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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical vortices in six-wave mixing

Matt M. Coles, Mathew D. Williams, Davıd L. Andrews

Published Feb 25, 2014• 0 citations

Abstract

Optical vortex light engendered with integer units of orbital angular momentum (OAM) may be involved in frequency upconversion. Second harmonic generation is usually forbidden in isotropic media due to parity constraints, but it becomes allowed by six-wave mixing. Here, we present a rigorous quantum analysis for the case of a Laguerre-Gaussian input beam comprising photons endowed with a single unit of OAM. Such a process gives rise to the novel entanglement of orbital momentum in two emergent photons; it transpires that the mechanism delivers a harmonic output whose polarization is essentially parallel to the incident radiation. This investigation ascertains the character of the emission, both under forward propagation and back-reflection geometries, and identifies in detail the form of distribution in the entangled total orbital momentum. A distinctive conical spread, originating from the entangled distribution in the emission pair, affords a potential means to determine the individual angular momenta.

DOI: 10.1117/12.2036767

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Abstract Up-conversion in an atomic vapor is known to produce photon pairs. If addressed by vortex beams, it produces pairs of orbital angular momenta (OAM), that are valuable bricks for quantum processes with OAM. The perfect vortex (PV) beam is a vortex class very pertinent in this context, because its ring radius and its Gouy phase are —in principle— independent of the OAM, giving a huge spiral bandwidth compared to the usual Laguerre-Gaussian (LG) beam. Our experimental study clarifies this point. The PV ring radius and thickness are found to vary hyperbolic-like vs . the OAM, which will limit the spiral bandwidth, but, unlike LG, the number of generated OAM pairs still remains quite comfortable for entanglement applications.

The orbital angular momentum (OAM) of light is a quantity explored for communication and quantum technology, its key strength being a wide set of values offering a large basis for quantum working. In this context we have studied the vortex conversion from a red optical vortex to a blue one, for OAMs ranging $\ensuremath{-}30$ to

+30

. The conversion is realized in a rubidium vapor, via the $5{S}_{1/2}\ensuremath{-}5{D}_{5/2}\phantom{\rule{0.16em}{0ex}}^{85}\mathrm{Rb}$ two-photon transition done with a Gaussian beam at

780\phantom{\rule{4pt}{0ex}}\mathrm{nm}

plus a Laguerre-Gaussian beam at

776\phantom{\rule{4pt}{0ex}}\mathrm{nm}

with the OAM $\ensuremath{\ell}$, producing a radiation at

420\phantom{\rule{4pt}{0ex}}\mathrm{nm}

. With copropagating input beams, we demonstrate a conversion from red to blue for high-$\ensuremath{\ell}$ input vortices. We show that the output blue vortex respects the azimuthal phase matching, has a size determined by the product of the input beams, and a power decreasing with $\ensuremath{\ell}$, in agreement with their overlap. Its propagation indicates that the generated blue wave is a nearly pure Laguerre-Gaussian mode. The vortex converter thus permits a correct OAM transmission.

Spontaneous Four Wave Mixing (SFWM) carried out in a vapor by two optical vortex beams is analyzed in the case of same handedness input orbital angular momenta. We show that the generated pair of waves carries orbital angular momenta whose entanglement strongly depends on the chosen four-levels atomic scheme, asymmetric or not. The illustration is done with two schemes of rubidium. In addition based on a theory-experiment comparison we show that the output is a partially coherent superposition of modes preserving the entanglement.

Abstract Laguerre-Gauss beams, and more generally the orbital angular momentum of light (OAM) provide valuable research tools for optical manipulation, processing, imaging and communication. High-efficiency frequency conversion of OAM is possible via four-wave mixing in rubidium vapour. Conservation of the OAM in the two pump beams determines the total OAM shared by the generated light fields at 420 nm and 5.2 μm—but not its distribution between them. Here we experimentally investigate the spiral bandwidth of the generated light modes as a function of pump OAM. A small pump OAM is transferred almost completely to the 420 nm beam. Increasing the total pump OAM broadens the OAM spectrum of the generated light, indicating OAM entanglement between the generated light fields. This clears the path to high-efficiency OAM entanglement between widely disparate wavelengths.