Elliptically cored fibres with large index differences have been drawn and shown to hold polarisation well, the modal beat length being less than 1 mm. An analysis of the propagation characteristics shows that there is a point below the higher-mode cutoff where the difference in group velocities between the two fundamental modes is zero but where there is a large enough difference in the phase velocities to preserve polarisation.
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Dyott et al. (1979) studied this question.