We examine the structure of infrared singularities in QCD and quantum General Relativity, from the point of view of the recently conjectured double copy property which relates scattering amplitudes in non-Abelian gauge theories with gravitational counterparts. We show that IR divergences in both theories are consistent with the double copy procedure, to all orders in perturbation theory, thus providing all loop-level evidence for the conjecture. We further comment on the relevance, or otherwise, to the so-called dipole formula, a conjecture for the complete structure of IR singularities in QCD.Comment: 33 pages, 10 figures. Sections 3.1 and 3.2 corrected and expanded; to appear in JHE

We describe several extensions to TIM, a raytracing program for ray-optics research. These include relativistic raytracing; simulation of the external appearance of Eaton lenses, Luneburg lenses and generalized focusing gradient-index lens (GGRIN) lenses, which are types of perfect imaging devices; raytracing through interfaces between spaces with different optical metrics; and refraction with generalised confocal lenslet arrays, which are particularly versatile METATOYs. Summary of revisions: added capabilities include simulation of different types of camera moving at relativistic speeds relative to the scene; visualisation of the external appearance of generalized focusing gradient-index (GGRIN) lenses, including Maxwell fisheye, Eaton and Luneburg lenses; calculation of refraction at the interface between spaces with different optical metrics; and handling of generalised confocal lenslet arrays (gCLAs), a new type of METATOY External routines/libraries: JAMA [1] (source code included) Nature of problem: visualisation of scenes that include scene objects that create wave-optically forbidden light-ray fields Solution method: ray tracing Unusual features: specifically designed to visualise wave-optically forbidden light-ray fields; can visualise ray trajectories and geometric optic transformations; can simulate photos taken with different types of camera moving at relativistic speeds, interfaces between spaces with different optical metrics, the view through METATOYs and generalised focusing gradient-index lenses; can create anaglyphs

We describe the most general homogenous, planar, light-ray-direction-changing sheet that performs one-to-one imaging between object space and image space. This is a nontrivial special case (of the sheet being homogenous) of an earlier result [Opt. Commun.282, 2480 (2009)]. Such a sheet can be realized, approximately, with generalized confocal lenslet arrays.

We derive the law of generalised refraction for generalised confocal lenslet arrays, which are arrays of misaligned telescopes. We have implemented this law of refraction in TIM, a custom open-source ray tracer.

Transformation optics is a recent paradigm for designing metamaterial structures that behave, to light, like curved spaces. The headline application, invisibility cloaking, has created much interest with scientists and the public alike. Transformation-optics devices built from metamaterials have many limitations, for example the very high cost of creating even tiny volumes of the nano-structured materials required for operation in the visible wavelength range, and the very narrow wavelength band over which metamaterials have the desired properties. Pairs of microlens arrays that are separated by the sum of their focal lengths form arrays of micro-telescopes. Such arrays are pixellated windows (each telescope is one pixel) that change, over a limited field of view but also over a wide wavelength range, the light-ray direction of transmitted light rays like the interface between different materials. In principle, they can also be manufactured cheaply and in bulk. By exploiting the fact that these windows are (in principle) perfectly imaging [S. Oxburgh and J. Courtial, J. Opt. Soc. Am. A 30, 2334 (2013)], we demonstrate that such windows, when combined into suitable structures, are pixellated transformation-optics devices. This new class of transformation-optics device can be macroscopic in size, and so such devices offer a very different compromise to metamaterial transformation-optics devices. This should significantly widen the applicability of transformation optics.