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

202 3 Simulation Results

Z z

a

β

O

Y

α

b

Fig. 3.3. Geometry of a prolate spheroid

Localized Sources

In our first example, we consider prolate spheroids in random and fixed orientation, and compare the results obtained with the TAXSYM code to the solutions computed with the codes developed by Mishchenko [167–169]. The orientation of the axisymmetric particle with respect to the global coordinate system is specified by the Euler angles of rotation αp and βp, and the incident field is a linearly polarized plane wave propagating along the Z-axis (Fig. 3.3). The rotational semi-axis (along the axis of symmetry) is ksa = 10, the horizontal semi-axis is ksb = 5, and the relative refractive index of the spheroid is mr = 1.5. The maximum expansion order and the number of integration points are Nrank = 17 and Nint = 100, respectively. In Figs. 3.4 and 3.5 we plot some elements of the scattering matrix for a randomly oriented spheroid. The agreement between the curves is acceptable. For a fixed orientation of the prolate spheroid, we list in Tables 3.1 and 3.2 the phase matrix elements Z11 and Z44, and Z21 and Z42, respectively. The Euler angles of rotation are αp = βp = 45◦, and the matrix elements are computed in the azimuthal planes ϕ = 45◦ and ϕ = 225◦ at three zenith angles: 30◦, 90◦, and 150◦. The relative error is around 10% for the lowest matrix element and remains below 1% for other elements.

In the next example, we show results computed for a perfectly conducting spheroid of size parameter ksa = 10, aspect ratio a/b = 2, and Euler angles of rotation αp = βp = 45◦. The perfectly conducting spheroid is simulated from the dielectric spheroid by using a very high value of the relative refractive index (mr = 1.e+30), and the version of the code devoted to the analysis of perfectly conducting particles is taken as reference. For this application, the

Fig. 3.4. Scattering matrix elements F11 and F22 of a dielectric prolate spheroid

Scattering Angle (deg)

Fig. 3.5. Scattering matrix elements F21 and F43 of a dielectric prolate spheroid

maximum expansion order is Nrank = 18, while the number of integration points is Nint = 200. The normalized di erential scattering cross-sections presented in Fig. 3.6 are similar for both methods.

To verify the accuracy of the code for isotropic, chiral particles, we consider a spherical particle of size parameter ksa = 10. The refractive index of the particle is mr = 1.5 and the chirality parameter is βki = 0.1, where ki = mrks. Calculations are performed for Nrank = 18 and Nint = 200. Figure 3.7 compares the normalized di erential scattering cross-sections computed with the

204 3 Simulation Results

Table 3.1. Phase matrix elements 11 and 44 computed with (a) the TAXSYM routine and (b) the code of Mishchenko

Table 3.2. Phase matrix elements 21 and 42 computed with (a) the TAXSYM routine and (b) the code of Mishchenko

Fig. 3.6. Normalized di erential scattering cross-sections of a perfectly conducting prolate spheroid

206 3 Simulation Results

Fig. 3.8. Variation of the normalized di erential scattering cross-sections with the axial position of a prolate spheroid illuminated by a Gaussian beam

Fig. 3.9. Variation of the normalized di erential scattering cross-sections with the o -axis coordinate of a prolate spheroid illuminated by a Gaussian beam

Distributed Sources

While localized sources are used for not extremely aspherical particles, distributed sources are suitable for analyzing particles with extreme geometries, i.e., particles whose shape di ers significantly from a sphere. Extremely deformed particles are encountered in various scientific disciplines as for instance