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

FDTD modelling of electromagnetic transformation based devices

PhDDuring this PhD study, several finite-difference time-domain (FDTD) methods were developed to numerically investigate coordinate transformation based metamaterial devices. A novel radially-dependent dispersive FDTD algorithm was proposed and applied to simulate electromagnetic cloaking structures. The proposed method can ac- curately model both lossless and lossy cloaks with ideal or reduced parameters. It was demonstrated that perfect “invisibility” from electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band. With a few modifications the method is able to simulate general media, such as concentrators and rotation coatings, which are produced by means of coordinate transformations techniques. The limitations of all these devices were thoroughly studied and explo- red. Finally, more useful cloaking structures were proposed, which can operate over a broad frequency spectrum. Several ways to control and manipulate the loss in the electromagnetic cloak ba- sed on transformation electromagnetics were examined. It was found that, by utili- sing inherent electric and magnetic losses of metamaterials, as well as additional lossy materials, perfect wave absorption can be achieved. These new devices demonstrate super-absorptivity over a moderate wideband range, suitable both for microwave and optical applications. Furthermore, a parallel three-dimensional dispersive FDTD method was introdu- ced to model a plasmonic nanolens. The device has its potential in subwavelength imaging at optical frequencies. The finiteness of such a nano-device and its impact on the system dynamic behaviour was numerically exploited. Lastly, a parallel FDTD method was also used to model another interesting coordinate transformation based device, an optical black hole, which can be characterised as an omnidirectional broad- band absorber

On near-cloaking for linear elasticity

We make precise some results on the cloaking of displacement fields in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosserat and Willis frameworks are shown to be equivalent to certain high contrast small defect problems for the usual Navier equations. We discuss near-cloaking for elasticity systems via a regularized transform and perform numerical experiments to illustrate our near-cloaking results. We also study the sharpness of the estimates from [H. Ammari, H. Kang, K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence of the solutions to the transmission problems is investigated, when the Lam\'e parameters in the inclusion tend to extreme values. Both soft and hard inclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose an approximate isotropic cloak algorithm for a symmetrized Cosserat cloak.Comment: 7 figures, 7 tables; Note that the earlier version of this preprint was titled 'Some results in near-cloaking for elasticity systems'. This new version of the manuscript has also seen some major upgrade. We have added a new section on 'Cloaking parameters and isotropic approximation'. In there, we propose an approximate isotropic cloak algorithm for a symmetrized Cosserat cloa

Design, Modeling, and Measurement of a Metamaterial Electromagnetic Field Concentrator

This document addresses the need to improve the design process for creating an optimized metamaterial. In particular, two challenges are addressed: creating an electromagnetic concentrator and optimizing the design of metamaterial used to create the electromagnetic concentrator. The first challenge is addressed by developing an electromagnetic field concentrator from a design of concentric geometric shapes. The material forming the concentrator is derived from the application of transformation optics. The resulting anisotropic, spatially variant constitutive parameter tensors are then approximated with metamatieral inclusions using the combination of an AFIT rapid metamaterial design process and a design process created for rapid metamaterial production. The second challenge of optimizing the design of the metamaterial is addressed by considering factors such as circuit board selection, various sets of metamaterial cell geometry combinations, and optimization of the ratio of the widths for the concentric geometric shapes. The resulting optimized design is simulated and shown to compress and concentrate the vertical electric field component of incident plane waves. A physical device is constructed based on the simulations and tested to confirm the entire design process. Experimental data do not definitely show concentration however an optimized design process has been proven

Transformation Thermotics and Extended Theories

This open access book describes the theory of transformation thermotics and its extended theories for the active control of macroscopic thermal phenomena of artificial systems, which is in sharp contrast to classical thermodynamics comprising the four thermodynamic laws for the passive description of macroscopic thermal phenomena of natural systems. This monograph consists of two parts, i.e., inside and outside metamaterials, and covers the basic concepts and mathematical methods, which are necessary to understand the thermal problems extensively investigated in physics, but also in other disciplines of engineering and materials. The analyses rely on models solved by analytical techniques accompanied by computer simulations and laboratory experiments. This monograph can not only be a bridge linking three first-class disciplines, i.e., physics, thermophysics, and materials science, but also contribute to interdisciplinary development

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

Transformation Thermotics and Extended Theories

This open access book describes the theory of transformation thermotics and its extended theories for the active control of macroscopic thermal phenomena of artificial systems, which is in sharp contrast to classical thermodynamics comprising the four thermodynamic laws for the passive description of macroscopic thermal phenomena of natural systems. This monograph consists of two parts, i.e., inside and outside metamaterials, and covers the basic concepts and mathematical methods, which are necessary to understand the thermal problems extensively investigated in physics, but also in other disciplines of engineering and materials. The analyses rely on models solved by analytical techniques accompanied by computer simulations and laboratory experiments. This monograph can not only be a bridge linking three first-class disciplines, i.e., physics, thermophysics, and materials science, but also contribute to interdisciplinary development

Roadmap on Transformation Optics

Transformation Optics asks Maxwell's equations what kind of electromagnetic medium recreate some smooth deformation of space. The guiding principle is Einstein's principle of covariance: that any physical theory must take the same form in any coordinate system. This requirement fixes very precisely the required electromagnetic medium. The impact of this insight cannot be overestimated. Many practitioners were used to thinking that only a few analytic solutions to Maxwell's equations existed, such as the monochromatic plane wave in a homogeneous, isotropic medium. At a stroke, Transformation Optics increases that landscape from `few' to `infinity', and to each of the infinitude of analytic solutions dreamt up by the researcher, corresponds an electromagnetic medium capable of reproducing that solution precisely. The most striking example is the electromagnetic cloak, thought to be an unreachable dream of science fiction writers, but realised in the laboratory a few months after the papers proposing the possibility were published. But the practical challenges are considerable, requiring meta-media that are at once electrically and magnetically inhomogeneous and anisotropic. How far have we come since the first demonstrations over a decade ago? And what does the future hold? If the wizardry of perfect macroscopic optical invisibility still eludes us in practice, then what compromises still enable us to create interesting, useful, devices? While 3D cloaking remains a significant technical challenge, much progress has been made in 2- dimensions. Carpet cloaking, wherein an object is hidden under a surface that appears optically flat, relaxes the constraints of extreme electromagnetic parameters. Surface wave cloaking guides sub-wavelength surface waves, making uneven surfaces appear flat. Two dimensions is also the setting in which conformal and complex coordinate transformations are realisable, and the possibilities in this restricted domain do not appear to have been exhausted yet. Beyond cloaking, the enhanced electromagnetic landscape provided by Transformation Optics has shown how fully analytic solutions can be found to a number of physical scenarios such as plasmonic systems used in electron energy loss spectroscopy (EELS) and cathodoluminescence (CL). Are there further fields to be enriched? A new twist to Transformation Optics was the extension to the space-time domain. By applying transformations to space-time, rather than just space, it was shown that events rather than objects could be hidden from view; Transformation Optics had provided a means of effectively redacting events from history. The hype quickly settled into serious nonlinear optical experiments that demonstrated the soundness of the idea, and it is now possible to consider the practical implications, particularly in optical signal processing, of having an `interrupt-without-interrupt' facility that the so-called temporal cloak provides. Inevitable issues of dispersion in actual systems have only begun to be addressed. Now that time is included in the programme of Transformation Optics, it is natural to ask what role ideas from General Relativity can play in shaping the future of Transformation Optics. Indeed, one of the earliest papers on Transformation Optics was provocatively titled `General Relativity in Electrical Engineering'. The answer that curvature does not enter directly into transformation optics merely encourages us to speculate on the role of Transformation Optics in defining laboratory analogues. Quite why Maxwell's theory defines a `perfect' transformation theory, while other areas of physics such as acoustics are not apparently quite so amenable, is a deep question whose precise, mathematical answer will help inform us of the extent to which similar ideas can be extended to other fields. The contributors to this roadmap review, who are all renowned practitioners or inventors of Transformation Optics, will give their perspectives into the field's status and future development