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.
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