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

n1

b1

Fig. 3.49. Geometry of a system of two prolate spheroids

and inhomogeneous, composite or layered particles. The flow diagram of the TMULT routine is as in Fig. 3.34.

Figure 3.49 illustrates a system of two spheroids of semi-axes ksa1 = ksa2 = 4 and ksb1 = ksb2 = 2, and relative refractive indices mr1 = mr2 = 1.5.

The Cartesian coordinates of the center of the second spheroid are ksx20 =

√

ksz20 = 4 2 and y20 = 0, while the Euler angles specifying the orientation of the spheroids are chosen as αp1 = βp1 = 0◦ and αp2 = βp2 = 45◦. The first computational step involves the calculation of the individual T -matrix of a spheroid by using the TAXSYM code, and for this calculation, the maximum expansion and azimuthal orders are Nrank = 10 and Mrank = 4, respectively. The individual T -matrices are then used to compute the T -matrix of the spheroids with respect to the origin O1, and the dimension of the system T - matrix is given by Nrank = 20 and Mrank = 18. In Fig. 3.50, we show the di erential scattering cross-sections computed with the TMULT routine and the multiple multipole method. The scattering curves are in good agreement.

As a second example, we consider a system of five spherical particles illuminated by a plane wave propagating along the Z-axis of the global coordinate system. The spheres are identical and have a radius of ksr = 2 and a relative refractive index of mr = 1.5, while the length specifying the position of the spheres is ksl = 6 (Fig. 3.51). The system T -matrix is computed with respect to the origin O and is characterized by Nrank = 18 and Mrank = 16. The scattering characteristics are computed with the TMULTSPH routine, and numerical results are again presented in the form of the di erential scattering cross-sections. The curves plotted in Fig. 3.52 correspond to a fixed orientation

234 3 Simulation Results

Scattering Angle (deg)

Fig. 3.54. Scattering matrix elements F21 and F43 of a system of five spheres computed with the TMULT routine and the code SCSMTM of Mackowski and Mishchenko [153]

OXY Z, two local coordinate systems O1x1y1z1 and O2x2y2z2 are defined, and the positions of the origins O1 and O2 are characterized by x01 = y01 = z01 = L and x02 = y02 = z02 = −L, respectively, where ksL = 6.5. In each local coordinate system, a system of two spheres is considered, and the distance between the sphere centers is 2ksl = 3.5, while the Euler angles specifying the orientation of the two-spheres system are αp1 = βp1 = 45◦ and αp2 = βp2 = 30◦. The Cartesian coordinates of the spheres are computed with respect to the global coordinate system and the TMULTSPH routine is used to compute the scattering characteristics. The dimension of the T - matrix of the four-sphere system is given by Nrank = 21 and Mrank = 19. A second technique for analyzing this scattering geometry involves the computation of the T -matrix of the two-sphere system by using the TMULT2SPH routine. In this case, Nrank = 16 and Mrank = 5, and the T -matrix of the twosphere system serves as input parameter for the TMULT routine. Figures 3.56 and 3.57 illustrate the di erential scattering cross-sections for a fixed (αp = βp = γp = 0◦) and a random orientation of the system of spheres. The far-field patterns are reproduced very accurately by both methods.

To demonstrate the capabilities of the TMULTSPH routine we present some exemplary results for polydisperse aggregates. Monodisperse aggregates of small spherical particles are characterized by the number of primary spherule N , the fractal dimension Df , the fractal pre-factor kf , the radius of gyration Rg, and the radius of the primary spherules rp. These morphological parameters are related in the form of a scaling law