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

3.9 Particle on or Near a Plane Surface

In this section, we present scattering results for an axisymmetric particle situated on or near a plane surface. For this purpose we use the TPARTSUB routine and a computer program based on the discrete sources method [59,60].

Figures 3.72–3.74 show the di erential scattering cross-sections for Fe-, Siand SiO-spheroids with semi-axes a = 0.05 µm and b = 0.025 µm. The relative refractive indices are: mr = 1.35 + 1.97j for Fe, mr = 4.37 + 0.08j for

Scattering Angle (deg)

Fig. 3.72. Normalized di erential scattering cross-sections of a Fe-spheroid computed with the TPARTSUB routine and the discrete sources method (DSM)

Scattering Angle (deg)

Fig. 3.73. Normalized di erential scattering cross-sections of a Si-spheroid computed with the TPARTSUB routine and the discrete sources method (DSM)

246 3 Simulation Results

Scattering Angle (deg)

Fig. 3.74. Normalized di erential scattering cross-sections of a SiO-spheroid computed with the TPARTSUB routine and the discrete sources method (DSM)

Si, and mr = 1.67 for SiO. The particles are situated on a silicon substrate, the wavelength of the incident radiation is λ = 0.488 µm, and the incident angle is β0 = 45◦. The plotted data show that the T -matrix method leads to accurate results.

In the next example, we investigate scattering of evanescent waves by particles situated on a glass prism. We note that evanescent wave scattering is important in various sensor applications such as the total internal reflection microscopy TIRM [195]. Choosing the wavelength of the external excitation as λ = 0.488 µm and taking into account that the glass prism has a refractive index of mrs = 1.5, we deduce that the evanescent waves appear for incident angles exceeding 41.8◦. In Figs. 3.75–3.77, we plot the di erential scattering cross-section for Ag-, diamond-, and Si-spheres with a diameter of d = 0.2 µm. The relative refractive indices of Agand diamond particles are mr = 0.25 + 3.14j and mr = 2.43, respectively. The scattering plane coincides with the incident plane and the angle of incidence is β0 = 60◦. The plotted data show a good agreement between the discrete sources and the T -matrix solutions.

3.10 E ective Medium Model

The e ective wave number of a half-space with randomly distributed spheroidal particles can be computed with the EFMED routine.

First we consider spherical particles and compare our results to the solutions obtained with the Matlab program QCAMIE included in the Electro-

Scattering Angle (deg)

Fig. 3.75. Normalized di erential scattering cross-sections of a metallic Ag-sphere computed with the TPARTSUB routine and the discrete sources method (DSM)

Scattering Angle (deg)

Fig. 3.76. Normalized di erential scattering cross-sections of a Diamond-sphere computed with the TPARTSUB routine and the discrete sources method (DSM)

magnetic Wave Matlab Library and available from www.emwave.com. This library contains several Matlab programs which are based on the theory given in the book of Tsang et al. [229]. Figures 3.78 and 3.79 show the normalized phase velocity ks/Re{Ks} and the e ective loss tangent 2Im{Ks}/Re{Ks} as functions of the size parameter x = ksR, and it is apparent that no substantial di erences between the curves exist.

248 3 Simulation Results

Scattering Angle (deg)

Fig. 3.77. Normalized di erential scattering cross-sections of a Si-sphere computed with the TPARTSUB routine and the discrete sources method (DSM)

Size Parameter

Fig. 3.78. Normalized phase velocity versus size parameter computed with the EFMED routine and the Matlab program QCAMIE

Next we consider the test examples given by Neo et al. [179] and compare the T -matrix results to the solutions obtained with the long-wavelength quasicrystalline approximation