Excitation of surface plasmon-polaritons in metal films with double periodic modulation: anomalous optical effects

We perform a thorough theoretical analysis of resonance effects when an arbitrarily polarized plane monochromatic wave is incident onto a double periodically modulated metal film sandwiched by two different transparent media. The proposed theory offers a generalization of the theory that had been build in our recent papers for the simplest case of one-dimensional structures to two-dimensional ones. A special emphasis is placed on the films with the modulation caused by cylindrical inclusions, hence, the results obtained are applicable to the films used in the experiments. We discuss a spectral composition of modulated films and highlight the principal role of ``resonance'' and ``coupling'' modulation harmonics. All the originating multiple resonances are examined in detail. The transformation coefficients corresponding to different diffraction orders are investigated in the vicinity of each resonance. We make a comparison between our theory and recent experiments concerning enhanced light transmittance and show the ways of increasing the efficiency of these phenomena. In the appendix we demonstrate a close analogy between ELT effect and peculiarities of a forced motion of two coupled classical oscillators.