scholarly journals Approximate cloaking for electromagnetic waves via transformation optics: Cloaking versus infinite energy

2019 ◽  
Vol 29 (08) ◽  
pp. 1511-1552 ◽  
Author(s):  
Hoai-Minh Nguyen ◽  
Loc Tran
Keyword(s):  
Electromagnetic Waves ◽  
Blow Up ◽  
Transformation Optics ◽  
Mapping Technique ◽  
Resonant Case ◽  
Time Harmonic ◽  
Infinite Energy

We study the approximate cloaking via transformation optics for electromagnetic waves in the time harmonic regime in which the cloaking device only consists of a layer constructed by the mapping technique. Due to the fact that no-lossy layer is required, resonance might appear and the analysis is delicate. We analyze both non-resonant and resonant cases. In particular, we show that the energy can blow up inside the cloaked region in the resonant case and/whereas cloaking is achieved in both cases. Moreover, the degree of visibility depends on the compatibility of the source inside the cloaked region and the system. These facts are new and distinct from known mathematical results in the literature.

Scattering of a Plane Elastic Wave From Objects Near an Interface

1972 ◽  
Vol 39 (4) ◽  
pp. 1019-1026 ◽  
Author(s):  
Stephen B. Bennett
Keyword(s):  
Elastic Wave ◽  
Electromagnetic Waves ◽  
Three Dimensions ◽  
Circular Cylinders ◽  
Scattering Problems ◽  
Reflection And Refraction ◽  
Time Harmonic ◽  
Incident Plane ◽  
Boundary Curves ◽  
Consistent Formulation

The displacement field generated by the reflection and refraction of plane (time harmonic) elastic waves by finite obstacles of arbitrary shape, in the neighborhood of a plane interface between two elastic media, is investigated. The technique employed allows a consistent formulation of the problem for both two and three dimensions, and is not limited either to boundary shapes which are level surfaces in appropriate coordinate systems, i.e., circular cylinders, spheres, etc., or to closed boundary curves or surfaces. The approach is due to Twersky, and has been applied to many problems of the scattering of electromagnetic waves. The method consists of expressing the net field due to all multiple scattering in terms of the field reflected from each boundary in isolation when subjected to an incident plane elastic wave. Thus the technique makes use of more elemental scattering problems whose solutions are extant. By way of illustration, a numerical solution to the scattering of a plane elastic wave by a rigid circular cylindrical obstacle adjacent to a plane free surface is considered.

Electromagnetic wave scattering by random surfaces: Shape holomorphy

2017 ◽  
Vol 27 (12) ◽  
pp. 2229-2259 ◽  
Author(s):  
Carlos Jerez-Hanckes ◽  
Christoph Schwab ◽  
Jakob Zech
Keyword(s):  
Uncertainty Quantification ◽  
Electromagnetic Waves ◽  
Convergence Rates ◽  
Order Reduction ◽  
Reduced Basis ◽  
Approximation Techniques ◽  
Field Patterns ◽  
Time Harmonic ◽  
First Order Second Moment ◽  
Domain Perturbations

For time-harmonic electromagnetic waves scattered by either perfectly conducting or dielectric bounded obstacles, we show that the fields depend holomorphically on the shape of the scatterer. In the presence of random geometrical perturbations, our results imply strong measurability of the fields, in weighted spaces in the exterior of the scatterer. These findings are key to prove dimension-independent convergence rates of sparse approximation techniques of polynomial chaos type for forward and inverse computational uncertainty quantification. Also, our shape-holomorphy results imply parsimonious approximate representations of the corresponding parametric solution families, which are produced, for example, by greedy strategies such as model order reduction or reduced basis approximations. Finally, the presently proved shape holomorphy results imply convergence of shape Taylor expansions of far-field patterns for fixed amplitude domain perturbations in a vicinity of the nominal domain, thereby extending the widely used asymptotic linearizations employed in first-order, second moment domain uncertainty quantification.

scholarly journals Broadband unidirectional behavior of electromagnetic waves based on transformation optics

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
XiaoFei Zang ◽  
YiMing Zhu ◽  
XueBin Ji ◽  
Lin Chen ◽  
Qing Hu ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Transformation Optics

Born non-scattering electromagnetic media

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Tilo Arens ◽  
John Sylvester
Keyword(s):  
Born Approximation ◽  
Electromagnetic Waves ◽  
Variational Equation ◽  
Plane Waves ◽  
Transformation Optics ◽  
Local Perturbation ◽  
Detectable Change ◽  
Scattering Media ◽  
First Order

AbstractWe consider the propagation of electromagnetic waves in an anisotropic medium. A local perturbation of the vacuum media that does not produce a detectable change in the far field is called non-scattering. Through testing by plane waves, we derive a variational equation characterizing non-scattering perturbations of permittivities and permeabilities to first order, i.e. in the Born approximation. We show that these perturbations can be characterized exactly by four functions. Three of these functions correspond to linearizations of known non-scattering media constructed by diffeomorphisms in transformation optics. The role of the fourth function is not yet understood, although some analytic properties can be derived.

Some applications of substructuring and domain decomposition techniques to radiation and scattering of time-harmonic electromagnetic waves

2006 ◽  
Vol 7 (5) ◽  
pp. 474-485 ◽  
Author(s):  
Nolwenn Balin ◽  
Abderrahmane Bendali ◽  
M'Barek Fares ◽  
Florence Millot ◽  
Nicolas Zerbib
Keyword(s):  
Domain Decomposition ◽  
Electromagnetic Waves ◽  
Decomposition Techniques ◽  
Time Harmonic

scholarly journals Spatial transformation-enabled electromagnetic devices: from radio frequencies to optical wavelengths

2015 ◽  
Vol 373 (2049) ◽  
pp. 20140363 ◽  
Author(s):  
Zhi Hao Jiang ◽  
Jeremy P. Turpin ◽  
Kennith Morgan ◽  
Bingqian Lu ◽  
Douglas H. Werner
Keyword(s):  
Electromagnetic Waves ◽  
Transformation Optics ◽  
Electromagnetic Properties ◽  
Wave Radiation ◽  
Experimental Investigations ◽  
Electromagnetic Spectrum ◽  
Coordinate Transformations ◽  
Electromagnetic Devices ◽  
Optical Wavelengths ◽  
Radio Frequencies

Transformation optics provides scientists and engineers with a new powerful design paradigm to manipulate the flow of electromagnetic waves in a user-defined manner and with unprecedented flexibility, by controlling the spatial distribution of the electromagnetic properties of a medium. Using this approach, over the past decade, various previously undiscovered physical wave phenomena have been revealed and novel electromagnetic devices have been demonstrated throughout the electromagnetic spectrum. In this paper, we present versatile theoretical and experimental investigations on designing transformation optics-enabled devices for shaping electromagnetic wave radiation and guidance, at both radio frequencies and optical wavelengths. Different from conventional coordinate transformations, more advanced and versatile coordinate transformations are exploited here to benefit diverse applications, thereby providing expanded design flexibility, enhanced device performance, as well as reduced implementation complexity. These design examples demonstrate the comprehensive capability of transformation optics in controlling electromagnetic waves, while the associated novel devices will open up new paths towards future integrated electromagnetic component synthesis and design, from microwave to optical spectral regimes.

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