Invisibility cloaks and the equivalence principle for electromagnetics

We have shown, in this communication, how the equivalence principle for electromagnetics can be used to design invisibility cloaks. A new mathematical approach was then devised: after determining the metric perturbation g that corresponds to the cloaking topology - which performs a left translation in a group structure by transforming the unperturbed metric g₁ into a new metric g₂ = lscr_g(g₁) -, we then use the equivalence principle to find out the metamaterial that creates that new geometry. We have illustrated this strategy through two examples: (i) the first one in spherical coordinates; (ii) the second one in elliptic cylinder coordinates. Both examples are, as far as the authors are aware, new cloaking devices - although the one in spherical coordinates is a generalized version of an example already considered in [2]. We believe that, with the method herein presented, new invisibility devices can be straightforwardly designed. We should finally stress, however, that only when full-wave numerical simulations are carried out do we have a complete understanding of how material perturbations and full-wave effects might affect the ideal solution.