Engineering of orbital angular momentum spectrum of down-converted photons with mode-invariant pump

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.