Achieving invisibility over a finite range of frequencies

Institut Fresnel, CNRS, Aix-Marseille Université, 13013 Marseille, France.
Optics Express (Impact Factor: 3.49). 05/2008; 16(8):5656-61. DOI: 10.1364/OE.16.005656
Source: PubMed


We analyze cloaking of transverse electric (TE) fields through homogenization of radially symmetric metallic structures. The two-dimensional circular cloak consists of concentric layers cut into a large number of small infinitely conducting sectors which is equivalent to a highly anisotropic permittivity. We find that a wave radiated by a magnetic line current source located a couple of wavelengths away from the cloak is almost unperturbed in magnitude but not in phase. Our structured cloak is shown to work for different wavelengths provided they are ten times larger than the outermost sectors.

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    • "It made the design and implementation of the experiments very complicated and expensive. Also, all the theoretical predictions and experiments reported worked only at a single frequency or in a narrow band [5] [6] [7] [8] [9] [10] [11]. However, regardless of how complicated the theory is, finally, it does not step beyond the scope of the principle of geometrical optics, or the electromagnetism theory of geometrical optics. "
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    ABSTRACT: An effective optical 'cloak' consisting of lenses was developed. Experiments show that it works well at multi-frequencies or in broadband in the visible range. The intensity distributions of the input beam and the output beam are almost the same, and the distortion of the wavefront of the output beam is negligible. This kind of 'cloak' is very simple and can be achieved with very low cost. Also, a theoretical explanation was given using theory of curvature sensing.
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    • "Huang et al. proposed a concentric multilayered design of cylindrical electromagnetic cloaks [29]. Farhat et al. further divided these layers in infinitely conducting sectors in the context of electromagnetics [30]. A very comphensive, yet rigorous, mathematical account of the homogenization approach to cloaking can be found in a physics paper by Greenleaf et al. [12], while numerical illustrations of this theory are discussed in Farhat et al. [13]. "
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    ABSTRACT: We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way toward the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulkmodulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous isotropic concentric layers is further proposed based on the effectivemediumtheory. This cloak is characterized by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with an inhomogeneous and anisotropic distribution ofmaterial parameters. The latter suffers fromsingularmaterial parameters on its inner surface. This singularity depends upon the sharpness of corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak becomes more and more singular when the number of vertices increases if it is star shaped.Wethus analyze the acoustic response of a non-singular spherical cloak designed by blowing up a small ball instead of a point, as proposed in [Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The multilayered approximation of this cloak requires less extreme densities (especially for the lowest bound). Finally, we investigate another type of non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev. Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.
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    • "Norris analysed cloaking mechanisms in the context of elasticity theory, whereby pressure and shear waves are fully coupled [23]. The practical realization of a broadband acoustic cloak was further demonstrated for surface liquid waves propagating through rigid pillars displaying certain periodicity [24], following some preliminary work on cloaking via homogenization of metallic photonic crystals in the context of transverse electromagnetic waves [25]. However, the previous mathematical model also holds for the case of anti-plane shear waves, which were shown to be smoothly bent around a homogeneous isotropic elastic material with radially symmetric freely vibrating cracks. "
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    ABSTRACT: We analyse numerically the acoustic stop band properties of an array of orthotropic coated cylinders whose elastic parameters are deduced from a geometric transform [H. Chen, C.T. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials, Appl. Phys. Lett. 91 (2007) 183518]. We find that whereas a single coated inclusion is acoustically neutral at any frequency, an array of them might display some stop bands. More precisely, an array of freely vibrating coated voids is always neutral, whereas an array of clamped coated inclusions might display a zero frequency stop band. Interestingly, an array of radially symmetric coated inclusions behaves as local Helmholtz resonators, for which the eigenfield within each cloak is obtained in closed form, leading to a frequency estimate associated with the lower edge of the low frequency stop band. A finite phononic crystal of such coated cylinders behaves either as an invisible material or a reflector depending on the frequency of an acoustic source.
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