As I understand by "the criteria of Bell" in this context you mean some sort of relation like that:
[tex]P_{VV}(\alpha,\beta) = sin^{2}\alpha\, sin^{2}\beta\, cos^{2}\theta_{l} + cos^{2}\alpha\, cos^{2}\beta\, sin^{2}\theta_{l} + \frac{1}{4}sin 2\alpha\, sin 2\beta\, sin 2\theta_{l}\, cos \phi [/tex]
This is equation (9) from paper -
http://arxiv.org/abs/quant-ph/0205171/"
This relation produces [tex]cos^{2}(\alpha-\beta)[/tex] law when [tex] \theta_{l}[/tex] is Pi/4 and [tex]\phi[/tex] is 0. But when for example [tex]\theta_{l}[/tex] is 0 it produces [tex]sin^{2}\alpha\, sin^{2}\beta[/tex] that is simply product of two probabilities from Malus law.
But interesting how do you view this PDC TypeI from QM perspective?
As I see it if we have one crystal incident photon is converted (sometimes) into two photons that go out of the crystal diverted in opposite directions from original direction. They are not polarization entangled.
However if these two photons encounter second crystal right after the first one if certain conditions are met two photons become polarization entangled.
It seems to me that pilot wave interpretation provides nice way to resolve this. Empty pilot wave of incident photon continues its way next to second crystal and gets partly downconverted there and then overlaps with downconverted photons (somehow) creating entangled state.
How would you explain creation of polarization entangled state in TypeI PDC?