Is orbital angular momentum always conserved in spontaneous parametric down-conversion?

In the non-linear optical process of type-II spontaneous parametric down-conversion, we present on an experiment showing that the two-photon detection amplitude of the down-converted beams does not generally reproduce the transverse profile of the pump beam that carries non-zero orbital angular momentum. We explain this observation by that orbital angular momentum is not conserved in the type-II non-linear process due to the broken rotational symmetry of the Hamiltonian.