Abstract
The advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible. For waves confined to a surface it is known that there is a simpler, but related, geometrical equivalence between the surface shape and the refractive index, and here we demonstrate that conventional devices possessing a singularity — that is, the requirement of an infinite refractive index — can be realised for waves confined to an appropriately sculpted surface. In particular, we redesign three singular omnidirectional devices: the Eaton lens, the generalized Maxwell Fish–Eye, and the invisible sphere. Our designs perfectly reproduce the behaviour of these singular devices, and can be achieved with simple isotropic media of low refractive index contrast.
Highlights
The advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible
For waves confined to a surface it is known that there is a simpler, but related, geometrical equivalence between the surface shape and the refractive index, and here we demonstrate that conventional devices possessing a singularity — that is, the requirement of an infinite refractive index — can be realised for waves confined to an appropriately sculpted surface
Following the same procedure used for the Eaton lens, we find the angle of the cone necessary toppffiffieffiffirffiffifffioffiffiffirffimffiffi the function of the generalized Maxwell fish eye is cotða=2Þ~ M2{1, upon which we place the refractive index profile, N(R) 5 2/(1 1 R2/a2)
Summary
The advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible. The idea of deforming the surface into a particular shape to construct ‘geodesic lenses’ has been well established for some time[14], in this article we demonstrate a new method where the shape of the surface is used in combination with the local refractive index to make otherwise unphysical optical devices practical We interpret this as a technique that is analogous to the aforementioned transmutation procedure, but with the added advantage that the required materials are isotropic and low contrast. Through modifying the shape of the surface, one may manipulate the rays in a way that would require points of infinite refractive index on a flat surface This means that it is possible to reproduce the propagation characteristics of devices with singular material properties through utilising surface curvature and finite refractive index profiles, allowing one to implement, in two dimensions, devices that were previously practically impossible to realise in three. We demonstrate the principle with three singular devices: the Eaton lens[8], the Invisible sphere[9] and the generalised Maxwell fish eye[21]
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