  The intimate interaction between phase-matched parametric amplification and
strong nonlinear mode coupling in a multimode optical fiber results in a
saturable spatial mode conversion that appears to violate the conservation of
momentum. We investigate, by theory and experiment, this new regime of strong
nonlinear interaction in multimode optical fibers and show that the appearance
of the non-conservation of linear momentum is merely a clever sleight of hand
by nature. This novel saturable mode conversion can potentially be used in a
variety of applications including the generation of exotic quantum states of
light.
