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Quantum Electronics and Laser Science Conference

Parametric down-conversion of higher-order Bessel beams in nonlinear crystals

V. Pyragaitė, A. Piskarskas, Kęstutis Regelskis, V. Smilgevičius, A. Stabinis, S. Mikalauskas

Published Dec 10, 2005• 0 citations
Publisher

Abstract

It is revealed that orbital angular momentum can be conserved within the spontaneous parametric down-conversion of higher-order Bessel beam. A qualitative agreement of theoretical predictions with experimental results is obtained.
DOI
10.1109/qels.2005.1548753

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We present a full vectorial analysis of the parametric downconversion process using a pump Bessel beam and a photon description based on Bessel wavefunctions. We find that, under the considered geometry, optical angular momentum is conserved but the crystal induces a coupling between the optical spin angular momentum (SAM) and the optical orbital angular momentum (OAM) ruled by the nonlinear properties of the crystal via the second order susceptibility tensor ?ijk(2). This leads to nontrivial correlations between the expected values of the SAM and OAM of the resulting two-photon states. Distributions of orbital angular momentum of the downconverted photons are evaluated in detail for a specific set-up.
Experimental observation of the conservation of orbital angular momentum in spontaneous parametric down-conversion has been theoretically attributed to phase-matching, transfer of plane-wave spectrum from pump beam to down-converted beams. However, according to quantum mechanics, the conservation of angular momentum arises from rotational symmetry of the Hamiltonian describing the studied physical process. Recently, experimental evidence has been found which shows that non-conservation of orbital angular momentum can occur in spontaneous parametric down-conversion due to rotational asymmetry of the Hamiltonian. In this paper, we theoretically show that all reported experimental results of conservation of orbital angular momentum in spontaneous parametric down-conversion are determined only by the Hamiltonian symmetry, and not by phase matching, transfer of plane-wave spectrum.
We study the two-photon detection amplitude of the down-converted beams in spontaneous parametric down-conversion when the physical variable of orbital angular momentum is involved, taking into account both conservation and non-conservation of angular momentum. Agreeing with experimental observations, our theoretical calculation shows that spatial structure of the two-photon detection amplitude of the down-converted beams carries important information about conservation or non-conservation of orbital angular momentum in spontaneous parametric down-conversion.
We show that the transfer of the plane-wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum.