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

TL;DR

This paper presents a simple method to generate perfect optical vortices of variable size using a convex lens and axicon, and investigates how vortex size influences the angular spectrum of down-converted photons in SPDC.

Contribution

A novel experimental scheme for generating perfect vortices of any radius with adjustable parameters using basic optical components.

Findings

Vortex radius can be varied from 0.3 to 1.18 mm by adjusting lens-axicon separation.

The angular spectrum of SPDC photons depends on the pump beam's spatial profile, not its OAM.

Asymmetric angular spectrum observed due to spatial walk-off effects, reducing with larger vortex radius.

Abstract

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