The spatial shape of photons in spontaneous parametric downconversion

This paper shows theoretically and experimentally that locally, paraxial measurements of the orbital angular momentum (OAM) conducted with entangled photons generated in noncollinear geometries, or nearly collinear geometries with Poynting vector walk off, they do not comply, in general, with the known selection rules for the spiral index of the pump, signal and idler mode functions. Conditions under which this selection rule can apply are also discussed.