The kinetics of the phase conjugate beam generated by standard four-wa
ve mixing in a BaTiO3 crystal has been investigated by means of an acc
urate numerical simulation. The transmission grating configuration has
been considered and depletion of pumps was allowed. Special care has
been taken in using, suitable parameters for this material and consequ
ently for the coupling coefficients gamma and grating response times T
. The influence on the reflectivity of the beam intensity ratios and c
oupling coefficients has been analysed. Oscillating as well as monoton
ic increasing kinetics has been found depending on the values of the c
oupling coefficients and the pump ratio. A comparison between the unde
pleted and depleted pump cases is performed finding that reflectivity
oscillations are more pronounced for higher coupling coefficients and
when the pumps were not depleted. Some comments on the origin of the o
scillations will be presented.