Thomas Rotation and Polarised Light: A non-Abelian Geometric Phase in Optics

We describe a non-Abelian Berry phase in polarisation optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarised light. The analogy permits a simple optical realization of the non-Abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincar\'{e} sphere in terms of the Pancharatnam phase.