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This paper concerns the analysis of a passive, broadband approximate cloaking scheme for the Helmholtz equation in Rd for d = 2 or d = 3. Using ideas from transformation optics, we construct an approximate cloak by “blowing up” a small ball of radius ϵ > 0 to one of radius 1. In the anisotropic cloaking layer resulting from the “blow-up” change of variables, we incorporate a Drude-Lorentz- type model for the index of refraction, and we assume that the cloaked object is a soft (perfectly conducting) obstacle. We first show that (for any fixed ϵ) there are no real transmission eigenvalues associated with the inhomogeneity representing the cloak, which implies that the cloaking devices we have created will not yield perfect cloaking at any frequency, even for a single incident time harmonic wave. Secondly, we establish estimates on the scattered field due to an arbitrary time harmonic incident wave. These estimates show that, as ϵ approaches 0, the L2 -norm of the scattered field outside the cloak, and its far field pattern, approach 0 uniformly over any bounded band of frequencies. In other words: our scheme leads to broadband approximate cloaking for arbitrary incident time harmonic waves.
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Scattering of EM waves from a Rotating Dispersive Very Good Conducting Cylinder
This research focuses on studying the scattering phenomenon. Scattering electromagnetic waves from a rotating conducting cylinder is investigated when the material of the conducting cylinder is linear, homogeneous, isotropic, and dispersive. This study is an extension of a previous work that investigated the effect of the rotating conducting cylinder on the scattered phase and amplitude, when the material of the conducting cylinder is linear, homogeneous, isotropic, and nondispersive. One of the important result of the previous work is that the Franklin transformation is a proper and more accurate method to calculate the effect of the rotation, and gives more accurate results than Galilean transformation. In this research, the Franklin transformation will be used to investigate the effect of the rotation of the object on the scattered phase and magnitude of the incident waves. The two types of incident waves (E-wave and H-wave) will be considered herein. The simulation results will clearly display the behavior of the scattered phase and magnitude with changes to the incident frequency, the speed of rotation, and the radius of the very good conducting cylinder. Moreover, this result is compared with the result of the previous work (non- dispersive material) to show the behavior of the scattered phase and magnitude when the incident frequency, speed of the rotation and radius of the very good conducting cylinder is changed.
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- Award ID(s):
- 1719501
- PAR ID:
- 10144088
- Date Published:
- Journal Name:
- 2019 IEEE International Conference on Wireless for Space and Extreme Environments (WiSEE)
- Page Range / eLocation ID:
- 15 to 20
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core–shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, weak and strong with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the strong NI is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed ‘unphysical’ materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/WiSEE.2019.8920366
