  We consider resonant tunneling of electromagnetic waves through an optical
barrier formed by dielectric layers with the frequency dispersion of their
dielectric permiability. The frequency region between lower and upper polariton
branches in these materials presents a stop band for electromagnetic waves. We
show that resonance tunneling through this kind of barriers is qualitatevely
different from tunneling through other kind of optical barriers as well as from
quantum mechanic tunneling through a rectangular barrier. We find that the
width of the resonance maxima of the transmission coeffcient tends to zero as
frequency approach the lower boundary of the stop band in a very sharp
non-analytical way. Resonance transmission peaks give rise to new photonic
bands inside the stop band if one considers periodical array of the layers.
