Parametric downconversion and the orbital angular momentum of light

Summary form only given.The orbital angular momentum of light is distinct from the intrinsic angular momentum associated with the polarization state of the light. Thus linearly polarized laser modes can carry angular momentum. Such orbital angular momentum is associated with light beams with helical wave fronts, one class of which are Laguerre-Gaussian laser modes. The azimuthal phase factor exp(il/spl phi/) in their field distribution, gives rise to an orbital angular momentum equivalent to l/spl planck/ per photon. Our previous investigations of second-harmonic generation using Laguerre-Gaussian modes confirmed that the conservation of orbital angular determines the mode structure of the frequency-doubled beam. It was shown that a Laguerre-Gaussian mode with an azimuthal index l is transformed into a frequency-doubled mode with twice the azimuthal index 2l, thus conserving the angular momentum within the light fields. Degenerate parametric downconversion can be considered as the inverse process to second-harmonic generation. An incoming pump wave generates two new fields, signal and idler, with half the pump frequency. Accordingly, a Laguerre-Gaussian pump beam with an even value of the azimuthal index l produces signal and idler beams that can both have integer azimuthal mode indices of l/2. Away from degeneracy, the signal and idler frequencies do not in general have an integer ratio. Consequently, the orbital angular momentum of the pump cannot be divided to give integer l-values for the signal and idler beams in the same ratio as their energy. Even for degenerate phase matching, an integer division of the orbital angular momentum will not be possible when the pump mode has an odd value of l. We investigate the role that the conservation of orbital angular momentum plays in the downconversion process.