Optical waveguide cores having refractive index profiles that vary angularly about a propagation axis of the core can provide single-mode operation with larger core diameters than conventional waveguides. In one representative embodiment, an optical waveguide comprises a core that extends along a propagation axis and has a refractive index profile that varies angularly about the propagation axis. The optical waveguide can also comprise a cladding disposed about the core and extending along the propagation axis. The refractive index profile of the core can vary angularly along a length of the propagation axis.