Evaluation and design of a large-scale cloaking device by the Hamiltonian-based ray-tracing method. Part II: design of the distribution of constitutive parameters

Tatsuo Tanaka; Osamu Matoba

doi:10.1364/JOSAB.34.001052

Journal of the Optical Society of America B
Vol. 34,
Issue 5,
pp. 1052-1059
(2017)
•https://doi.org/10.1364/JOSAB.34.001052

Evaluation and design of a large-scale cloaking device by the Hamiltonian-based ray-tracing method. Part II: design of the distribution of constitutive parameters

Tatsuo Tanaka and Osamu Matoba

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Tatsuo Tanaka and Osamu Matoba, "Evaluation and design of a large-scale cloaking device by the Hamiltonian-based ray-tracing method. Part II: design of the distribution of constitutive parameters," J. Opt. Soc. Am. B 34, 1052-1059 (2017)

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Abstract

Improvement in cloaking performance by the design of distributions of the constitutive parameters is investigated. The distributions are changed by employing Navier’s equation with various distributions of Young’s modulus as the partial differential equation for the solution of the Jacobian transformation matrix used in transformation optics. The cloaking performance is evaluated by Hamiltonian-based ray tracing. The numerical results show the proposed design method can improve the cloaking performance. The design method can contribute to the realization of large-scale cloaking devices by taking account of the finite resolution of the manufacture.

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Number	Relative Full-Mesh Resolution	Equations		$Δ θ$ (°)
1	$4.17 e - 02$	Navier’s Eq.	$Y = d^{- 5}$	11.1
2			$Y = d^{- 3}$	11.7
3			$Y = d^{- 1}$	12.2
4			$Y = d^{0}$	12.4
5			$Y = d^{1}$	12.9
6			$Y = d^{3}$	13.1
7			$Y = d^{5}$	14.2
8		Laplace’s Eq.		12.1
9	$1.67 e - 02$	Navier’s Eq.	$Y = d^{- 5}$	4.12
10			$Y = d^{- 3}$	5.04
11			$Y = d^{- 1}$	5.31
12			$Y = d^{0}$	5.26
13			$Y = d^{1}$	5.32
14			$Y = d^{3}$	6.74
15			$Y = d^{5}$	7.20
16		Laplace’s Eq.		5.19
17	$8.33 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	4.26
18			$Y = d^{- 3}$	4.12
19			$Y = d^{- 1}$	4.50
20			$Y = d^{0}$	4.63
21			$Y = d^{1}$	4.62
22			$Y = d^{3}$	4.70
23			$Y = d^{5}$	4.61
24		Laplace’s Eq.		4.51
25	$4.17 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	0.729
26			$Y = d^{- 3}$	0.887
27			$Y = d^{- 1}$	1.46
28			$Y = d^{0}$	1.51
29			$Y = d^{1}$	2.48
30			$Y = d^{3}$	2.74
31			$Y = d^{5}$	1.74
32		Laplace’s Eq.		1.43
33	$1.67 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	0.144
34			$Y = d^{- 3}$	0.198
35			$Y = d^{- 1}$	0.108
36			$Y = d^{0}$	0.154
37			$Y = d^{1}$	0.151
38			$Y = d^{3}$	0.340
39			$Y = d^{5}$	0.374
40		Laplace’s Eq.		0.113

Number	Relative Full-Mesh Resolution	Equations		$Δ θ$ (°)
1	$1.67 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	0.259
2		Navier’s Eq.	$Y = d^{- 3}$	0.458
3			$Y = d^{- 1}$	0.447
4		Laplace’s Eq.		2.54

Number	Relative Full-Mesh Resolution	Equations		$Δ θ$ (°)
1	$4.17 e - 02$	Navier’s Eq.	$Y = d^{- 5}$	11.1
2			$Y = d^{- 3}$	11.7
3			$Y = d^{- 1}$	12.2
4			$Y = d^{0}$	12.4
5			$Y = d^{1}$	12.9
6			$Y = d^{3}$	13.1
7			$Y = d^{5}$	14.2
8		Laplace’s Eq.		12.1
9	$1.67 e - 02$	Navier’s Eq.	$Y = d^{- 5}$	4.12
10			$Y = d^{- 3}$	5.04
11			$Y = d^{- 1}$	5.31
12			$Y = d^{0}$	5.26
13			$Y = d^{1}$	5.32
14			$Y = d^{3}$	6.74
15			$Y = d^{5}$	7.20
16		Laplace’s Eq.		5.19
17	$8.33 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	4.26
18			$Y = d^{- 3}$	4.12
19			$Y = d^{- 1}$	4.50
20			$Y = d^{0}$	4.63
21			$Y = d^{1}$	4.62
22			$Y = d^{3}$	4.70
23			$Y = d^{5}$	4.61
24		Laplace’s Eq.		4.51
25	$4.17 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	0.729
26			$Y = d^{- 3}$	0.887
27			$Y = d^{- 1}$	1.46
28			$Y = d^{0}$	1.51
29			$Y = d^{1}$	2.48
30			$Y = d^{3}$	2.74
31			$Y = d^{5}$	1.74
32		Laplace’s Eq.		1.43
33	$1.67 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	0.144
34			$Y = d^{- 3}$	0.198
35			$Y = d^{- 1}$	0.108
36			$Y = d^{0}$	0.154
37			$Y = d^{1}$	0.151
38			$Y = d^{3}$	0.340
39			$Y = d^{5}$	0.374
40		Laplace’s Eq.		0.113

Number	Relative Full-Mesh Resolution	Equations		$Δ θ$ (°)
1	$1.67 e - 03$	Navier’s Eq.	$Y = d^{- 5}$	0.259
2		Navier’s Eq.	$Y = d^{- 3}$	0.458
3			$Y = d^{- 1}$	0.447
4		Laplace’s Eq.		2.54

Abstract

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Figures (10)

Tables (2)

Equations (12)

Journal of the Optical Society of America B