Second-harmonic generation and the orbital angular momentum of light

Second-harmonic generation has been obtained by the use of Laguerre-Gaussian beams in a variety of mode orders. Each mode becomes doubled in frequency and transformed to a higher order. We show this to be a consequence of the phase-matching conditions. The experiment is consistent with the interpretation that the orbital angular momentum of the Laguerre-Gaussian mode is directly proportional to the azimuthal mode index $l$.