By Pu, Zhang
ISBN-10: 917415947X
ISBN-13: 9789174159479
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Additional resources for Theory of transformation optics and invisibility cloak design
Example text
Its CP can be calculated with the orthogonal formulation of TrO (Eq. 65)). To proceed further, the Jacobian matrices of spherical CS and the transformation Eq. 67) must first be found. Spherical CS and Cartesian CS are related as r = x 2 + y 2 + z 2 , cos θ = z / r , tan φ = y / x, x = r sin θ cos φ , y = r sin θ sin φ , z = r cos θ . 69) and the metric tensor is also obtained thanks to the relation in Eq. 17), 1 ⎛ g −1 = TTT = diag ⎜1 2 ⎝ r 1 r sin 2 θ 2 ⎞ ⎟. 70) For the transformation Eq. 67), the Jacobian matrix is ⎛ R − R1 ⎞ 1 1⎟ .
We can not expect the semi-cylindrical cover alone to perform as well as a half-space cloak on an indefinite dielectric ground. This is also confirmed by numerical simulation of EM wave scattering from the semi-cylindrical cover on a dielectric ground (see below in the simulation part). Relatively weak reflection at the ground interface right below the semi-cylindrical cover is observed. Half‐space Cloaking on a Dielectric Ground the ground interface must be uniform everywhere. Two vertical matching strips are inserted below the cover to induce proper reflection strength, as shown in Fig.
1) In the design strategy, we make the wrong assumption of radially invariant μθ whereby Eq. 1) becomes 1 ∂ 2 Ez 1 1 ∂Ez 1 1 ∂ 2 Ez + + + k02 Ez = 0. 2) Though not accurate, Eq. 2) does provide a guide for designing reduced cloaks in some sense. Products εzμθ and εzμr can specify Eq. 2) completely. As long as the products for reduced cloaks are kept the same as those for perfect cloaks, we can expect similar EM wave behaviors as in the case of perfect invisibility. Reduced Two‐dimensional Cloaks of Arbitrary Shapes 2 2 ε z μθ ⎛ R2 ⎞ ε z μr ⎛ R2 ⎞ ⎛ r − R1 ⎞ .
Theory of transformation optics and invisibility cloak design by Pu, Zhang
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