  In this article we investigate the orbital angular momentum spectrum of
photons produced in parametric down conversion process. We study how the
transverse profile of the pump mode affects the spectrum as compared to a
gaussian pump beam. We show that using perfect optical vortex mode as pump the
spectrum can be highly narrowed down. We further study the entanglement between
the two down converted photons in the orbital angular momentum basis. We
observe that photons entangled in Laguerre-Gaussian modes exhibit greater
higher dimensional entanglement.
