Roadmap on transformation optics

Abstract

Transformation Optics asks Maxwell's equations what kind of electromagnetic medium recreate some smooth deformation of space. The guiding principle is Einstein's principle of covariance: that any physical theory must take the same form in any coordinate system. This requirement fixes very precisely the required electromagnetic medium. The impact of this insight cannot be overestimated. Many practitioners were used to thinking that only a few analytic solutions to Maxwell's equations existed, such as the monochromatic plane wave in a homogeneous, isotropic medium. At a stroke, Transformation Optics increases that landscape from 'few' to 'infinity', and to each of the infinitude of analytic solutions dreamt up by the researcher, corresponds an electromagnetic medium capable of reproducing that solution precisely. The most striking example is the electromagnetic cloak, thought to be an unreachable dream of science fiction writers, but realised in the laboratory a few months after the papers proposing the possibility were published. But the practical challenges are considerable, requiring meta-media that are at once electrically and magnetically inhomogeneous and anisotropic. How far have we come since the first demonstrations over a decade ago? And what does the future hold? If the wizardry of perfect macroscopic optical invisibility still eludes us in practice, then what compromises still enable us to create interesting, useful, devices? While 3D cloaking remains a significant technical challenge, much progress has been made in 2dimensions. Carpet cloaking, wherein an object is hidden under a surface that appears optically flat, relaxes the constraints of extreme electromagnetic parameters. Surface wave cloaking guides subwavelength surface waves, making uneven surfaces appear flat. Two dimensions is also the setting in which conformal and complex coordinate transformations are realisable, and the possibilities in this restricted domain do not appear to have been exhausted yet. Beyond cloaking, the enhanced electromagnetic landscape provided by Transformation Optics has shown how fully analytic solutions can be found to a number of physical scenarios such as plasmonic systems used in electron energy loss spectroscopy (EELS) and cathodoluminescence (CL). Are there further fields to be enriched? A new twist to Transformation Optics was the extension to the space-time domain. By applying transformations to space-time, rather than just space, it was shown that events rather than objects could be hidden from view; Transformation Optics had provided a means of effectively redacting events from history. The hype quickly settled into serious nonlinear optical experiments that demonstrated the soundness of the idea, and it is now possible to consider the practical implications, particularly in optical signal processing, of having an 'interrupt-without-interrupt' facility that the socalled temporal cloak provides. Inevitable issues of dispersion in actual systems have only begun to be addressed. Now that time is included in ...

Camouflage

“…The invisibility cloaks of fiction and, thanks to a branch of physics known as transformation optics, ever‐closer to science fact (McCall et al ., ), are not found in nature, but many organisms are transparent. Allowing light from the background to pass through you would seem to be the ideal camouflage, because concealment is not background or behaviour dependent; you match the background because what the viewer sees is the background.…”

Surface second-harmonic generation from metallic-nanoparticle configurations: A transformation-optics approach

“…Transformation optics (TO) is a theoretical tool recently developed that allows an unprecedented control over light propagation and confinement [1][2][3]. TO relies on the form-invariance of Maxwell's equations under coordinate transformations to provide the connection between a given electromagnetic effect, coded into a geometric transformation, and the material parameters (ε, µ) required for its realization [3,4].…”

Electromagnetism, axions, and topology: A first-order operator approach to constitutive responses provides greater freedom

“…There is much current interest in the concepts and applications of transformation optics in both space and spacetime [40][41][42][43], most notably involving various sorts of spatial and spacetime cloaking in free space [44][45][46][47], against or on surfaces [48][49][50], and at distance [51].…”