Transfer matrix method for point sources radiating in classes of negative refractive index materials with 2n-fold antisymmetry

Abstract

We introduce a transfer matrix algorithm well-suited for negative refractive index materials. We achieve a clean mathematical derivation of the electromagnetic field radiated by finite and countable sets of harmonic point sources within a class of perfect lenses [1] which present some periodicity along one axis. In the case of a periodic set of point sources, combining a coordinate transformation [2] with the transfer matrix method enables a rigorous calculation of the vector field within perfect corner lenses consisting of intersecting planes delimiting positive and negative index media, in the spirit of [3]. In contrast to [4] where two negative corners sharing the same vertex led to spatial oscillations of surface plasmons being inversely as ln (σ), we observe that 2n negative corners (related by 2n-fold antisymmetry) lead to linearly decreasing absorption σ, for large n. This may result in a better trap for light in a practical device such as a poor man's corner reflector made out of thin sectors alternating air and silver, as suggested by an effective medium approach and some accurate numerical results based on constant frequency dispersion diagrams.