The helical phase of chiral nematic liquid crystals as the Bianchi VII(0) group manifold

Understand

We show that the optical structure of the helical phase of a chiral nematic is naturally associated with the Bianchi VII(0) group manifold, of which we give a full account.

• The Joets-Ribotta metric governing propagation of the extraordinary rays is invariant under the simply transitive action of the universal cover of the three dimensional Euclidean group of two dimensions.
• Thus extraordinary light rays are geodesics of a left-invariant metric on this Bianchi type VII(0) group.
• We are able to solve by separation of variables both the wave equation and the Hamilton-Jacobi equation for this metric.