title: Topological charge algebra of optical vortices in nonlinear interactions.
abstract: We investigate the transfer of orbital angular momentum among multiple beams involved in a coherent Raman interaction. We use a liquid crystal light modulator to shape pump and Stokes beams into optical vortices with various integer values of topological charge, and cross them in a Raman-active crystal to produce multiple Stokes and anti-Stokes sidebands. We measure the resultant vortex charges using a tilted-lens technique. We verify that in every case the generated beams' topological charges obey a simple relationship, resulting from angular momentum conservation for created and annihilated photons, or equivalently, from phase-matching considerations for multiple interacting beams.
authors.forename: Alexandra A
authors.initials: AA
authors.lastname: Zhdanova
authors.forename: Mariia
authors.initials: M
authors.lastname: Shutova
authors.forename: Aysan
authors.initials: A
authors.lastname: Bahari
authors.forename: Miaochan
authors.initials: M
authors.lastname: Zhi
authors.forename: Alexei V
authors.initials: AV
authors.lastname: Sokolov