Theoretical analysis of collinear spontaneous parametric down conversion properties in BiB3O6

In this paper, we report on the collinear spontaneous parametric down conversion (SPDC) with quantum theory in angle picture. Based on angle-dependent refractive index of biaxial crystal and the dielectric dispersion, we numerically simulate the effective nonlinear coefficients of BiB 3 O 6 (BIBO) crystal in principle planes. The results indicate that the most effective phase matching scheme is the type I in yz plane, while the secondary options are the type I, type II in xz plane. Considering the derivation of angular phase matching conditions, the calculation is convenient, and it is superior in determination of the spatial distribution of entangled photons.