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Designs for optical cloaking with high-order transformations

Wenshan Cai, Uday K. Chettiar, Alexander V. Kildishev, and Vladimir M. Shalaev

Open Access Open Access

Abstract

Recent advances in metamaterial research have provided us a blueprint for realistic cloaking capabilities, and it is crucial to develop practical designs to convert concepts into real-life devices. We present two structures for optical cloaking based on high-order transformations for TM and TE polarizations respectively. These designs are possible for visible and infrared wavelengths. This critical development builds upon our previous work on nonmagnetic cloak designs and high-order transformations.

©2008 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. The principle of constructing a non-magnetic cloak in the TM mode with high-order transformations. The thick solid and dashed lines represent the two Wiener bounds ε ‖(f) and ε ⊥(f), respectively. Basic material properties for this calculation: ε1 =εAg =-10.6+0.14i and ε2 =εSiO2 =2.13 at λ=532 nm.

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Fig. 2.
Fig. 2. Schematic of a cylindrical non-magnetic cloak with high-order transformations for TM polarization.

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Fig. 3.
Fig. 3. Anisotropic material parameters εr and εθ of a non-magnetic cloak made of silversilica alternating slices corresponding to the third row (λ=532 nm) in Table 1. The solid lines represent the exact parameters determined by Eq. (2), and the diamond markers show the parameters on the Wiener’s bounds given by Eq. (4).

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Fig. 4.
Fig. 4. Schematic of a cylindrical non-magnetic cloak with high-order transformations for TE polarization.

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Fig. 5.
Fig. 5. The required and the calculated effective parameters μr and εz for a cylindrical TE cloak with SiC wire arrays for λ=13.5 µm.

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Tables (1)

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Table 1. Approximate quadratic transformations and materials for constructing a cloak with alternating slices

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Equations (10)

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ε r = μ r = ( r ' r ) ∂ g ( r ' ) ∂ r ' ; ε θ = μ θ = 1 ε r ; ε z = μ z = ( r ' r ) [ ∂ g ( r ' ) ∂ r ' ] − 1
μ r = ( r ' r ) 2 [ ∂ g ( r ' ) ∂ r ' ] 2 ; μ θ = 1 ; ε z = [ ∂ g ( r ' ) ∂ r ' ] − 2
ε r = ( r ' r ) 2 ; ε θ = [ ∂ g ( r ' ) ∂ r ' ] − 2 ; μ z = 1
ε ║ = f ε 1 + ( 1 − f ) ε 2 ; ε ⊥ = ε 1 ε 2 ( f ε 2 + ( 1 − f ) ε 1 )
ε m ε d ( ∂ g ( r ' ) ∂ r ' ) 2 + ( r ' g ( r ' ) ) 2 − ( ε m + ε d ) = 0
g ( 0 ) = a ; g ( b ) = b ; ∂ g ( r ' ) ∂ r ' > 0
r = g ( r ' ) = [ 1 − a b + p ( r ' − b ) ] r ' + a
f ( r ) = Re ( ε d ) − ( g − 1 ( r ) r ) 2 Re ( ε d − ε m )
ε SiC = ε ∞ [ ω 2 − ω L 2 + i γ ω ] [ ω 2 − ω T 2 + i γ ω ]
μ r = 2 k L 1 2 L 1 J 1 ( k L 1 ) − t J 1 ( k t ) + a 0 t H 1 ( 1 ) ( k t ) − a 0 L 1 H 1 ( 1 ) ( k L 1 ) + c 0 t J 1 ( n k t ) n J 0 ( k L 2 2 ) − a 0 H 0 ( 1 ) ( k L 2 2 )
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