A Completely Covariant Approach to Transformation Optics

We show that the Plebanski based approach to transformation optics overlooks some subtleties in the electrodynamics of moving dielectrics that restricts its applicability to a certain class of transformations. An alternative, completely covariant, approach is developed that is more generally applicable and provides a clearer picture of transformation optics.Comment: 10 pages. This version: Additional references added, corrected a small error in Eq. (28) (Eq. (29) in present version), some revision of the text, appendix content moved to the main body of the text, figure removed. Corresponds more closely to published version. Prepared for a special issue on transformation optics published by Journal of Optic

The scattering of a cylindrical invisibility cloak: reduced parameters and optimization

We investigate the scattering of 2D cylindrical invisibility cloaks with simplified constitutive parameters with the assistance of scattering coefficients. We show that the scattering of the cloaks originates not only from the boundary conditions but also from the spatial variation of the component of permittivity/permeability. According to our formulation, we propose some restrictions to the invisibility cloak in order to minimize its scattering after the simplification has taken place. With our theoretical analysis, it is possible to design a simplified cloak by using some peculiar composites like photonic crystals (PCs) which mimic an effective refractive index landscape rather than offering effective constitutives, meanwhile canceling the scattering from the inner and outer boundaries.Comment: Accepted for J. Phys.

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

Dynamically tunable transformation thermodynamics

Recently, the introduction of transformation thermodynamics has provided a way to design thermal media that alter the flow of heat according to any spatial deformation, enabling the construction of novel devices such as thermal cloaks or concentrators. However, in its current version, this technique only allows static deformations of space. Here, we develop a space-time theory of transformation thermodynamics that incorporates the possibility of performing time-varying deformations. This extra freedom greatly widens the range of achievable effects, providing an additional degree of control for heat management applications. As an example, we design a reconfigurable thermal cloak that can be opened and closed dynamically, therefore being able to gradually adjust the temperature distribution of a given region.C G-M acknowledges support from Generalitat Valenciana through the VALi+d postdoctoral program (exp APOSTD/2014/044).García Meca, C.; Barceló, C. (2016). Dynamically tunable transformation thermodynamics. Journal of Optics. 18(4):044026-1-044026-5. https://doi.org/10.1088/2040-8978/18/4/044026S044026-1044026-5184Guenneau, S., Amra, C., & Veynante, D. (2012). Transformation thermodynamics: cloaking and concentrating heat flux. Optics Express, 20(7), 8207. doi:10.1364/oe.20.008207Schittny, R., Kadic, M., Guenneau, S., & Wegener, M. (2013). Experiments on Transformation Thermodynamics: Molding the Flow of Heat. Physical Review Letters, 110(19). doi:10.1103/physrevlett.110.195901McCall, M. W., Favaro, A., Kinsler, P., & Boardman, A. (2011). A spacetime cloak, or a history editor. Journal of Optics, 13(2), 029501-029501. doi:10.1088/2040-8978/13/2/029501Cummer, S. A., & Thompson, R. T. (2010). Frequency conversion by exploiting time in transformation optics. Journal of Optics, 13(2), 024007. doi:10.1088/2040-8978/13/2/024007García-Meca, C., Carloni, S., Barceló, C., Jannes, G., Sánchez-Dehesa, J., & Martínez, A. (2013). Analogue Transformations in Physics and their Application to Acoustics. Scientific Reports, 3(1). doi:10.1038/srep02009García-Meca, C., Carloni, S., Barceló, C., Jannes, G., Sánchez-Dehesa, J., & Martínez, A. (2014). Space–time transformation acoustics. Wave Motion, 51(5), 785-797. doi:10.1016/j.wavemoti.2014.01.008Kinsler, P., & McCall, M. W. (2014). Transformation devices: Event carpets in space and space-time. Physical Review A, 89(6). doi:10.1103/physreva.89.063818Kinsler, P., & McCall, M. W. (2013). Cloaks, editors, and bubbles: applications of spacetime transformation theory. Annalen der Physik, 526(1-2), 51-62. doi:10.1002/andp.201300164Leonhardt, U., & Philbin, T. G. (2006). General relativity in electrical engineering. New Journal of Physics, 8(10), 247-247. doi:10.1088/1367-2630/8/10/247Guenneau, S., & Puvirajesinghe, T. M. (2013). Fick’s second law transformed: one path to cloaking in mass diffusion. Journal of The Royal Society Interface, 10(83), 20130106. doi:10.1098/rsif.2013.0106Guenneau, S., Petiteau, D., Zerrad, M., Amra, C., & Puvirajesinghe, T. (2015). Transformed Fourier and Fick equations for the control of heat and mass diffusion. AIP Advances, 5(5), 053404. doi:10.1063/1.4917492García-Meca, C., Carloni, S., Barceló, C., Jannes, G., Sánchez-Dehesa, J., & Martínez, A. (2014). Analogue transformation acoustics and the compression of spacetime. Photonics and Nanostructures - Fundamentals and Applications, 12(4), 312-318. doi:10.1016/j.photonics.2014.05.001Schittny, R., Kadic, M., Buckmann, T., & Wegener, M. (2014). Invisibility cloaking in a diffusive light scattering medium. Science, 345(6195), 427-429. doi:10.1126/science.1254524Chester, M. (1963). Second Sound in Solids. Physical Review, 131(5), 2013-2015. doi:10.1103/physrev.131.2013Ali, Y. M., & Zhang, L. C. (2005). Relativistic heat conduction. International Journal of Heat and Mass Transfer, 48(12), 2397-2406. doi:10.1016/j.ijheatmasstransfer.2005.02.003López Molina, J. A., Rivera, M. J., & Berjano, E. (2014). Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2172), 20140547. doi:10.1098/rspa.2014.0547Christov, C. I., & Jordan, P. M. (2005). Heat Conduction Paradox Involving Second-Sound Propagation in Moving Media. Physical Review Letters, 94(15). doi:10.1103/physrevlett.94.154301Cho, J., Losego, M. D., Zhang, H. G., Kim, H., Zuo, J., Petrov, I., … Braun, P. V. (2014). Electrochemically tunable thermal conductivity of lithium cobalt oxide. Nature Communications, 5(1). doi:10.1038/ncomms5035Ihlefeld, J. F., Foley, B. M., Scrymgeour, D. A., Michael, J. R., McKenzie, B. B., Medlin, D. L., … Hopkins, P. E. (2015). Room-Temperature Voltage Tunable Phonon Thermal Conductivity via Reconfigurable Interfaces in Ferroelectric Thin Films. Nano Letters, 15(3), 1791-1795. doi:10.1021/nl504505

The rarity of terrestrial gamma-ray flashes

We report on the first search for Terrestrial Gamma-ray Flashes (TGFs) from altitudes where they are thought to be produced. The Airborne Detector for Energetic Lightning Emissions (ADELE), an array of gamma-ray detectors, was flown near the tops of Florida thunderstorms in August/September 2009. The plane passed within 10 km horizontal distance of 1213 lightning discharges and only once detected a TGF. If these discharges had produced TGFs of the same intensity as those seen from space, every one should have been seen by ADELE. Separate and significant nondetections are established for intracloud lightning, negative cloud-to-ground lightning, and narrow bipolar events. We conclude that TGFs are not a primary triggering mechanism for lightning. We estimate the TGF-to-flash ratio to be on the order of 10^(−2) to 10^(−3) and show that TGF intensities cannot follow the well-known power-law distribution seen in earthquakes and solar flares, due to our limits on the presence of faint events

Double-negative acoustic metamaterials based on quasi-two-dimensional fluid-like shells

A structured cylindrical scatterer with low-frequency resonances in both the effective bulk modulus and the dynamical mass density is designed and characterized. The proposed scattering unit is made of a rigid cylinder surrounded by a fluid-like shell embedded in a two-dimensional waveguide of height less than the length of the cylindrical scatterer. It is demonstrated that the acoustic metamaterials based on this building unit have negative acoustic parameters in a broad range of frequencies. It is also shown that double-negative behavior can be tailored by adjusting the dimensions and properties of the materials forming the structured scattering unit.This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion (MICINN) under contracts TEC2010-19751 and CSD2008-66 (the CONSOLIDER program) and by the US Office of Naval Research. The authors acknowledge Victor M Garcia-Chocano for useful discussions and Kimee Moore for proofreading the paper.Graciá Salgado, R.; Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2012). Double-negative acoustic metamaterials based on quasi-two-dimensional fluid-like shells. New Journal of Physics. 14. https://doi.org/10.1088/1367-2630/14/10/103052S1

Full-wave invisibility of active devices at all frequencies

There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. Previous results have either been on the level of ray tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP] and experimental [SMJCPSS] work has provided evidence for invisibility at frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$ contained in a domain $\Omega$ from measurements of Cauchy data of waves at \p \Omega; we pay particular attention to cloaking not just a passive object, but an active device within $D$, interpreted as a collection of sources and sinks or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic

Analysis of the wave propagation properties of a periodic array of rigid cylinders perpendicular to a finite impedance surface

The effect of the presence of a finite impedance surface on the wave propagation properties of a two-dimensional periodic array of rigid cylinders with their axes perpendicular to the surface is both numerically and experimentally analyzed in this work. In this realistic situation both the incident and the scattered waves interact with these two elements, the surface and the array. The interaction between the excess attenuation effect, due to the destructive interference produced by the superposition of the incident wave and the reflected one by the surface, and the bandgap, due to the periodicity of the array, is fundamental for the design of devices to control the transmission of waves based on periodic arrays. The most obvious application is perhaps the design of Sonic Crystals Noise Barriers. Two different finite impedance surfaces have been analyzed in the work in order to observe the dependence of the wave propagation properties on the impedance of the surface

General Relativistic Contributions in Transformation Optics

One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the spherically symmetric Schwarzschild geometry. Finally, I estimate the magnitude of curvature induced contributions to satellite-borne transformation media in Earth orbit and comment on the level of precision required for metamaterial fabrication before such contributions become important.Comment: 14 pages, 3 figures. Latest version has expanded analysis, corresponds to published versio