Two-photon optics of Bessel-Gaussian modes

Abstract

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks, a blazed axicon, binary axicon and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.

8 pages, 10 figures

References in corpus (4)

• Entangled Bessel beams
• Full-field quantum correlations of spatially entangled photons
• Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement
• Observation of non-diffracting behavior at the single-photon level

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• Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states
• Producing an Efficient, Collimated and Thin Annular Beam with a Binary Axicon
• All-optical mode conversion via spatially-multimode four-wave mixing
• Dichroism for Orbital Angular Momentum using Stimulated Parametric Down Conversion