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The perfect vortex is a new class of optical vortex beam having ring radiusindependent of its topological charge (order). One of the simplest techniquesto generate such beams is the Fourier transformation of the Bessel-Gauss beam.The variation in ring radius of such vortices require Fourier lenses ofdifferent focal lengths and or complicated imaging setup. Here we report anovel experimental scheme to generate perfect vortex of any ring radius using aconvex lens and an axicon. As a proof of principle, using a lens of focallength f=200mm, we have varied the radius of the vortex beam across 0.3-1.18mmsimply by adjusting the separation between the lens and axicon. This is also asimple scheme to measure the apex angle of an axicon with ease. Using suchvortices we have studied non-collinear interaction of photons having orbitalangular momentum (OAM) in spontaneous parametric down-conversion (SPDC) processand observed that the angular spectrum of the SPDC photons are independent ofOAM of the pump photons rather depends on spatial profile of the pump beam. Inthe presence of spatial walk-off effect in nonlinear crystals, the SPDC photonshave asymmetric angular spectrum with reducing asymmetry at increasing vortexradius.

Generation of perfect vortex of variable size and its effect in angular spectrum of the down-converted photons