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On the Twisted Director Field of the Blue Phases

We study the properties of special double-twist fields with toroidal symmetry on S3. The simplest case corresponds to the unfrustrated field tangent to the Hopf fibration. The excited states are labelled by an integral winding number m. For each value of m we derive a lower bound for the energy. The double-twist tube is also studied in physical space (which is locally obtained by letting the S3 radius tend to infinity). We show that an effective cholesteric pitch, larger than the natural one, is expected in the double-twist tubes. The tube radius is therefore reduced, an effect that could be observed experimentally.