Strong-field physics with singular light beams (original) (raw)

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

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 beams. 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 = 200 mm, we have varied the radius of the vortex beam across 0.3–1.18 mm 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. Spontaneous parametric down-conversion (SPDC) 1,2 , one of the most important nonlinear processes, is of paramount interest especially in the field of quantum optics 3 for its intrinsic capability in generating entangled photon pairs. In this process, a photon (pump) of higher energy while interacting with second order nonlinear crystals splits into a pair of low energy photons (signal-idler) subject to energy conservation and phase matching. Depending upon the phase matching conditions inside the nonlinear crystals, the down converted photons are known to be emitted in variety of spatial distributions. For example, pump beam of Gaussian mode under type-I (where the signal and idler have same polarization but orthogonal to the pump polarization), non-collinear phase-matching produces down converted photons in an annular ring, with photon of each pair at diametrically opposite points. As such, these photon pairs are entangled in the spatial degrees of freedom 4 and other degrees of freedom including orbital angular momentum (OAM) 5. The angular spectrum and hence the entanglement properties of these paired photons are highly influenced by different crystal parameters including birefringence and length, and the spatial structure of the pump beam 6. Therefore, it is imperative to study the angular spectrum of the SPDC photons for different crystal parameters, pump beams of different spatial structures and OAM. Optical vortices having phase singularities (phase dislocations) in the wavefront, carries vanishing intensity at the singular point. Due to the screw-like (helical) phase structure around the point of singularity, such beams carry OAM. The characteristic phase distribution of optical vortices is represented as exp(ilθ), where θ is the azi-muthal angle. The integer l is called the topological charge or the order of the vortex. It has been observed 7 that the OAM of the classical beam can be transferred to the heralded single photon generated through SPDC process. Therefore, it is important to study the spatial distribution of the SPDC photons while pumped with different order optical vortices. Recently we have reported 8 that unlike Gaussian beam, the vortex pump beams produce SPDC photons in asymmetric annular rings and the asymmetry increases with the order of the vortex. As the divergence 9 and the radius of the vortex beam increases with its order 10 , it is difficult to ascertain the contribution of the spatial distribution of the vortex beam and it's OAM in the asymmetry of SPDC ring separately.