Propagation of electromagnetic solitary waves in dispersive nonlinear dielectrics

We have derived the wave equation of electromagnetic field coupling with TO phonons in second-order nonlinear dielectrics. If the loss of the medium can be ignored, theoretical calculation shows that the propagation of electromagnetic pulses without distortion in the dispersive medium is possible due to the dependence of the index of refraction on the electromagnetic field. This electromagnetic field is governed by a Boussinesq equation that has soliton solutions. If the loss of the medium is sufficiently strong that the damping distance is much smaller than the signal width, we find electromagnetic shock-wave solutions. Possible experiments in ${\mathrm{LiTaO}}_3$ are discussed.