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Conversion of spin and orbital angular momentum in the third harmonic generation process in the bulk of an isotropic medium

The interaction between spin and orbital components of the angular momentum of an elliptically polarized beam with helicoidal phase profile and arbitrary axially symmetric intensity profile in the third-harmonic generation process is investigated. The third-harmonic beam is generated in an isotropic medium with cubic nonlinearity within undepleted pump approximation. The conservation of the total projections of both the spin angular momentum and orbital angular momentum components in four-wave mixing is demonstrated for interacting waves.