Transformation optics and hidden symmetries

Abstract

Symmetry plays an important role in physics providing a means of classification and a route to understanding. Here we show that an apparently unsymmetrical structure, in our example an ellipse/spheroid, has a more symmetrical partner with an identical spectrum and through which its electromagnetic properties can be classified and calculated analytically. We use the powerful tool of transformation optics to establish this relationship which has wide application beyond the simple example we give in this paper.

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

“…Despite transforming the FF solution back to the TW frame, α ω still continues to act as the propagation constant for the TW system [43]. As a consequence, the phase of the linear field E ω ⊥ on the circumference of the identical TW is given by exp 2iaα ω |y|/(x 2 + y 2 ) [27, Eqs.…”

Hidden symmetries in plasmonic gratings

“…Our tool of choice is transformation optics [3,4] which shows how the parameters ǫ and µ in Maxwell's equations change when one geometry is transformed into another. For example when a cylinder is transformed into an ellipse [5], or when a knife edge is transformed into a series of waveguides [6]. The tool is particularly powerful in two dimensional systems where conformal transformations leave the in-plane components of ǫ and µ unchanged.…”

Tunable plasmonic metasurface for perfect absorption

“…[24,25] for more details). Hence, in the electrostatic limit, both structures have the same plasmon resonance condition [35,36]. By applying the transformation optics framework, this analytical mapping allows to derive closed expressions for the reflection and transmission coefficients of the modulated graphene for p-polarized radiation at normal incidence,…”