  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.
