X-entangled biphotons: Schmidt number for 2D model

We calculate the Schmidt number for a two-dimensional model of the nonfactorable spatiotemporal wave-function of biphotons produced in type-I spontaneous parametric down-conversion with degenerate and collinear phase-matching taking into consideration a major part of the broad spectral and angular bandwidth of the down-converted light. We deduce an analytical expression for the Schmidt number as a function of the filter bandwidth in the limit of spectrally narrow pump and consider a possibility of tailoring a Gaussian model for the description of this kind of entanglement.