Non-collinear interaction of photons with orbital angular momentum

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We elucidate the consequences of a phase-matching theory that describes second-harmonic generation of two non-collinear incident light beams that carry orbital angular momentum (OAM). More specifically, the two incident beams generate a third that, depending on the incident OAM, may experience a significantly smaller conversion efficiency in comparison to that based on the conventional phase-matching theory. This is the case even for incident angles substantially less than those required for non-conservation of OAM in the nonlinear interaction. Experiments are performed under different conditions and are in excellent agreement with the theory. Our results have implications beyond the specific case studied here of second-harmonic generation, in particular for parametric down-conversion of photons.