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Journal of Modern Optics

Orbital angular momentum exchange in parametric down conversion

J. A. O. Huguenin, M. Martinelli, D. P. Caetano, B. Coutinho dos Santos, Marcelo Pereira de Almeida, P. H. Souto Ribeiro, P. Nussenzveig, Antonio Zelaquett Khoury

Published Feb 21, 2006• 14 citations
Publisher

Abstract

Orbital angular momentum exchange, both in cavity free stimulated parametric down conversion and in an optical parametric oscillator, is studied. In both cases, the conditions for parametric amplification are discussed in terms of the orbital angular momentum exchange between the interacting fields. It is shown that in cavity free parametric down conversion, parametric amplification is conditioned to conserve orbital angular momentum. However, for parametric oscillation, cavity and anisotropy effects play a crucial role in the orbital angular momentum exchange between the interacting fields.

DOI
10.1080/09500340500217548

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Orbital angular momentum exchange, both in cavity free stimulated parametric down conversion and in an optical parametric oscillator, is studied. In both cases, the conditions for parametric amplification are discussed in terms of the orbital angular momentum exchange between the interacting fields. It is shown that in cavity free parametric down conversion, parametric amplification is conditioned to conserve orbital angular momentum. However, for parametric oscillation, cavity and anisotropy effects play a crucial role in the orbital angular momentum exchange between the interacting fields.
Several wave-function approximations describing spontaneous parametric down-conversion can be found in the literature. Basically all cases are derived from the standard Hamiltonian for parametric down-conversion. Most frequently, particular cases describing collinear or paraxial approximations are described. This work presents a wave function in compact form, valid for all cases of single photon-pair conversion (Type I or Type II), for all angles allowed by the phase-matching conditions and for all orbital angular momentum values lll. Examples are given of coincidence structures to be expected for signal and idler photons. Partial transfer of orbital angular momentum from the pump laser to the photon pair is discussed. Some hypothesis for the decay channels of the nontransferred part of the orbital angular momentum is made.
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 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.