Rough layer scattering filled by elliptical cylinders from the method of moments combined with the characteristic basis function method and the Kirchoff approximation

Christophe Bourlier

doi:10.1364/JOSAA.430309

Journal of the Optical Society of America A
Vol. 38,
Issue 10,
pp. 1581-1593
(2021)
•https://doi.org/10.1364/JOSAA.430309

Rough layer scattering filled by elliptical cylinders from the method of moments combined with the characteristic basis function method and the Kirchoff approximation

Christophe Bourlier

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Christophe Bourlier, "Rough layer scattering filled by elliptical cylinders from the method of moments combined with the characteristic basis function method and the Kirchoff approximation," J. Opt. Soc. Am. A 38, 1581-1593 (2021)

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Abstract

In this paper, the electromagnetic field scattered by several 2D scatterers of any shape is calculated rigorously from the boundary integral equations discretized by the method of moments with the point matching method and pulse basis functions. In addition, the resulting linear system is efficiently solved from the domain decomposition method named the characteristic basis function method. To accelerate the computation of the primary basis functions, which requires solving sublinear systems, the Kirchoff approximation is applied for metallic and dielectric objects. The efficiency of the method is tested on several applications met in practice: stack of rough interfaces separating homogeneous media, collection of metallic and dielectric elliptical cylinders, collection of coated elliptical cylinders, and a combination of the previous scenarios.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (47)

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Name	Definition
$P$	Number of scatterers
$B$	Number of blocks ( $= P$ )
$N$	Total number of unknowns
$N_{i}$	Number of unknowns of scatterer $i$
$N_{I P W, p}$	CBFM plane wavenumber of block $i$
$N_{I P W, S V D, p}$	CBFM plane wavenumber of block $i$ after SVD truncation
$ϵ_{C B F M, S V D}$	CBFM threshold of the SVD truncation
$\bar{N}$	Mean value of $N_{i}$ over $p \in [1; B]$
${\bar{N}}_{I P W}$	Mean value of $N_{I P W, i}$ over $i \in [1; B]$
${\bar{N}}_{I P W, S V D}$	Mean value of $N_{I P W, S V D, i}$ over $i \in [1; B]$

Scenario	$ϵ_{C B F M, S V D}$	$N$	$N_{R}$	$N_{R, S V D}$	$t_{L U}$	$t_{C B F M - L U}$	$t_{C B F M - K A}$
1	$10^{- 4}$	14,400	4,392	2,925	98	20	16
2	$10^{- 5}$	4,074	1096	1036	15	0.6	0.5
3	$10^{- 4}$	11,436	3,336	2,168	48	5	4
4	$10^{- 5}$	11,056	3,326	2,690	81	13	11

Medium $Ω_{i}$	$ϵ_{r, i}$	Scatterer $i$	$σ_{z, i} [λ_{0}]$	$L_{c, i} [λ_{0}]$	$h_{i} [λ_{0}]$
0	1
1	$2 + 0.01 j$	1	0.1	1	0
2	$2.5 + 0.02 j$	2	0.15	1.5	−2
3	$3 + 0.03 j$	3	0.2	2	−4
4	$2 + 0.01 j$	4	0.1	1	−6
5	$2.5 + 0.02 j$	5	0.15	1.5	−8
6	$3 + 0.03 j$	6	0.2	2	−10

Name	Definition
$P$	Number of scatterers
$B$	Number of blocks ( $= P$ )
$N$	Total number of unknowns
$N_{i}$	Number of unknowns of scatterer $i$
$N_{I P W, p}$	CBFM plane wavenumber of block $i$
$N_{I P W, S V D, p}$	CBFM plane wavenumber of block $i$ after SVD truncation
$ϵ_{C B F M, S V D}$	CBFM threshold of the SVD truncation
$\bar{N}$	Mean value of $N_{i}$ over $p \in [1; B]$
${\bar{N}}_{I P W}$	Mean value of $N_{I P W, i}$ over $i \in [1; B]$
${\bar{N}}_{I P W, S V D}$	Mean value of $N_{I P W, S V D, i}$ over $i \in [1; B]$

Scenario	$ϵ_{C B F M, S V D}$	$N$	$N_{R}$	$N_{R, S V D}$	$t_{L U}$	$t_{C B F M - L U}$	$t_{C B F M - K A}$
1	$10^{- 4}$	14,400	4,392	2,925	98	20	16
2	$10^{- 5}$	4,074	1096	1036	15	0.6	0.5
3	$10^{- 4}$	11,436	3,336	2,168	48	5	4
4	$10^{- 5}$	11,056	3,326	2,690	81	13	11

Abstract

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Tables (3)

Equations (47)

Journal of the Optical Society of America A