When a left-circularly polarised Gaussian light beam, which has spin angular momentum (SAM) J sp = σħ = 1ħ 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 = ℓħ = 0, while the

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... irst order beam is right-circularly polarized but carries OAM of J orb = 1ħ per photon. Thus, taken together the two beams have zero SAM and J orb = ½ħ 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 ± 1ħ