Generation of continuously tunable fractional optical orbital angular momentum using internal conical diffraction

When a left-circularly polarised Gaussian light beam, which has spin angular momentum (SAM) J(sp) = sigmah = 1h per photon, is incident along one of the optic axes of a slab of biaxial crystal it undergoes internal conical diffraction and propagates as a hollow cone of light in the crystal. The emergent beam is a superposition of equal amplitude zero and first order Bessel like beams. The zero order beam is left-circularly polarised with zero orbital angular momentum (OAM) J(orb) = [see text]h = 0, while the first order beam is right-circularly polarized but carries OAM of J(orb) = 1h per photon. Thus, taken together the two beams have zero SAM and J(orb) = (1/2)h per photon. In this paper we examine internal conical diffraction of an elliptically polarised beam, which has fractional SAM, and demonstrate an all-optical process for the generation light beams with fractional OAM up to +/- 1h.