Cylindrical optimized nonmagnetic concentrator with minimized scattering

Borui Bian; Shaobin Liu; Shenyun Wang; Xiangkun Kong; Yanan Guo; Xin Zhao; Ben Ma; Chen Chen

doi:10.1364/OE.21.00A231

Optics Express
Vol. 21,
Issue S2,
pp. A231-A240
(2013)
•https://doi.org/10.1364/OE.21.00A231

Cylindrical optimized nonmagnetic concentrator with minimized scattering

Borui Bian, Shaobin Liu, Shenyun Wang, Xiangkun Kong, Yanan Guo, Xin Zhao, Ben Ma, and Chen Chen

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Borui Bian, Shaobin Liu, Shenyun Wang, Xiangkun Kong, Yanan Guo, Xin Zhao, Ben Ma, and Chen Chen, "Cylindrical optimized nonmagnetic concentrator with minimized scattering," Opt. Express 21, A231-A240 (2013)

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Related Topics
Table of Contents Category
- Electro-magnetic Concentrators
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: September 26, 2012
- Revised Manuscript: January 11, 2013
- Manuscript Accepted: January 11, 2013
- Published: January 29, 2013

Abstract

By using optimized transformation function, we research on a minimized scattering nonmagnetic concentrator, which can realize impedance matching at the inner and the outer boundaries. It has been demonstrated that the optimized transformation function method can improve the concentrating performance remarkably. The cylindrical anisotropic shell can be mimicked by radial symmetrical sectors which alternate in composition between two profiles of isotropic dielectrics, and the permittivity in each sector can be properly determined by the effective medium theory. The nonmagnetic concentrator has been validated by full-wave finite element simulations. We can believe that this work will improve the flexibilities for the EM concentrator design.

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Fig. 1 Sketch of the cylindrical nonmagnetic concentrator.

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Fig. 2 Comparison of different coordinate transformation functions in core and circular region.

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Fig. 3 The material parameter values for the concentrator constructed through the polynomial function. (a) The material parameter value in core region. (b) The material parameter value in circular region.

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Fig. 4 (a) Magnetic field distribution of the concentrator with linear transformation function, (b) Normalized power flow of the concentrator with linear transformation function, (c) Magnetic field distribution of the concentrator with polynomial transformation function, (d) Normalized power flow of the concentrator with polynomial transformation function.

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Fig. 5 Normalized power flow of the concentrator with linear transformation and polynomial transformation on the centre line of core region (

x = 0, y \in [- 0.2, 0.2]

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Fig. 6 The normalized far field scattering patterns of the nonmagnetic concentrator with different transformation functions. The black dashed curve indicates the case of linear transformation, and the red real curve indicates the case of polynomial transformation.

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Fig. 7 The region permittivity patterns without magnetic response for (a) profile-A of core region, (b) profile-B of core region, (c) profile-A of circular region, (d) profile-B of circular region.

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Fig. 8 Transverse magnetic field distributions of (

2 M = 80

) layered nonmagnetic concentrator with (a) linear transformation, and (b) polynomial transformation.

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Fig. 9 Transverse magnetic field distributions of (

2 M = 160

) layered nonmagnetic concentrator with (a) linear transformation function, and (b) polynomial transformation function.

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Equations (12)

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r^{'} = f (r), \begin{matrix}  \end{matrix} θ^{'} = θ, \begin{matrix}  \end{matrix} z^{'} = z

ε_{r} = μ_{r} = \frac{f (r)}{r f^{'} (r)}, \begin{matrix}  \end{matrix} ε_{θ} = μ_{θ} = \frac{1}{ε_{r}}, \begin{matrix}  \end{matrix} ε_{z} = μ_{z} = \frac{f^{'} (r) f (r)}{r}

ε_{r} = {(\frac{f (r)}{r})}^{2}, \begin{matrix}  \end{matrix} ε_{θ} = {(f^{'} (r))}^{2}, \begin{matrix}  \end{matrix} μ_{z} = 1

f_{c o r} (r) = \frac{R_{2}}{R_{1}} r

f_{c i r} (r) = \frac{R_{3} - R_{2}}{R_{3} - R_{1}} (r + \frac{R_{2} - R_{1}}{R_{3} - R_{2}} R_{3})

\begin{array}{l} ε_{(c o r) r} = ε_{(c o r) θ} = {(\frac{R_{2}}{R_{1}})}^{2}, \begin{matrix}  \end{matrix} μ_{(c o r) z} = 1 \\ ε_{(c i r) r} = ε_{(c i r) θ} = {(\frac{R_{3} - R_{2}}{R_{3} - R_{1}})}^{2}, \begin{matrix}  \end{matrix} μ_{(c i r) z} = 1 \end{array}

\begin{array}{l} f_{c o r} (0) = 0, \begin{matrix}  \end{matrix} f_{c o r} (R_{1}) = R_{2}, \begin{matrix}  \end{matrix} f_{c i r} (R_{1}) = R_{2} \\ f_{c i r} (R_{3}) = R_{3}, \begin{matrix}  \end{matrix} {f^{'}}_{c i r} (R_{3}) = 1, \begin{matrix}  \end{matrix} {f^{'}}_{c o r} (R_{1}) = {f^{'}}_{c i r} (R_{1}) \end{array}

f_{c o r} (r) = (\frac{R_{1} - R_{2}}{R_{1}^{2}}) r^{2} + \frac{2 R_{2} - R_{1}}{R_{1}} r

f_{c i r} (r) = A r^{3} + B r^{2} + C r + D

ε_{(c o r) r} = {(\frac{R_{1} - R_{2}}{R_{1}^{2}} r + \frac{2 R_{2} - R_{1}}{R_{1}})}^{2}, \begin{matrix}  \end{matrix} ε_{(c o r) θ} = {(2 \frac{R_{1} - R_{2}}{R_{1}^{2}} r + \frac{2 R_{2} - R_{1}}{R_{1}})}^{2}, \begin{matrix}  \end{matrix} μ_{(c o r) z} = 1

ε_{(c i r) r} = {(A r^{2} + B r + C + D / r)}^{2}, \begin{matrix}  \end{matrix} ε_{(c i r) θ} = {(3 A r^{2} + 2 B r + C)}^{2}, \begin{matrix}  \end{matrix} μ_{(c i r) z} = 1

ε_{r} = \frac{ε_{A} + ε_{B}}{2}, \begin{matrix}  \end{matrix} \frac{1}{ε_{θ}} = \frac{1}{2 ε_{A}} + \frac{1}{2 ε_{B}}

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Equations (12)

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