Transformation optics and hidden symmetries

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.