  Nonlinear interactions of waves via instantaneous cross-phase modulation can
be cast in the same way as ponderomotive wave-particle interactions in
high-frequency electromagnetic field. The ponderomotive effect arises when rays
of a probe wave scatter off perturbations of the underlying medium produced by
a second, modulation wave, much like charged particles scatter off a
quasiperiodic field. Parallels with the point-particle dynamics, which itself
is generalized by this theory, lead to new methods of wave manipulation,
including asymmetric barriers for light.
