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

Finite elements modelling of scattering problems for flexural waves in thin plates: Application to elliptic invisibility cloaks, rotators and the mirage effect

We propose a finite elements algorithm to solve a fourth order partial differential equation governing the propagation of time-harmonic bending waves in thin elastic plates. Specially designed perfectly matched layers are implemented to deal with the infinite extent of the plates. These are deduced from a geometric transform in the biharmonic equation. To numerically illustrate the power of elastodynamic transformations, we analyse the elastic response of an elliptic invisibility cloak surrounding a clamped obstacle in the presence of a cylindrical excitation i.e. a concentrated point force. Elliptic cloaking for flexural waves involves a density and an orthotropic Young's modulus which depend on the radial and azimuthal positions, as deduced from a coordinates transformation for circular cloaks in the spirit of Pendry et al. [Science {\bf 312}, 1780 (2006)], but with a further stretch of a coordinate axis. We find that a wave radiated by a concentrated point force located a couple of wavelengths away from the cloak is almost unperturbed in magnitude and in phase. However, when the point force lies within the coating, it seems to radiate from a shifted location. Finally, we emphasize the versatility of transformation elastodynamics with the design of an elliptic cloak which rotates the polarization of a flexural wave within its core.Comment: 14 pages, 5 figure

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

Sub-wavelength imaging with a left-handed material flat lens

We study numerically, by means of the pseudospectral time-domain method, the unique features of imaging by a flat lens made of a left-handed metamaterial that possesses the property of negative refraction. We confirm the earlier finding that a left-handed flat lens can provide near-perfect imaging of a point source and a pair of point sources with clear evidence of the sub-wavelength resolution. We illustrate the limitation of the resolution in the time-integrated image due to the presence of surface waves.Comment: 4 pages, RevTeX, 6 figures; added references and some discussio

Multi-Layer Evolution of Acoustic-Gravity Waves and Ionospheric Disturbances Over the United States After the 2022 Hunga Tonga Volcano Eruption

e Hunga-Tonga Hunga-Ha\u27apai volcano underwent a series of large-magnitude eruptions that generated in the atmosphere. We investigate the spatial and temporal evolutions of fluctuations driven by atmospheric acoustic-gravity waves (AGWs) and, in particular, the Lamb wave modes in high spatial resolution data sets measured over the Continental United States (CONUS), complemented with data over the Americas and the Pacific. Along with \u3e800 barometer sites, tropospheric observations, and Total Electron Content data from \u3e3,000 receivers, we report detections of volcano-induced AGWs in mesopause and ionosphere-thermosphere airglow imagery and Fabry-Perot interferometry. We also report unique AGW signatures in the ionospheric D-region, measured using Long-Range Navigation pulsed low-frequency transmitter signals. Although we observed fluctuations over a wide range of periods and speeds, we identify Lamb wave modes exhibiting 295–345 m s−1 phase front velocities with correlated spatial variability of their amplitudes from the Earth\u27s surface to the ionosphere. Results suggest that the Lamb wave modes, tracked by our ray-tracing modeling results, were accompanied by deep fluctuation fields coupled throughout the atmosphere, and were all largely consistent in arrival times with the sequence of eruptions over 8 hr. The ray results also highlight the importance of winds in reducing wave amplitudes at CONUS midlatitudes. The ability to identify and interpret Lamb wave modes and accompanying fluctuations on the basis of arrival times and speeds, despite complexity in their spectra and modulations by the inhomogeneous here, suggests opportunities for analysis and modeling to understand their signals to constrain features of azardous events

Amplification of evanescent waves in a lossy left-handed material slab

We carry out finite-difference time-domain (FDTD) simulations, with a specially-designed boundary condition, on pure evanescent waves interacting with a lossy left-handed material (LHM) slab. Our results provide the first full-wave numerical evidence for the amplification of evanescent waves inside a LHM slab of finite absorption. The amplification is due to the interactions between the evanescent waves and the coupled surface polaritons at the two surfaces of the LHM slab and the physical process can be described by a simple model.Comment: 4 pages, 2 figure

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