Surface Polaritons and Their Coupling with Emitters in Periodic Structures

We derive the characteristic dispersion relations for a number of surface polaritons, including surface plasmon polaritons, surface phonon polaritons and surface exciton polaritons. The system we consider is a one-dimensional periodic array of nanorods (or microrods) located on the planar interface between vacuum and metal (or semiconductor). The dispersion relations display frequency
bands and band gaps. Variations of the band structure for each type of polaritons are explored with the varying parameters, including inter-rod spacing, nanorod (microrod) characteristics and the type of media involved. The quantisation of the surface polaritons allows us to explore their coupling to quantum emitters in the vicinity of the interface, as well as the manipulation of the interaction. This may have implications for quantum information
processing.

We also analyse a two-dimensional periodic nanowire array, and in particular the related surface plasmon polaritons. We show that they display a discrete frequency spectrum.