The polarization dependence of degenerate four-wave mixing for isotrop
ic saturable gain media is theoretically and numerically studied. The
weak-probe limit is no longer needed in our model for developing nonli
near vectorial coupled-wave equations for the interacting beams. Discr
epancy between the two models is presented. It is found that, by compa
rison with our model, the weak-probe-limit model is no longer valid wh
en the fluence of the pump beams approaches the saturation fluence of
the material or the fluence of the probe beam exceeds one-tenth that o
f the pump beams. The results also show that switching occurs between
the transmission and reflection gratings when the forward pump fluence
is changed.