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

Scattering Angle (deg)

Fig. 3.16. Normalized di erential scattering cross-sections of an oblate cylinder with a = 0.03 µm and b = 3.0 µm. The curves are computed with the TAXSYM routine and the discrete sources method (DSM)

10−3

Scattering Angle (deg)

Fig. 3.17. Normalized di erential scattering cross-sections of a Cassini particle with a = 1.1 and b = 1.125. The curves are computed with the TAXSYM routine and the discrete sources method (DSM)

mr = 1.5. The T -matrix calculations are performed with Nrank = 30 sources distributed in the complex plane and by using Nint = 300 integration points on the generatrix curve. The scattering characteristics plotted in Fig. 3.18 are calculated for the Euler angles of rotation αp = βp = 0◦ and for the case of normal incidence. Also shown are the results computed with the discrete

z

a

Fig. 3.20. Geometry of a hexagonal prism

a dielectric cube of length 2ksa = 10 and relative refractive index mr = 1.5. The incident wave propagates along the Z-axis of the global coordinate system and the Euler orientation angles are αp = βp = γp = 0◦. Convergence is achieved for Nrank = 14 and Mrank = 12, while the numbers of integration

0.628 µm, and the orientation of the hexagonal prism is specified by the Euler angles αp = βp = 0◦ and γp = 90◦. For this application, the maximum expansion and azimuthal orders are Nrank = 22 and Mrank = 20, respectively. Figure 3.21 compares results obtained with the TNONAXSYM routine and the finite integration technique. The agreement between the curves is acceptable.

Figure 3.22 illustrates the normalized di erential scattering cross-sections for a positive uniaxial anisotropic cube of length 2a = 0.3 µm, and relative refractive indices mrx = mry = 1.5 and mrz = 1.7. The principal coordinate system coincides with the particle coordinate system, i.e., αpr = βpr = 0◦. Calculations are performed at a wavelength of λ = 0.3 µm and for the case of normal incidence. The parameters controlling the T -matrix calculations are Nrank = 18 and Mrank = 18, while the numbers of integration points on each cube face are Nint1 = Nint2 = 50. The behavior of the far-field patterns obtained with the TNONAXSYM routine, discrete dipole approximation and finite integration technique is quite similar.

Figure 3.23 shows plots of the di erential scattering cross-sections versus the scattering angle for a negative uniaxial anisotropic ellipsoid of semi-axis lengths a = 0.3 µm, b = 0.2 µm and c = 0.1 µm, and relative refractive indices mrx = mry = 1.5 and mrz = 1.3. The orientation of the principal coordinate system is given by the Euler angles αpr = βpr = 0◦ and the wavelength of

Scattering Angle (deg)

Fig. 3.23. Normalized di erential scattering cross-sections of a uniaxial anisotropic ellipsoid computed with the TNONAXSYM routine and the finite integration technique (CST)

Nint2 = 100, respectively. The curves show that the di erential scattering cross-sections are reasonably well reproduced by the TNONAXSYM routine.

Next we present calculations for a dielectric, a perfectly conducting and a chiral cube of length 2ksa = 10. The refractive index of the dielectric cube is mr = 1.5 and the chirality parameter is βki = 0.1. The scattering characteristics are computed by using the symmetry properties of the transition matrix. For particles with a plane of symmetry perpendicular to the axis of rotation (mirror symmetric particles with the surface parameterization r(θ, ϕ) = r(π − θ, ϕ)) the T matrix can be computed by integrating θ over the interval [0, π/2], while for particles with azimuthal symmetry (particles with the surface parameterization r(θ, ϕ) = r(θ, ϕ+2π/N ), where N ≥ 2) the T matrix can be computed by integrating ϕ over the interval [0, 2π/N ]. For T -matrix calculations without mirror and azimuthal symmetries, the numbers of integration points on each square surface are Nint1 = Nint2 = 30. For calculations using azimuthal symmetry, the numbers of integration points on the top and bottom quarter-square surfaces are Nint1 = Nint2 = 20, while for calculations using mirror symmetry, the numbers of integration points on the lateral half-square surface are Nint1 = Nint2 = 20. The integration surfaces are shown in Fig. 3.24, and the di erential scattering cross-sections are plotted in Figs. 3.25–3.27. The results obtained using di erent techniques are generally close to each other.