Abstract
Spontaneous degenerate parametric scattering [down-conversion] is a 3-photon process with one pump photon of frequency 2ω and two output photons of frequency ω. We report the first (to our knowledge) experimental observation of the down conversion with the optical vortex serving as a pump beam. An optical vortex is defined as a beam containing a phase singularity, i.e. the change of phase around the center of the beam equals 2 πm; where the integer m is the topological charge. Each photon in the vortex beam possess orbital angular momentum L = mℏ. The law of conservation of angular momentum is expected to be valid in a homogenous linear or nonlinear medium. Topological charge conservation was confirmed in second-harmonic generation experiments,1 and may be expected to hold under degenerate parametric scattering.2 However, in the quantum domain, the uncertainly relations, ΔϕΔN > 2π, (where ϕ is the phase and N is the number of photons) provides an opportunity to violate this conservation principle, since the phase of the two down- converted photons is undetermined to within Δϕ = 2π/2 for every converted fundamental photon. That is, the down converted signal may contain no information about the topological phase of the pump beam. Based on our experiments and numerical calculations of the down-converted signal we suggest that the phase information is indeed lost under down conversion, therefore violating the conservation of topological charge.
© 1999 Optical Society of America
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