I n t r o d u c t o r y   n o t e s   

The efficiency of interaction of radiation with a particle and hence its optical properties depend on the particle chemical composition, size, shape, structure, etc. [1,2]. The optical constants characterizing the optical properties of different materials are discussed in another section of the DOP while basic effects of the chemical composition (the refractive index) on the optical properties are illustrated in our graphics library. Here we address other primary characteristics of scatterers.

Size. Particle size expressed in units of the wavelength of incident radiation, together with chemical composition, most strongly affects the optical properties of a scatterer. The simplest model that allows one to consider the influence of size and composition variations is that of a homogeneous sphere. The Mie theory is the solution to the light scattering from a sphere and is applicable in the entire range of parameter values. Note that the interaction of large molecules/very small grains (e.g., polycyclic aromatic hydrocarbons, PAH) with radiation is not described by the macroscopic quantities and requires quantum mechanical consideration [3].

Shape. Real dust grains certainly differ from homogeneous spheres. Deviations of their shapes from the spherical one can be of different kinds - from small-scale surface fluctuations to large-scale shape defects. The asphericity characterized by the ratio of the maximum to minimum dimension of a scatterer looks to be most essential in astronomy and some other fields and can be well modelled using spheroidal particles as their shapes can vary from needles or disks to spheres. Thus, the spheroidal model allows one to analyze the effects of composition, size, and, to some extent, shape.

There are many methods to solve the light-scattering problem for a homogeneous spheroid (our survey of the light-scattering methods see here). First among them should be mentioned the separation of variables method (SVM) where the wave equation is formulated and the spheroidal wave functions are used in the solution to expand the incident, internal and scattered fields. Another popular approach - the extended boundary condition method (EBCM) coupled with the T-matrix method (TMM) consists of forming surface integral equation, but utilizes the simpler spherical wave functions in the expansion. For spheroids, the SVM and to a lesser degree the EBCM conform more readily to the system geometries, and as a result, the methods are much more fast and exact than other (more universal) approaches like the discrete dipole approximation (DDA) or finite difference time domain (FDTD) method [2,4]. Note that medium scale defects of the scatterer surface (like cavities) can be considered using the model of the Chebyshev particles and the EBCM (see, e.g., [5] and references therein). Scatterers with random surface fluctuations were studied, for instance, in [6].

Structure. Solid particles in real (e.g., cosmic) conditions hardly are homogeneous. Their internal structures can include layers, large and small (in comparison with the particle size) inclusions, and so on. In principle, scatterers of any structure can be treated by the methods using the representation of the scattering problem in the form of volume integral equation (e.g., the widely used DDA). The back sides of this universality are strong demands for computer memory and speed which often make computations impossible. Layered scatterers could be treated by the SVM and EBCM, which would allow really extensive calculations, but the theoretical methods are not yet well developed. If the dimensions of inclusions are smaller than the wavelength of incident radiation and their volume fraction is not large, one can calculate the effective refractive index of a composite particle using a rule of the effective medium theory (EMT; see, e.g., [7] for a review) and then apply any light scattering method for homogeneous particles.

Applicability of scatterer models - example of astronomy. For astronomical applications, the models of homogeneous and core-mantle spheres (and infinite cylinders) are primarily used. Models for homogeneous spheroids (and ellipsoids) have been applied only seldomly. Thus, the combined effects of shape and structure of cosmic dust grains have barely been studied. It should be added that although inhomogeneous non-spherical aggregates were utilized in a number of papers on cosmic dust modeling, very little attention has been paid on these effects (see, e.g., [8]).

Figure 1:   Applicability ranges (domains left to the curves) of different methods in the case of dielectric prolate spheroids. Calculations were made with codes based on the Rayleigh (RA) and quasistatic (QSA) approximations, the discrete dipole (DDA), separation of variables (SVM) and extended boundary condition/T-matrix (TMM) methods.

Several methods and codes have been recently developed to solve the light scattering problem for inhomogeneous (multilayered) non-spherical particles [9]. Both exact and approximate approaches were considered as they are useful in astronomy (in particular the Rayleigh approximation in the infrared). The ranges of applicability of these methods are shown in Fig.1 for the case of homogeneous dielectric spheroids. For layered particles, the ranges are generally similar [10].


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Mishchenko, M.I., Hovenier, J.W., and Travis, L.D. (2000) Light Scattering by Nonspherical Particles. Academic Press, San Diego.

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Last modified: 06/03/03, V.I.