An analytical study of 2D photonic structures

An analytical treatment of optical surface plasmon-polaxitons (SPP) existing on double-periodic high reflective media is presented. Periodicity., caused by the modulation of either complex dielectric permittivity or relief of the surface leads to the change of SPP dispersion relation due to coupling of the inoculating SPPs existing on the unmodulated boundary, and frequency gaps arising at the Brillouin zone edges. The SPP spectra for different types of periodicity/symmetry are investigated, in particular, the different couplings between several initial SPP are compared. Simple analytical expressions for the SPP dispersion relation are obtained using modified perturbation theory. The dependence of the dispersion relation on the parameters of the problem is examined.