Design and analytically full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations

We investigate a general class of electromagnetic devices created with any continuous transformation functions by rigorously calculating the analytical expressions of the electromagnetic field in the whole space. Some interesting phenomena associated with these transformation devices, including the invisibility cloaks, concentrators, and field rotators, are discussed. By carefully choosing the transformation function, we can realize cloaks which are insensitive to perturbations at both the inner and outer boundaries. Furthermore, we find that when the coating layer of the concentrator is realized with left-handed materials, energy will circulate between the coating and the core, and the energy transmits through the core of the concentrator can be much bigger than that transmits through the concentrator. Therefore, such concentrator is also a power flux amplifier. Finally, we propose a spherical field rotator, which functions as not only a wave vector rotator, but also a polarization rotator, depending on the orientations of the spherical rotator with respect to the incident wave direction. The functionality of these novel transformation devices are all successfully confirmed by our analytical full wave method, which also provides an alternate computational efficient validation method in contrast to numerical validation methods.Comment: 22 pages, 3 figure

Cloaking and anamorphism for light and mass diffusion

We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we consider the equation for diffusive photon density in transformed coordinates, which is valid for diffusive light in scattering media. More precisely, generalizing transformations for star domains introduced in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we numerically demonstrate that infinite conducting objects of different shapes scatter diffusive light in exactly the same way. We also propose a design of external light-diffusion cloak with spatially varying sign-shifting parameters that hides a finite size scatterer outside the cloak. We next analyse non-physical parameter in the transformed Fick's equation derived in [Guenneau and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a non-linear transform that overcomes this problem. We finally investigate other form invariant transformed diffusion-like equations in the time domain, and touch upon conformal mappings and non-Euclidean cloaking applied to diffusion processes.Comment: 42 pages, Latex, 14 figures. V2: Major changes : some formulas corrected, some extra cases added, overall length extended from 21 pages (V1) to 42 pages (present version V2). The last version will appear at Journal of Optic

A Review of Metamaterial Invisibility Cloaks

The exciting features of metamaterial in conjunction with transformation optics leads to various applications in the microwave regime with such examples as invisible cloak, frequency selective surfaces (FSS), radomes, etc. The concept of electromagnetic invisibility is very much important in aerospace platform. Hence to study the feasibility of implementation of this concept for stealth, an extensive literature survey of metamaterial cloaks has been carried out and reported in this paper along with the basic concept of cloaking. To make the review more effective, the technical papers are classified into three broad sections viz. mathematical modeling, design and simulations, and fabrications and experimental demonstration. Further the design and simulation is focused on different techniques implemented such as finite difference time domain (FDTD), finite element method (FEM), finite integration technique (FIT), inductor-capacitor representation of metamaterial (LC MTM) etc. The review also reports the methods implemented for analysis of metamaterial cloaks with possibility of application to the specific frequency rang

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

Design of Arbitrarily Shaped Inertial and Three Dimensional Pentamode Acoustic Cloaks

Acoustic cloaks are devices that can make a space acoustically invisible. Acoustic cloaks can be designed using transformation acoustics. The properties of these cloaks are, by necessity, anisotropic. Inertial acoustic cloaks have anisotropic density and isotropic bulk modulus, while pentamode cloaks have isotropic density and anisotropic stiffness. The ultimate goal of this work is to build cloaks of arbitrary 2D and 3D shape that are composed of homogenous materials. Five different design methods are presented which contribute toward this goal. The first contribution of the work is a method of designing 2D inertial acoustic cloaks having arbitrary shapes, based on transformation acoustics to map along radial directions. The derived properties are complicated. By dividing the cloak into small sections, the transverse anisotropy is removed, but the radial anisotropy remains. The properties within each section are inhomogeneous, but could theoretically be realized using layered media. The second and third contributions of the work are two methods of designing 2D arbitrarily shaped cloaks such that homogeneous material properties occur. One method accomplishes homogeneity by simply dividing the cloaks into triangular patterns. Each triangle in physical space is mapped to a corresponding triangle in virtual space, resulting in homogeneous properties. The second method is through the use of multiple transforms. Arc sections are divided into two triangles. The first triangle undergoes a single transform, while the second undergoes two. The fourth contribution of the work is extending these methods to three dimensions. Here, 3D arbitrarily shaped cloaks can be composed of homogeneous tetrahedral parts. The fifth contribution of the work is the introduction of a new pentamode material that is amenable to designing 3D cloaks. Pentamode materials have special structures such that only compressional waves are supported. Hexagonal cells with double-cone structures (DCS) are designed and analyzed, which can approximate the shape of a layered spherical pentamode structure. From the dispersion relations, it is observed that there are bandgaps where all shear modes disappear. The effect of the unit cell geometry on the acoustic properties is studied. Unit cells for a 3D pentamode acoustic cloak are explored

Making waves round a structured cloak: lattices, negative refraction and fringes

Using the framework of transformation optics, this paper presents a detailed analysis of a non-singular square cloak for acoustic, out-of-plane shear elastic and electromagnetic waves. Analysis of wave propagation through the cloak is presented and accompanied by numerical illustrations. The efficacy of the regularized cloak is demonstrated and an objective numerical measure of the quality of the cloaking effect is provided. It is demonstrated that the cloaking effect persists over a wide range of frequencies. As a demonstration of the effectiveness of the regularized cloak, a Young’s double slit experiment is presented. The stability of the interference pattern is examined when a cloaked and uncloaked obstacle are successively placed in front of one of the apertures. This novel link with a well-known quantum mechanical experiment provides an additional method through which the quality of cloaks may be examined. In the second half of the paper, it is shown that an approximate cloak may be constructed using a discrete lattice structure. The efficiency of the approximate lattice cloak is analysed and a series of illustrative simulations presented. It is demonstrated that effective cloaking may be obtained by using a relatively simple lattice structure, particularly, in the low-frequency regime