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Register a new userElectromagnetic wave propagation in metamaterials: a visual guide to Fresnel-Kummer surfaces and their singular points
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Authors
Alberto Favaro
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The propagation of light through bianisotropic materials is studied in the geometrical optics approximation. For that purpose, we use the quartic general dispersion equation specified by the Tamm-Rubilar tensor, which is cubic in the electromagnetic response tensor of the medium. A collection of different and remarkable Fresnel (wave) surfaces is gathered, and unified via the projective geometry of Kummer surfaces.
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It is known that the Fresnel wave surfaces of transparent biaxial media have 4 singular points, located on two special directions. We show that, in more general media, the number of singularities can exceed 4. In fact, a highly symmetric linear material is proposed whose Fresnel surface exhibits 16 singular points. Because, for every linear material, the dispersion equation is quartic, we conclude that 16 is the maximum number of isolated singularities. The identity of Fresnel and Kummer surfaces, which holds true for media with a certain symmetry (zero skewon piece), provides an elegant interpretation of the results. We describe a metamaterial realization for our linear medium with 16 singular points. It is found that an appropriate combination of metal bars, split-ring resonators, and magnetized particles can generate the correct permittivity, permeability, and magnetoelectric moduli. Lastly, we discuss the arrangement of the singularities in terms of Kummers (16,6)-configuration of points and planes. An investigation parallel to ours, but in linear elasticity, is suggested for future research.
Traditionally, a black hole is a region of space with huge gravitational field, which absorbs everything hitting it. In history, the black hole was first discussed by Laplace under the Newton mechanics, whose event horizon radius is the same as the Schwarzschilds solution of the Einsteins vacuum field equations. If all those objects having such an event horizon radius but different gravitational fields are called as black holes, then one can simulate certain properties of the black holes using electromagnetic fields and metamaterials due to the similar propagation behaviours of electromagnetic waves in curved space and in inhomogeneous metamaterials. In a recent theoretical work by Narimanov and Kildishev, an optical black hole has been proposed based on metamaterials, in which the theoretical analysis and numerical simulations showed that all electromagnetic waves hitting it are trapped and absorbed. Here we report the first experimental demonstration of such an electromagnetic black hole in the microwave frequencies. The proposed black hole is composed of non-resonant and resonant metamaterial structures, which can trap and absorb electromagnetic waves coming from all directions spirally inwards without any reflections due to the local control of electromagnetic fields and the event horizon corresponding to the device boundary. It is shown that the absorption rate can reach 99% in the microwave frequencies. We expect that the electromagnetic black hole could be used as the thermal emitting source and to harvest the solar light.
We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwells equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials obeying Drudes and Lorentz models. The causality and the passivity are the two main assumptions and play a crucial role in the analysis. It is worth noting that by contrast the well-posedness in the frequency domain is not ensured in general. We also provide some numerical experiments using the Drudes model to illustrate its dispersive behaviour.
Geometrical optics describes, with good accuracy, the propagation of high-frequency plane waves through an electromagnetic medium. Under such approximation, the behaviour of the electromagnetic fields is characterised by just three quantities: the temporal frequency $omega$, the spatial wave (co)vector $k$, and the polarisation (co)vector $a$. Numerous key properties of a given optical medium are determined by the Fresnel surface, which is the visual counterpart of the equation relating $omega$ and $k$. For instance, the propagation of electromagnetic waves in a uniaxial crystal, such as calcite, is represented by two light-cones. Kummer, whilst analysing quadratic line complexes as models for light rays in an optical apparatus, discovered in the framework of projective geometry a quartic surface that is linked to the Fresnel one. Given an arbitrary dispersionless linear (meta)material or vacuum, we aim to establish whether the resulting Fresnel surface is equivalent to, or is more general than, a Kummer surface.
Merging supermassive black hole binaries produce low-frequency gravitational waves, which pulsar timing experiments are searching for. Much of the current theory is developed within the plane-wave formalism, and here we develop the more general Fresnel formalism. We show that Fresnel corrections to gravitational wave timing residual models allow novel measurements to be made, such as direct measurements of the source distance from the timing residual phase and frequency, as well as direct measurements of chirp mass from a monochromatic source. Probing the Fresnel corrections in these models will require future pulsar timing arrays with more distant pulsars across our Galaxy (ideally at the distance of the Magellanic Clouds), timed with precisions less than $100$ ns, with distance uncertainties reduced to the order of the gravitational wavelength. We find that sources with chirp mass of order $10^9 mathrm{M}_odot$ and orbital frequency $omega_0 > 10$ nHz are good candidates for probing Fresnel corrections. With these conditions met, the measured source distance uncertainty can be made less than 10 per cent of the distance to the source for sources out to $sim 100$ Mpc, source sky localization can be reduced to sub-arcminute precision, and source volume localization can be made to less than $1 text{Mpc}^3$ for sources out to 1-Gpc distances.
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