Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus 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 effective medium theory. This cloak is characterised by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with a inhomogeneous and anisotropic distribution of material parameters. The latter suffers from singular material 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. We thus analyse 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.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloak

On electromagnetic and quantum invisibility

The principle objective of this dissertation is to investigate the fundamental properties of electromagnetic wave interactions with artificially fabricated materials i.e., metamaterials for application in advanced stealth technology called electromagnetic cloaking. The main goal is to theoretically design a metamaterial shell around an object that completely eliminates the dipolar and higher order multipolar scattering, thus making the object invisible. In this context, we developed a quasi-effective medium theory that determines the optical properties of multi-layered-composites beyond the quasi-static limit. The proposed theory exactly reproduces the far-field scattering/extinction cross sections through an iterative process in which mode-dependent quasi-effective impedances of the composite system are introduced. In the large wavelength limit, our theory is consistent with Maxwell-Garnett formalism. Possible applications in determining the hybridization particle resonances of multi-shell structures and electromagnetic cloaking are identified. This dissertation proposes a multi-shell generic cloaking system. A transparency condition independent of the object\u27s optical and geometrical properties is proposed in the quasi-static regime of operation. The suppression of dipolar scattering is demonstrated in both cylindrically and spherically symmetric systems. A realistic tunable low-loss shell design is proposed based on the composite metal-dielectric shell. The effects due to dissipation and dispersion on the overall scattering cross-section are thoroughly evaluated. It is shown that a strong reduction of scattering by a factor of up to 103 can be achieved across the entire optical spectrum. Full wave numerical simulations for complex shaped particle are performed to validate the analytical theory. The proposed design does not require optical magnetism and is generic in the sense that it is independent of the object\u27s material and geometrical properties. A generic quantum cloak analogous to the optical cloak is also proposed. The transparency conditions required for the shells to cloak an object impinged by a low energy beam of particles are derived. A realistic cloaking system with semiconductor material shells is studied

Scattering from Multilayered Graphene-Based Cylindrical and Spherical Particles

This chapter discusses various approaches for calculating the modified Mie-Lorenz coefficients of the graphene-based multilayered cylindrical and spherical geometries. Initially, the Kubo model of graphene surface conductivity is discussed. Then, according to it, the formulations of scattering from graphene-based conformal particles are extracted. So, we have considered a graphene-wrapped cylinder and obtained its scattering coefficients by considering graphene surface currents on the shell. Later, a layered nanotube with multiple stacked graphene-dielectric interfaces is introduced, and for analyzing the plane wave scattering, graphene surface conductivity is incorporated in the transfer matrix method (TMM). Unlike the previous section, the dielectric model of graphene material is utilized, and the boundary conditions are applied on an arbitrary graphene interface, and a matrix-based formulation is concluded. Then, various examples ranging from super-scattering to super-cloaking are considered. For the scattering analysis of the multilayered spherical geometries, recurrence relations are introduced for the corresponding modified Mie-Lorenz coefficients by applying the boundary conditions at the interface of two adjacent layers. Later, for a sub-wavelength nanoparticle with spherical morphology, the full electrodynamics response is simplified in the electrostatic regime, and an equivalent circuit is proposed. Various practical examples are included to clarify the importance of scattering analysis for graphene-based layered spheres in order to prove their importance for developing novel optoelectronic devices

Artificial Impedance Surfaces and Wire Media for Absorption and Cloaking

The main objective of this dissertation is to investigate the ability of utilizing artificial impedance surfaces and wire media for absorption and cloaking applications. The dissertation includes two parts which focus on the electromagnetic wave propagation in absorbers formed by stacked metasurfaces and structured wire media, and electromagnetic wave interaction with the cylindrical cloaking structures. In the first part, we propose a variety of physical systems that show multiband and wideband absorption properties in the microwave regime. For the multiband absorbers, we propose a simple analytical model to study the absorption properties. Further, using the same circuit model, the physical mechanisms of the observed behavior is clearly explained in terms of the open/coupled Fabry-Pérot resonators. To design wideband absorbers, we first analyze a single-layer wire medium loaded with an arbitrary material (a thin copper patch with finite bulk conductivity and a graphene patch characterized by its complex surface conductivity) at one end and a ground plane at the other. Based on the properties of the single-layer structure (which acts as a narrowband absorber), we next propose a novel multilayered mushroom structure with thin resistive patches at the wire-medium junctions for wideband absorption. To characterize the wideband properties, here, we derive new additional boundary conditions and solve the scattering problem using an analytical model developed particularly for the problem at hand. We also show a methodology to design these absorbers and explain the wideband absorption mechanisms. The second part focuses on the application of various metasurfaces for cloaking dielectric and conducting cylinders for plane-wave incidence and for line sources in close proximity. The cloaking mechanism is based on a mantle cloaking technique, wherein the scattered field produced by the object is cancelled by the cloak. The purpose of this work is to design the mantle cloaks using the metasurfaces, to render the objects invisible. The analysis here is carried out using a rigorous analytical model which employs the Lorenz Mie-scattering theory. Two-sided impedance boundary conditions are applied at the interface of the metasurfaces and analytical grid-impedance expressions derived for the planar cases have been successfully used in tailoring the reactances of the cylindrical surfaces. Further, the analytical results presented in the dissertation are verified using the numerical simulations