Electromagnetic wave scattering by highly elongated and geometrically composite objects of large size parameters: the generalized multipole technique

H. M. Al-Rizzo; J. M. Tranquilla

doi:10.1364/AO.34.003502

Applied Optics
Vol. 34,
Issue 18,
pp. 3502-3521
(1995)
•https://doi.org/10.1364/AO.34.003502

Electromagnetic wave scattering by highly elongated and geometrically composite objects of large size parameters: the generalized multipole technique

H. M. Al-Rizzo and J. M. Tranquilla

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H. M. Al-Rizzo and J. M. Tranquilla, "Electromagnetic wave scattering by highly elongated and geometrically composite objects of large size parameters: the generalized multipole technique," Appl. Opt. 34, 3502-3521 (1995)

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Abstract

The potency and versatility of a numerical procedure based on the generalized multipole technique (GMT) are demonstrated in the context of full-vector electromagnetic interactions for general incidence on arbitrarily shaped, geometrically composite, highly elongated, axisymmetric perfectly conducting or dielectric objects of large size parameters and arbitrary constitutive parameters. Representative computations that verify the accuracy of the technique are given for a large category of problems that have not been considered previously by the use of the GMT, to our knowledge. These problems involve spheroids of axial ratios as high as 20 and with the largest dimension of the dielectric object along the symmetry axis equal to 75 wavelengths; sphere–cone–sphere geometries; peanut-shaped scatterers; and finite-length cylinders with hemispherical, spherical, and flat end caps. Whenever possible, the extended boundary-condition method has been used in the process of examining the applicability of the suggested solution, with excellent agreement being achieved in all cases considered. It is believed that the numerical-scattering results presented here represent the largest detailed three-dimensional precise modeling ever verified as far as expansion functions that fulfill Maxwell’s equations throughout the relevant domain of interest are concerned.

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Figure	Q _e /πa ²	Q _b /πa ²
3(a)	1.8792	0.6355
3(b)	1.8792	0.1791
4(a)	5.434 × 10⁻²	2.4336 × 10⁻⁴
4(b)	4.5645 × 10⁻²	2.3356 × 10⁻⁴
5(a)	2.6619 × 10⁻³	1.1223 × 10⁻⁶
5(b)	3.7179 × 10⁻³	4.7901 × 10⁻⁵

Figure	Numerical Method	Q _e /πa ²	Q _b /πa ²
6(a)	GMT	9.9684 × 10⁻⁴	1.3728 × 10⁻³
	EBCM	9.8645 × 10⁻⁴	1.3612 × 10⁻³
6(b)	GMT	1.9567	0.7011
	EBCM	1.9496	0.6781
7(a)	GMT	4.2184 × 10⁻²	2.0725 × 10⁻²
7(b)	GMT	2.4397	1.7192
8(a)	GMT	4.0872	1.5250
	EBCM	4.0848	1.5157
8(b)	GMT	7.9327	13.0459
	EBCM	7.9236	13.2017
9(a)	GMT	0.8746	6.1796 × 10⁻²
9(b)	GMT	1.3481	25.3489
9(c)	GMT	3.0316 × 10⁻¹	1.0540 × 10⁻³
	EBCM	3.0327 × 10⁻¹	1.0815 × 10⁻³
9(d)	GMT	6.2282 × 10⁻¹	5.8412 × 10⁻³
	EBCM	6.2288 × 10⁻¹	5.8621 × 10⁻³
9(e)	GMT	5.4026 × 10⁻⁴	1.6329 × 10⁻⁵
	EBCM	5.4499 × 10⁻⁴	1.6294 × 10⁻⁵
9(f)	GMT	3.3461 × 10⁻³	1.1555 × 10⁻⁵
	EBCM	3.3681 × 10⁻³	1.0840 × 10⁻⁵
9(g)	GMT	5.5822	27.9303
	EBCM	5.5983	29.9760
9(h)	GMT	2.9640	2.9261
	EBCM	2.9641	2.9257
10(a)	GMT	1.7424	16.1832
	EBCM	1.7420	16.1834
10(b)	GMT	1.8542	1.1715
	EBCM	1.8235	1.0965
	GMT	1.8620	1.6253
	EBCM	1.8452	1.7366
10(e)	GMT	1.3245	32.6606
10(f)	GMT	0.9279	24.0430
10(g)	GMT	0.1394	0.1219
10(h)	GMT	9.4432 × 10⁻²	4.9521 × 10⁻³
11(d)	GMT	2.6794	0.8396
	EBCM	2.6859	0.8337
11(e)	GMT	1.8442	0.2950
	EBCM	1.8490	0.2975
11(f)	GMT	1.7082 × 10⁻¹	4.4222 × 10⁻³
	EBCM	1.7256 × 10⁻¹	4.4523 × 10⁻³
11(g)	GMT	3.0123 × 10⁻¹	5.3179 × 10⁻²
	EBCM	3.0194 × 10⁻¹	5.5376 × 10⁻²
12(a)	GMT (Model1)	1.5902	0.3968
	GMT (Model2)	1.4284	0.3732
	EBCM	1.6220	0.3589
12(b)	GMT (Model1)	6.5091 × 10⁻²	2.4151 × 10⁻²
	GMT (Model2)	6.7456 × 10⁻²	2.0920 × 10⁻²
	EBCM	6.5486 × 10⁻²	2.2123 × 10⁻²
12(c)	GMT (Model1)	1.0044 × 10⁻²	3.8265 × 10⁻³
	GMT (Model2)	1.1617 × 10⁻²	3.9076 × 10⁻³
	EBCM	1.0671 × 10⁻²	3.9459 × 10⁻³
12(d)	GMT (Model1)	3.0260 × 10⁻³	1.1899 × 10⁻³
	GMT (Model2)	2.9924 × 10⁻³	1.2398 × 10⁻³
	EBCM	3.0791 × 10⁻³	1.1908 × 10⁻³

Location of Field Points	Right Circular Cylinder with Hemispherical Caps k ₀ a = 0.2772, a/b = 3, ɛ _r = 1.88 + j0.69			a/b = 8, λ₀ = 0.4 μm, a = 100 nm, ɛ _r = 3.058 + j2.59		a/b = 11, λ₀ = 10 μm, a = 0.22 μm, ɛ _r = 3 + j1

	PMT (Ref. 18)	VIEF (Ref. 28)	GMT	IEBCM (Ref. 29)	GMT	IEBCM (Ref. 29)	VIEF (Ref. 28)	GMT
a	0.71	0.70	0.7189	0.6174	0.6423	0.481	0.478	0.4889
b	0.70	0.72	0.7039	0.4543	0.4311	0.488	0.482	0.4890
c	0.71	0.71	0.6880	0.4377	0.4406	0.490	0.490	0.4893
d	0.71	0.70	0.6830	0.4429	0.4458	0.507	0.491	0.4896
e	0.71	0.70	0.6879	0.4482	0.4478	0.492	0.503	0.4898
f	0.71	0.71	0.6936	0.4490	0.4474	0.492	0.495	0.4899
g	0.69	0.72	0.7126	0.4711	0.4550	0.490	0.482	0.4899
h	0.70	0.70	0.7254	0.6401	0.6697	0.483	0.478	0.4898
Q _e /πa ²	—	—	2.3855 × 10⁻²	—	1.7292 × 10⁻²	3.7026 × 10⁻⁴	3.7289 × 10⁻⁴	3.6523 × 10⁻⁴
Q _s /πa ²	—	—	3.7490 × 10⁻⁵	—	5.2545 × 10⁻⁴	9.3388 × 10⁻⁹	9.8649 × 10⁻⁹	8.8198 × 10⁻⁹
P _a (W)	—	—	1.9315 × 10⁻¹⁷	—	6.9864 × 10⁻¹⁹	0.747 × 10⁻¹⁹	0.752 × 10⁻¹⁹	0.7352 × 10⁻¹⁹

Location of Field Points	a/b = 15, λ₀ = 10 μm, a = 0.3 μm, ɛ _r = 3 + j1			a/b = 20, λ₀ = 10 μm, a = 0.4 μm, ɛ _r = 3 + j1

	IEBCM (Ref. 23)	VIEF (Ref. 28)	GMT	IEBCM (Ref. 29)	VIEF (Ref. 28)	GMT
a	0.483	0.473	0.4765	0.487	0.472	0.4911
b	0.487	0.487	0.4836	0.487	0.482	0.4830
c	0.489	0.488	0.4866	0.487	0.487	0.4846
d	0.488	0.489	0.4876	0.487	0.491	0.4864
e	0.489	0.492	0.4878	0.487	0.490	0.4866
f	0.488	0.487	0.487	0.486	0.486	0.4874
g	0.490	0.484	0.4849	0.485	0.482	0.4893
h	0.488	0.473	0.4791	0.482	0.472	0.4841
Q _e /πa ²	2.6631 × 10⁻⁴	2.6879 × 10⁻⁴	2.6596 × 10⁻⁴	1.9834 × 10⁻⁴	1.9894 × 10⁻⁴	1.9032 × 10⁻⁴
Q _s /πa ²	8.7358 × 10⁻⁹	9.6907 × 10⁻⁹	8.7072 × 10⁻⁹	8.5943 × 10⁻⁹	9.5095 × 10⁻⁹	8.5327 × 10⁻⁹
P _a (W)	0.100 × 10⁻¹⁸	0.101 × 10⁻¹⁸	9.9731 × 10⁻²⁰	0.132 × 10⁻¹⁸	0.133 × 10⁻¹⁸	0.1268 × 10⁻¹⁸

Figure	Q _e /πa ²	Q _b /πa ²
3(a)	1.8792	0.6355
3(b)	1.8792	0.1791
4(a)	5.434 × 10⁻²	2.4336 × 10⁻⁴
4(b)	4.5645 × 10⁻²	2.3356 × 10⁻⁴
5(a)	2.6619 × 10⁻³	1.1223 × 10⁻⁶
5(b)	3.7179 × 10⁻³	4.7901 × 10⁻⁵

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Tables (4)

Equations (23)

Applied Optics