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Electromagnetic cloaking by layered structure of homogeneous isotropic materials

Ying Huang, Yijun Feng, and Tian Jiang

Open Access Open Access

Abstract

Electromagnetic invisibility cloak requires material with anisotropic distribution of the constitutive parameters as first proposed by Pendry et al. [Science 312, 1780 (2006)]. In this paper, we proposed an electromagnetic cloak structure that does not require metamaterials with subwavelength structured inclusions to realize the anisotropy or inhomogeneity of the material parameters. We constructed a concentric layered structure of alternating homogeneous isotropic materials that can be treated as an effective medium with the required radius-dependent anisotropy. With proper design of the permittivity or the thickness ratio of the alternating layers, we demonstrated the low-reflection and power-flow bending properties of the proposed cloaking structure through rigorous analysis of the scattered electromagnetic fields. The proposed cloaking structure could be possibly realized by normal materials, therefore may lead to a practical path to an experimental demonstration of electromagnetic cloaking, especially in the optical range.

©2007 Optical Society of America

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Supplementary Material (2)

Media 1: MOV (3759 KB)     
Media 2: MOV (3761 KB)     

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Figures (5)
Fig. 1.
Fig. 1. TM wave incident on an infinite conducting cylinder (in yellow) shelled with (a) concentric layers structure with alternating layers of dielectric A and B, (b) equivalent anisotropic cylindrical medium with radius-dependent, anisotropic material parameters. Both of the shells have inner and outer radius of a and b, respectively.

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Fig. 2.
Fig. 2. Comparison of the far-field scattering patterns for a bare conducting cylinder, the conducting cylinder shelled with a concentric layered structure of different number of layers, and that shelled with an anisotropic cylindrical medium. All values have been normalized to the scattering pattern of the bare conducting cylinder at θ=0.

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Fig. 3.
Fig. 3. The relative permittivity components required for an ideal reduced set of parameter (εr(r), εθ(r)), and that for the corresponding layered structure with alternating dielectric A and B (εA(m), εB(m)). The inset describes the anisotropic shell divided into stepwise homogeneous N-layer (with permittivity as εr(m), εθ(m)), and the mimic of each layer by alternating layers of dielectric A and B (totally 2N layers).

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Fig. 4.
Fig. 4. The calculated magnetic-field distribution around the conducting cylinder (a) with a cloak of concentric layered structure (movie, 3.67 MB) [Media 1], and (b) without cloak (movie, 3.67 MB) [Media 2], (c) the far-field scattering pattern. Power-flow lines (in black) in (a) show the smooth deviation of electromagnetic power around the cloaked object. The white circles outline the cloak.

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Fig. 5.
Fig. 5. The magnetic-field distribution around the conducting cylinder, (a) with a cloak of layered structure, and (b) without cloak, for a TM incident wave from a line source. The white circles outline the cloak.

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Equations (13)

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ε θ = ε A + η ε B 1 + η ,
1 ε r = 1 1 + η ( 1 ε A + η ε B ) .
η = d B d A .
H z i = H 0 ∑ n = − ∞ n = ∞ j − n J n ( k 0 r ) e jn θ ,
H z s = H 0 ∑ n = − ∞ n = ∞ C n j − n H n ( 2 ) ( k 0 r ) e jn θ ,
H z m t = H 0 ∑ n = − ∞ n = ∞ j − n ( A mn J n ( k m r ) + B mn H n ( 2 ) ( k m r ) ) e jn θ ,
E r = − 1 r j ω μ k 2 ∂ H z ∂ θ , E θ = j ω μ k 2 ∂ H z ∂ r .
H z i = − ω ε 0 I m 4 H 0 ( 2 ) ( k 0 ∣ r − r 0 ∣ ) .
ξ ( θ ) = ∣ ∑ n = − ∞ n = ∞ C n e jn θ ∣ 2 .
ε r = μ r = r − a r , ε θ = μ θ = r r − a ,
ε z = μ z = ( b b − a ) 2 r − a r .
μ z = 1 , ε θ = ( b b − a ) 2 ,
ε r = ( b b − a ) 2 ( r − a r ) 2 .
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