Invisibility Cloaking, Dr. Ulf Leonhardt, Univ. of St. Andrews

 Introduction
The development of transformation optics [1–10] and metamaterials [11–16] had lead to the
theoretical prediction of invisible dipoles [17,18] and invisibility cloaks [4,5]. Since then
the principles behind invisibility have been demonstrated in a number of experiments that
feature cloaking in some reduced form. Electromagnetic cloaking was first realised for mi-
crowaves of one frequency and polarisation [19]. Numerous subsequent electromagnetic ex-
periments achieved “carpet cloaking” [20–26]. A carpet cloak does not make things invisible,
but makes them appear to be flat. Approximate cloaking has also been realised through
tapered waveguides [27,28]. Invisibility by plasmonic covering [17] was demonstrated as
well [29]. Furthermore, non-electromagnetic forms of cloaking have been demonstrated for
acoustic waves [30,31].
However, the realisation of electromagnetic cloaking suffers from a practical and a fundamental
problem [32–34]. The practical problem is that the material requirements for electromagnetic
cloaking are very difficult to meet, whereas the fundamental problem is that perfect invisi-
bility [5] requires that light should propagate in certain cloaking regions with a superluminal
phase velocity that tends to infinity. In principle, this can be achieved by metamaterials, but
only for discrete frequencies that correspond to the resonant frequencies of the cloaking mate-
rial [6,34]. In contrast, acoustic cloaking [30,31] is much easier to achieve, since acoustic waves
are not effected by relativistic causality and thus they are not restricted by their velocity in
air.
Broadband cloaking based on non-Euclidean geometries has been proposed in [32,33] to avoid
the requirement for infinite light velocities for electromagnetic cloaking. In this proposal the
speed of light is finite in the entire cloaking region and, therefore, this cloak has the potential
of working for a broad range of frequencies. However a fundamental problem still remains.
Since space has to be expanded to make room for the invisible region within the cloak, the
implementation of this device will still demand superluminal propagation (i.e. propagation
with a velocity that exceeds the speed of light in vacuum). The same is true for “carpet
cloaking” [20–26] where the velocity of light in the cloaking device must exceed the speed of
light in the host material, i.e. vacuum if such devices were to find practical applications.
In this paper we give an example of a device that achieves complete electromagnetic cloaking—
not just “carpet cloaking”—while all light velocities within the cloak are finite and less than
the speed of light1. Through this example we demonstrate that invisibility cloaking is possible
without superluminal propagation and anomalous material requirements. 

 

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