Determination the Material Parameters for Arbitrary Cloak Based on Poisson's Equation

Ma, Jiajun; Cao, Xiangyu; Yu, Kuanglu; Liu, Tao

doi:10.2528/pierm09091405

Cited by 14 publications

(10 citation statements)

References 15 publications

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“…The complex extension can be also used in static problems, [12,13]. As a simple example, consider the potential due to a electric dipole placed in the origin of a coordinate system, and given by Φ 3D (r, θ) = p cos θ/(4πε 0 r 2 ), where pζ is the electric dipole moment.…”

Section: Potential Theorymentioning

confidence: 99%

Complex Polar Coordinates in Electromagnetics

González-Morales¹,

Mahillo-Isla²,

Gago-Ribas³

et al. 2011

Journal of Electromagnetic Waves and Applications

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The definition of a complex polar coordinate system that unifies complex distances and complex angles together with their relations with the real observation space is presented in this paper. Its utility is shown through some applications to electromagnetic problems: (i) new solutions are obtained from well-known solutions in real polar coordinates, (ii) the parameterization of the real space in terms of the complex polar coordinates helps to understand the physical behaviour of those solutions, and (iii) the results provide a better physical insight of the complex distances and angles.

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Section: Potential Theorymentioning

confidence: 99%

Complex Polar Coordinates in Electromagnetics

González-Morales¹,

Mahillo-Isla²,

Gago-Ribas³

et al. 2011

Journal of Electromagnetic Waves and Applications

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show abstract

“…We might, for example, use an alternate radial cloak using the logarithm function [37] so that it could be more smoothly matched than the original (linear) radial cloak [1], at its outer boundary. The log radial cloak is designed using on fig.…”

Section: A Cylindrical Cloakmentioning

confidence: 99%

Generalized transformation design: Metrics, speeds, and diffusion

Kinsler

McCall

2018

Wave Motion

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h i g h l i g h t s• A general prescription for transformation design is given.• Our method covers optics, simple acoustics, rays, and even diffusion processes.• A transformation induces an effective metric, which steers the propagation by means of a speed profile. t r a c tWe show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalized ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.

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“…mapping based on the logarithmic function (as in [32]). The core boundary is at = r R e, and the halo boundary-its interface with the exterior-is at = r R.…”

Section: Radial Transformation Designsmentioning

confidence: 99%

Impedance rescaling and scattering from transformation optics devices

Kinsler

2018

J. Phys. Commun.

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I investigate the scattering properties of transformation devices as the impedance matching criteria are altered. Starting from an analysis of traditional impedance calculations, we see how to preserve the cloak's 'steering' refractive index profile whilst adjusting the 'scattering' impedance profile. Results are presented for transformation devices in a cylindrical geometry, but the lessons apply to both simpler and more complicated transformation devices. One technique used here is the use of impulsive field inputs, so that scattered fields are more easily distinguished from non-scattered fields. A two-axis continuous range of impedance profiles is shown to cover the three most important cases. This range is investigated numerically, with the summed scattering field being used as an indicator of device performance. We see that the standard 'k-medium' case where e m = gives best performance, but with different rescalings giving different levels of deterioration.

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Determination the Material Parameters for Arbitrary Cloak Based on Poisson's Equation

Cited by 14 publications

References 15 publications

Complex Polar Coordinates in Electromagnetics

Complex Polar Coordinates in Electromagnetics

Generalized transformation design: Metrics, speeds, and diffusion

Impedance rescaling and scattering from transformation optics devices

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