Negative group velocity and three-wave mixing in dielectric crystals
  Extraordinary features of optical parametric amplification of Stokes electromagnetic waves are investigated, which originate from three-wave mixing of two ordinary electromagnetic and one backward phonon wave with negative group velocity. A similarity with the counterpart in the negative-index plasmonic metamaterials and differences with those utilizing contra-propagating ordinary electromagnetic waves as well as electromagnetic and acoustic phonon waves are shown. They stem from backwardness of optical phonons with negative dispersion. Nonlinear-optical photonic devices with the properties similar to those predicted for the negative-index metamaterials are proposed. 
Vitaly V. Slabko, Sergey A. Myslivets, Mikhail I. Shalaev and   Alexander K. Popov
physics.optics