  We make a phenomenological model of optical two-beam interaction in a model
planar liquid crystal cell. The liquid crystal is subject to homeotropic
anchoring at the cell walls, is surrounded by thin photosensitive layers, and
is subject to a variable potential across the cell. These systems are often
known as liquid crystal photorefractive systems. The interference between the
two obliquely incident beams causes a time-independent periodic modulation in
electric field intensity in the direction transverse to the cell normal. Our
model includes this field phenomenologically by affecting the potential at the
walls of the cell. The transverse periodic surface potential causes spatially
periodic departures from a pure homeotropic texture. The texture modulation
acts as a grating for the incident light. The incident light is both directly
transmitted and also subject to diffraction. The first diffracted beams result
in energy exchange between the beams. We find that the degree of energy
exchange can be strongly sensitive to the mean angle of incidence, the angle
between the beams, and the imposed potential across the cell. We use the model
to speculate about what factors optimize non-linear optical interaction in
liquid crystalline photorefractive systems.
