On the Jones Birefringence

The possibility that a physical system may possess simultaneously two independent linear birefringences is a consequence of the Jones calculus formulated in 1948. Before this only one linear birefringence was known. The new one is characterized by a pair of orthogonal fast and slow axes that bisect those of the traditional linear birefringence. Apparently overlooked since it was initially postulated, the Jones birefringence is the subject of the present investigation. Pictorial symmetry arguments and a Mueller matrix method are used to identify systems in which both linear birefringences may exist. They are found to occur naturally in certain magnetic and non-magnetic crystals, for which the relevant uniaxial classes are listed. In addition, it is shown that the Jones birefringence may be induced in a fluid by the application of uniform electric and magnetic fields E and B, parallel to each other and transverse to the light path, the dependence being linear in EB. A quantitative theory relates both birefringences to physical property tensors and confirms the symmetry predictions. From the theory an assessment is made of the magnitude of the effect in a crystal and a gas, and although very much smaller than known linear birefringences, it should be capable of measurement.