The refraction of an optical vortex at a nonlinear refractive index interface in a nematic liquid crystal is studied using modulation theory and numerical solutions. It is found that the refraction of an optical vortex differs in fundamental ways from the refraction of an optical solitary wave. This is due to an optical solitary wave having an inherent instability mode which can be triggered if it interacts too strongly with the interface, leading to the break-up of the vortex into solitary

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... s. Vortex refraction is studied using both an approximate modulation theory, based on an averaged Lagrangian formulation of the governing equations, and numerical solutions. Excellent agreement is found between the approximate analytical theory and numerical solutions.