Transformation Optics and the Geometry of Light

Metamaterials are beginning to transform optics and microwave technology thanks to their versatile properties that, in many cases, can be tailored according to practical needs and desires. Although metamaterials are surely not the answer to all engineering problems, they have inspired a series of significant technological developments and also some imaginative research, because they invite researchers and inventors to dream. Imagine there were no practical limits on the electromagnetic properties of materials. What is possible? And what is not? If there are no practical limits, what are the fundamental limits? Such questions inspire taking a fresh look at the foundations of optics and at connections between optics and other areas of physics. In this article we discuss such a connection, the relationship between optics and general relativity, or, expressed more precisely, between geometrical ideas normally applied in general relativity and the propagation of light, or electromagnetic waves in general, in materials. We also discuss how this connection is applied: in invisibility devices, perfect lenses, the optical Aharonov-Bohm effect of vortices and in analogues of the event horizon.Comment: 72 pages, 18 figures, preprint with low-resolution images. Introduction to transformation optics, to appear in Progress in Optics (edited by Emil Wolf

All-frequency reflectionlessness

7 pagesThis is the author accepted manuscript. The final version is available from IOP via the DOI in this record.We derive planar permittivity profiles that do not reflect perpendicularly exiting radiation of any frequency. The materials obey the Kramers-Kronig relations and have no regions of gain. Reduction of the Casimir force by means of such materials is also discussed.Financial support was received from EPSRC under Program Grant EP/I034548/

Reply to the Comment on Perfect imaging with positive refraction in three dimensions

Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution

Making geometrical optics exact

5 pagesThis is the author accepted manuscript. The final version is available from Taylor & Francis via the DOI in this record.Geometrical optics (GO) is widely used in studies of electromagnetic materials because of its ease of use compared to full-wave numerical simulations. Exact solutions for waves can, however, differ significantly from the GO approximation. In particular, effects that are "perfect" for waves cannot usually be derived using GO. Here we give a method for designing materials in which GO is exact for some waves. This enables us to find interesting analytical solutions for exact wave propagation in inhomogeneous media. Two examples of the technique are given: a material in which two point sources do not interfere, and a perfect isotropic cloak for waves from a point source. We also give the form of material response required for GO to be exact for all waves

No quantum friction between uniformly moving plates

Copyright © 2009 IOP PublishingOpen Access journalThe Casimir forces between two plates moving parallel to each other are found by calculating the vacuum electromagnetic stress tensor. The perpendicular force between the plates is modified by the motion but there is no lateral force on the plates. Electromagnetic vacuum fluctuations do not therefore give rise to "quantum friction" in this case, contrary to previous assertions. The result shows that the Casimir-Polder force on a particle moving at constant speed parallel to a plate also has no lateral component

An alternative calculation of the Casimir forces between birefringent plates

Copyright © 2008 The American Physical SocietyBarash has calculated the Casimir forces between parallel birefringent plates with optical axes parallel to the plate boundaries [Izv. Vyssh. Uchebn.\ Zaved., Radiofiz., {\bf 12}, 1637 (1978)]. The interesting new feature of the solution compared to the case of isotropic plates is the existence of a Casimir torque which acts to line up the optical axes if they are not parallel or perpendicular. The forces were found from a calculation of the Helmholtz free energy of the electromagnetic field. Given the length of the calculations in this problem and hopes of an experimental measurement of the torque, it is important to check the results for the Casimir forces by a different method. We provide this check by calculating the electromagnetic stress tensor between the plates and showing that the resulting forces are in agreement with those found by Barash

Hawking tunneling and boomerang behaviour of massive particles with E < m

Copyright © 2012 American Institute of PhysicsTowards New Paradigms: Proceeding of the Spanish Relativity Meeting 2011 (ERE2011), 29 August–2 September 2011, Madrid, SpainMassive particles are radiated from black holes through the Hawking mechanism together with the more familiar radiation of massless particles. For E ≥ m, the emission rate is identical to the massless case. But E < m particles can also tunnel across the horizon. A study of the dispersion relation and wave packet simulations show that their classical trajectory is similar to that of a boomerang. The tunneling formalism is used to calculate the probability for detecting such E < m particles, for a Schwarzschild black hole of astrophysical size or in an analogue gravity experiment, as a function of the distance from the horizon and the energy of the particle

Casimir stress in an inhomogeneous medium

Copyright © 2010 ElsevierThe Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect

Active absorption of electromagnetic pulses in a cavity

7 pages, 4 figuresAuthor version of the article. The version of record is available from the publisher via: http://dx.doi.org/10.1088/1367-2630/17/5/053050 and is an open access article.© 2015 IOP Publishing Ltd and Deutsche Physikalische GesellschaftWe show that a pulse of electromagnetic radiation launched into a cavity can be completely absorbed into an infinitesimal region of space, provided one has a high degree of control over the current flowing through this region. We work out explicit examples of this effect in a cubic cavity and a cylindrical one, and experimentally demonstrate the effect in the microwave regime.Engineering and Physical Sciences Research Council (EPSRC)Czech Science Foundatio

Hawking radiation and the boomerang behaviour of massive modes near a horizon

Copyright © 2011 American Physical SocietyWe discuss the behaviour of massive modes near a horizon based on a study of the dispersion relation and wave packet simulations of the Klein-Gordon equation. We point out an apparent paradox between two (in principle equivalent) pictures of black hole evaporation through Hawking radiation. In the picture in which the evaporation is due to the emission of positive-energy modes, one immediately obtains a threshold for the emission of massive particles. In the picture in which the evaporation is due to the absorption of negative-energy modes, such a threshold apparently does not exist. We resolve this paradox by tracing the evolution of the positive-energy massive modes with an energy below the threshold. These are seen to be emitted and move away from the black hole horizon, but they bounce back at a "red horizon" and are re-absorbed by the black hole, thus compensating exactly for the difference between the two pictures. For astrophysical black holes, the consequences are curious but do not affect the terrestrial constraints on observing Hawking radiation. For analogue gravity systems with massive modes, however, the consequences are crucial and rather surprising