We present a quantum-optics approach for describing stimulated parametric down-conversion in the two-type-I crystal “sandwich” configuration, which allows for parametric interaction of vector vortex beams. We analyze the conditions for which phase conjugation of the seed vector beam occurs. We then use two strategies for defining generalized Stokes parameters to describe phase conjugation of vector vortex beams. These allow for geometrical representations, such as higher-order Poincaré spheres. Our results are useful for the description and design of stimulated and spontaneous parametric down-conversion experiments with vector vortex beams.

• Received 4 May 2020
• Revised 9 June 2020
• Accepted 6 July 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.024048

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Published by the American Physical Society