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

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226 3 Simulation Results

a1 a

Fig. 3.40. Geometry of a layered spheroid

Table 3.6. Parameters of calculation for an oblate layered spheroid

Type of sources Nrank-host particle		Nrank-inclusion Nint
Localized	17	12	500
Distributed	14	8	2,000

along the symmetry axis of the prolate spheroids. The maximum expansion orders are Nrank = 20 for the host spheroid and Nrank = 13 for the inclusion. The global number of integration points is Nint = 200 for localized sources, and Nint = 1000 for distributed sources. The TINHOM routine uses as input parameter the inclusion T -matrix, which is characterized by Nrank = 13 and Mrank = 5. The results presented in Figs. 3.41 and 3.42 show a complete agreement between the di erent methods.

Scattering by oblate spheroids can be computed with localized and discrete sources distributed in the complex plane. Figure 3.43 compares results obtained with localized and distributed sources for an oblate layered spheroid with ksa = 5, ksb = 10, ksa1 = 3 and ksb1 = 5. The relative refractive indices are mr = 1.2 and mr1 = 1.5, and the parameters of calculation are given in Table 3.6.

						3.5	Layered Particles		227
	101			TLAY - localized sources - parallel
				TLAY - localized sources - parallel
	100			TLAY - localized sources - perpendicular
	100			TLAY - distributed sources - parallel
				TLAY - distributed sources - parallel
	10−1			TLAY - distributed sources - perpendicular
	10−1			TINHOM - parallel
				TINHOM - perpendicular
DSCS	10−2
DSCS	−3
	10
	10−4
	10−5
	−6
	10	0	60	120	180	240	300	360
				Scattering Angle (deg)

Fig. 3.41. Normalized di erential scattering cross-sections of a layered spheroid

<DSCS>

101
	TLAY - localized sources - parallel
	TLAY - localized sources - perpendicular
100	TLAY - distributed sources - parallel
100	TLAY - distributed sources - perpendicular
	TINHOM - parallel
	TINHOM - perpendicular

10−1

10−2

−3
10	0	30	60	90	120	150	180

Scattering Angle (deg)

Fig. 3.42. Averaged di erential scattering cross-sections of a layered spheroid

For highly elongated particles, distributed sources are required to achieve convergence. The results plotted in Fig. 3.44 correspond to a layered cylinder with ksL = 10, ksr = 2, ksL1 = 5 and ksr1 = 1 (Fig. 3.45). The relative refractive indices of the host particle and the inclusions are mr = 1.2 and mr1 = 1.4, respectively. The maximum expansion orders are Nrank = 14 for

228 3 Simulation Results

DSCS

101
100			parallel - distributed sources
100			parallel - localized sources
10−1			perpendicular - distributed sources
10−1			perpendicular - localized sources
10−2
10−3
10−4
10−5
10−6
10−7	0	60	120	180	240	300	360
			Scattering Angle (deg)

Fig. 3.43. Normalized di erential scattering cross-sections of an oblate layered spheroid

	100
	10−1				parallel
					perpendicular
	10−2
	10−3
DSCS	10−4
DSCS	10−5
	10−5
	10−6
	10−7
	10−80	60	120	180	240	300	360
			Scattering Angle (deg)

Fig. 3.44. Normalized di erential scattering cross-sections of a layered cylinder

the host particle and Nrank = 8 for the inclusion, while the global number of integration points is Nint = 1,000.

In the next example, the host particle is a sphere of radius ksR = 10, the inclusion is a prolate spheroid with ksa1 = 8 and ksb1 = 3, and the relative refractive indices are mr = 1.2 and mr1 = 1.5. Figures 3.46 and 3.47 compare results obtained with the routines TLAY, TINHOMSPH and TINHOM. The agreement between the scattering curves is very good.

3.5 Layered Particles

229

	z	r
		r
	r1
		L
L 1		x
		x

			Fig. 3.45. Geometry of a layered cylinder
	2
	10
	101				TLAY - parallel
	101				TLAY - perpendicular
					TINHOMSPH - parallel
	0				TINHOMSPH - perpendicular
	10				TINHOM - parallel
					TINHOM - parallel
DSCS	10−1				TINHOM - perpendicular
	10−1
	−2
	10
	10−3
	10−4
	10−5	0	60	120	180	240	300	360
				Scattering Angle (deg)

Fig. 3.46. Normalized di erential scattering cross-sections of a layered particle consisting of a host sphere and a spheroidal inclusion

In Fig. 3.48, we show results for a concentrically layered sphere consisting of three layers of radii ksr1 = 10, ksr2 = 7 and ksr3 = 4. The relative refractive indices with respect to the ambient medium are mr1 = 1.2 + 0.2j, mr2 = 1.5 + 0.1j and mr3 = 1.8 + 0.3j. The scattering curves obtained with the TSPHERE and TLAY routines are close to each other.

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