number of new developments in DDA and their consequences for convergence.

Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy

We propose an extrapolation technique that allows accuracy improvement of discrete dipole approximation computations. The performance of this technique was studied empirically on the basis of extensive simulations for five test cases using many different discretizations. The quality of the extrapolation improves with refining discretization, reaching extraordinary performance especially for cubically shaped particles. A 2-order-of-magnitude decrease of error is demonstrated. We also propose estimates of the extrapolation error, which are proven to be reliable. Finally, we propose a simple method to directly separate shape and discretization errors and illustrate this for one test case.

Initial phase of laser-induced air optical breakdown: a new picture

Optical breakdown has been generated by focusing YAG laser radiation in the air. The laser radiation itself was scattered due to laser-induced air optical breakdown. Angular distributions of scattered radiation at 1064, 532, and 355 nm were measured. Analysis of the distributions has been performed in terms of Mie scattering. It has been assumed that scattering of laser radiation is due mainly to highly ionized plasma balls in the initial phase of air optical breakdown. The wavelength-dependent angular distribution has been analyzed with two parameters. The mean radius and the plasma frequency of the plasma balls have been determined by a least-squares fit procedure. Observed wavelength-dependent angular distributions are in good agreement with ones calculated by Mie theory.

Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals

A new geometric-optics model has been developed for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. The model uses the ray-tracing technique to solve the near field on the ice crystal surface, which is then transformed to the far field on the basis of the electromagnetic equivalence theorem. From comparisons with the results computed by the finite-difference time domain method, we show that the novel geometric-optics method can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as ~6. Overall agreement has also been obtained for the phase function when size parameters along the minimum dimension are larger than ~20. We demonstrate that the present model converges to the conventional ray-tracing method for large size parameters and produces single-scattering results close to those computed by the finite-difference time domain method for size parameters along the minimum dimension smaller than ~20. The present geometric-optics method can therefore bridge the gap between the conventional ray-tracing and the exact numerical methods that are applicable to large and small size parameters, respectively.

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.

Application of the exact solution for scattering by an infinite cylinder to the estimation of scattering by a finite cylinder

A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.

Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation

We report the results of an extensive study of the scattering of light by size and size-shape distributions of randomly oriented prolate and oblate spheroids with the index of refraction 1.5 + 0.02i typical of some mineral terrestrial aerosols. The scattering calculations have been carried out with Waterman's T-matrix approach, as developed recently by Mishchenko [J. Opt. Soc. Am. A 8, 871 (1991); Appl. Opt. 32, 4562 (1993)]. Our main interest is in light scattering by polydisperse models of nonspherical particles because averaging over sizes provides more realistic modeling of natural ensembles of scattering particles and washes out the interference structure and ripple typical of monodisperse scattering patterns, thus enabling us to derive meaningful conclusions about the effects of particle nonsphericity on light scattering. Following Hansen and Travis [Space Sci. Rev. 16, 527 (1974)], we show that scattering properties of most physically plausible size distributions of randomly orientednonspherical part cles depend primarily on the effective equivalent-sphere radius and effective variance of the distribution, the actual shape of the distribution having a minor influence. To minimize the computational burden, we have adopted a computationally convenient power law distribution of particle equivalent-sphere radii n(r) α r(-3),r(1) ≤ r≤r(2). The effective variance of the size distribution is fixed at 0.1, and the effective size parameter continuously varies from 0 to 15. We present results of computer calculations for 24 prolate and oblate spheroidal shapes with aspect ratios from 1.1 to 2.2. The elements of the scattering matrix for the whole range of size parameters and scattering angles are displayed in the form of contour plots. Computational results are compared with analogous calculations for surface-equivalent spheres, and the effects of particle shape on light scattering are discussed in detail.

Single scattering of light by circular cylinders

We consider two topics pertaining to light scattering by circular cylinders. (A) Scattering properties of cylinders with increasing aspect ratio are studied. It is shown that the solution for finite cylinders does not converge to the solution for infinitely long cylinders if the aspect ratio increases. This is due to differences in the treatment of diffraction for finite and infinite cylinders. (B) Finite cylinders have sharp edges, so their scattering properties differ from those of spheroids having the same aspect ratio. To illustrate these differences we present scattering matrix elements of cylinders and spheroids for a large set of aspect ratios. To handle the large amount of data, the scattering matrix elements as functions of aspect ratio and scattering angle are presented in so-called three-dimensional figures.

Experimental determination of scattering matrices of water droplets and quartz particles

An experimental setup for measuring scattering matrices of various kinds of small particles is described. By using polarization modulation eight scattering-matrix elements, six of which are independent (or four in the case of spheres), can be obtained from four separate measurements. Test results for water droplets are presented as well as preliminary results for irregularly shaped quartz (SiO(2)) particles with an effective radius of approximately 15 microm. Four inequalities yielding conditions for combinations of scattering-matrix elements were used for checking all the results presented.