Abstract
We study the nonlinear interaction between two non-collinear light beams that carry orbital angular momentum (OAM). More specifically, two incident beams interact at an angle in a medium with a second order nonlinearity and thus generate a third, non-collinear beam at the second harmonic frequency that experiences a reduced conversion efficiency in comparison to that expected based on conventional phase-matching theory. This reduction scales with the input beam OAM and, differently from previous spiral bandwidth calculations, is due to a geometric effect whereby the input OAM is projected along the non-collinear interaction direction. The effect is relevant even at small interaction angles and is further complicated at large angles by a non-conservation of the total 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 or in general for phase-matched non-collinear interactions between beams with different OAM.
Highlights
We study the nonlinear interaction between two non-collinear light beams that carry orbital angular momentum (OAM)
Our goal is to present the essence of our theory in order to explore its experimental consequences for non-collinear second harmonic generation (SHG) with OAM beams
To proceed we describe the basic geometry and equations used to treat the non-collinear interaction of OAM beams in a crystal with second order (x(2)) nonlinearity
Summary
We study the nonlinear interaction between two non-collinear light beams that carry orbital angular momentum (OAM). Two incident beams interact at an angle in a medium with a second order nonlinearity and generate a third, non-collinear beam at the second harmonic frequency that experiences a reduced conversion efficiency in comparison to that expected based on conventional phase-matching theory. We show that when the interaction angle is properly accounted for, the oribital angular momentum of the pump significantly modifies the phase matching relations and leads to a marked reduction in the conversion efficiency These results apply to the PDC case and imply a significantly smaller spiral bandwidth than may otherwise be expected, even for angles less than those required for non-conservation of OAM
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