Файл: Doicu A., Wriedt T., Eremin Y.A. Light scattering by systems of particles (OS 124, Springer, 2006.pdf

Fig. 3.10. Variation of the normalized di erential scattering cross-sections with the beam waist radius

Fig. 3.11. Particles with extreme geometries: prolate spheroid, fibre, oblate cylinder and Cassini particle

astrophysics, atmospheric science and optical particle sizing. For example, light scattering by finite fibres is needed in optical characterization of asbestos or other mineral fibres, while flat particles are encountered as aluminium or mica flakes in coatings.

Figure 3.11 summarizes the particle shapes considered in our exemplary simulation results. The spheroid is a relatively simple shape but convergence problems occur for large size parameters and high aspect ratios. The finite fibre is a more extreme shape because the flank is even and without convexities. This shape is modeled by a rounded prolate cylinder, i.e., by a cylinder with two half-spheres at the ends. In polar coordinates, a rounded prolate cylinder as shown in Fig. 3.12 is described by

208 3 Simulation Results

z

2b

z1

z2

x

O

2a

zN

Fig. 3.12. Geometry of a prolate cylinder and the distribution of the discrete sources on the axis of symmetry

where θ0 = arctan[b/(a − b)]. The rounded oblate cylinder is constructed quite similar, i.e., the flank is rounded and top and bottom are flat. An oblate cylinder as shown in Fig. 3.13 is described in polar coordinates by

where θ0 = arctan[(b − a)/a]. Cassini particles are a real challenge for light scattering simulations because the generatrix contains concavities on its top and bottom. The Cassini ovals can be described in polar coordinates by the equation

and the shape depends on the ratio b/a. If a < b the curve is an oval loop, for a = b the result is a lemniscate, and for a > b the curve consists of two separate loops. If a is chosen slightly smaller than b we obtain a concave, bone-like shape, and this concavity becomes deeper as a approaches to b.

For the prolate particles considered in our simulations, the sources are distributed on the axis of symmetry as in Fig. 3.12, while for the oblate particles, the sources are distributed in the complex plane as in Fig. 3.13. The wavelength of the incident radiation is λ = 0.6328 µm, the relative refractive index

z

Fig. 3.13. Geometry of an oblate cylinder and the distribution of the discrete sources in the complex plane

Table 3.3. Surface parameters of particles with extreme geometries

Table 3.4. Maximum expansion and azimuthal orders for particles with extreme geometries

is mr = 1.5 and the scattering characteristics are computed in the azimuthal plane ϕ = 0◦. The parameters describing the geometry and orientation of the particles are given in Table 3.3, while the parameters controlling the convergence process are listed in Table 3.4. Note that the Cassini particle has a diameter of about 3.15 µm and an aspect ratio of about 1/4.