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 mon
ochromatic 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 2
-
dimensions. 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 sub
-
wavelength 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 implica
tions,
particularly in optical signal processing, of having an ‘interrupt-without-
interrupt’ facility that the so
-
called temporal cloak provides. Inevitable issues of dispersion in actual systems have only begun to
be addressed.
Now that time is included in the programme of Transformation Optics, it is natural to ask what role
ideas from General Relativity can play in shaping the future of Transformation Optics. Indeed, one of the earliest papers on Transformation Optics was provocatively titled ‘General R
elativity in Electrical
Engineering’. The answer that curvature does not enter directly into transformation optics merely
encourages us to speculate on the role of Transformation Optics in defining laboratory analogues.
Quite
why
Maxwell’s theory defines a ‘perfect’ transformation theory, while other areas of physics
such as acoustics are not apparently quite so amenable, is a deep question whose precise,
mathematical answer will help inform us of the extent to which similar ideas can be extended to other
fields.
The contributors to this roadmap review, who are all renowned practitioners or inventors of
Transformation Optics, will give their perspectives into the field’s status and future development.