Resonant transmittance through periodically modulated films

We analyze the optical transmittance at normal incidence for an electron gas without losses. The electron gas is supposed to have a plane parallel slab geometry and its dielectric permittivity is assumed to be periodically modulated in one direction parallel to the interfaces. Due to surface plasmon polariton mode excitation, there exist resonance frequencies where the transmittance equals to unity. The number and positions of peaks are investigated analytically and a comparison with the analytic theory by Dykhne et al. [6] is made.