  The phonon-polariton spectrum in dielectric medium with the third order
nonlinearity was theoretically obtained. Dependence of number of polariton
spectrum branches on intensity of electromagnetic field was investigated. The
appearance of new branches located in the polariton spectrum gap was caused by
the influence of dispersion of the third order dielectric susceptibility at
increment of the field intensity in the medium. The soliton and cnoidal wave
solutions for the polariton excitations for these new spectrum branches were
obtained. The all-optical logic gates OR and NOT are proposed as an example of
the theory application.
