  Using the model of parametric interaction based on the spatio-spectral
Schmidt modes and generalized parametric approximation, we analyze coherence
and mode structure of ultra-intense twin beams generated in the regime with
pump depletion. We show that the increase of spatial and spectral coherence
with the increasing pump power observed for moderate powers is replaced by the
decrease for the pump powers at which pump depletion occurs. This behavior of
coherence is opposed to that exhibited by the number of spatio-spectral modes
effectively constituting the twin beam. The conditions for maximal coherence
are analyzed considering pump-beam parameters (spectral width, transverse
radius). The existence of additional coherence maxima occurring at even higher
pump powers is predicted and explained by the oscillatory evolution of the
modes' populations.
