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In this article we investigate the orbital angular momentum spectrum ofphotons produced in parametric down conversion process. We study how thetransverse profile of the pump mode affects the spectrum as compared to agaussian pump beam. We show that using perfect optical vortex mode as pump thespectrum can be highly narrowed down. We further study the entanglement betweenthe two down converted photons in the orbital angular momentum basis. Weobserve that photons entangled in Laguerre-Gaussian modes exhibit greaterhigher dimensional entanglement.

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