  Entangled twin-beams generated by parametric down-conversion are among the
favorite sources for imaging-oriented applications, due their multimodal nature
in space and time. However, a satisfactory theoretical description is still
lacking. In this work we propose a semi-analytic model which aims to bridge the
gap between time-consuming numerical simulations and the unrealistic plane-wave
pump theory. The model is used to study the quantum correlation and the
coherence in the angle-frequency domain of the parametric emission, and
demonstrates a $g^{{1/2}} $ growth of their size as the gain $g$ increases,
with a corresponding contraction of the space-time distribution. These
predictions are systematically compared with the results of stochastic
numerical simulations, performed in the Wigner representation, of the full
model equations: an excellent agreement is shown even for parameters well
outside the expected limit of validity of the model.
