  Starting from the standard Hamiltonian describing the optical non-linear
process of spontaneous parametric down-conversion, we theoretically show that
the generated entangled photon-pairs carry non-negligible orbital angular
momentum in the degrees of freedom of relative movement in the type-II cases
due to spatial symmetry breaking. We also show that the orbital angular
momentum carried by photon-pairs in these degrees of freedom escapes detection
in the traditional measurement scheme, which demands development of new
techniques for further experimental investigations.
