We introduce a recipe for producing a new type of electromagnetic cloak, the electromagnetic spacetime cloak, which conceals events rather than mere objects. Non-emitting events occurring during a restricted period are never suspected by a distant observer. The cloak works by locally manipulating the speed of light of an initially uniform light distribution, whilst the light rays themselves always follow straight paths. Any 'perfect' spacetime cloak would necessarily rely upon the technology of electromagnetic metamaterials, which has already been shown to be capable of deforming light in ways hitherto unforseen -to produce for example an electromagnetic object cloak. Nevertheless, we show how it is possible to use intensity dependent refractive indices to construct an approximate STC, an implementation that would enable the distinct signature of successful event cloaking to be observed. Potential demonstrations include systems that apparently violate quantum statistics, 'interrupt-without-interrupt' computation on convergent data channels, and the illusion of a Star-Trek transporter. * Electronic address: m.mccall@imperial.ac.uk
Based on a recent work by Schuller et al., a geometric representation of all skewonless, nonbirefringent linear media is obtained. The derived constitutive law is based on a "core", encoding the optical metric up to a constant. All further corrections are provided by two (anti-)selfdual bivectors, and an "axion". The bivectors are found to vanish if the optical metric has signature (3,1) -that is, if the Fresnel equation is hyperbolic. We propose applications of this result in the context of transformation optics and premetric electrodynamics.
Complete determination of the polarization state of light requires at least four distinct projective measurements of the associated Stokes vector. Stability of state reconstruction, however, hinges on the condition number κ of the corresponding instrument matrix. Optimization of redundant measurement frames with an arbitrary number of analysis states, m, is considered in this Letter in the sense of minimization of κ. The minimum achievable κ is analytically found and shown to be independent of m, except for m=5 where this minimum is unachievable. Distribution of the optimal analysis states over the Poincaré sphere is found to be described by spherical 2 designs, including the Platonic solids as special cases. Higher order polarization properties also play a key role in nonlinear, stochastic, and quantum processes. Optimal measurement schemes for nonlinear measurands of degree t are hence also considered and found to correspond to spherical 2t designs, thereby constituting a generalization of the concept of mutually unbiased bases.
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K ijkl . This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T ijkl , which is antisymmetric in its first two and its last two indices:If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as 1 defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R ijkl of a Riemann-Cartan spacetime, then K ∼ R 3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4, R) and, subsequently, under the Lorentz group SO(1, 3).
The Poynting vector is an invaluable tool for analysing electromagnetic problems. However, even a rigorous stress-energy tensor approach can still leave us with the question: is it best defined as E × H or as D × B? Typical electromagnetic treatments provide yet another perspective: they regard E × B as the appropriate definition, because E and B are taken to be the fundamental electromagnetic fields. The astute reader will even notice the fourth possible combination of fields: i.e. D × H. Faced with this diverse selection, we have decided to treat each possible flux vector on its merits, deriving its associated energy continuity equation but applying minimal restrictions to the allowed host media. We then discuss each form, and how it represents the response of the medium. Finally, we derive a propagation equation for each flux vector using a directional fields approach; a useful result which enables further interpretation of each flux and its interaction with the medium. Eur. J. Phys. 30, 983 (2009). 1 This arXiv version has updates not present in the published version. Published in
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