Selection rules for optical activity and linear birefringence bilinear in electric and magnetic fields

All independent geometric factors are derived for the possible polarisation dependence of optical activity and linear birefringence effects bilinear in a static electric and magnetic field, for fluids. The extension to oriented systems is illustrated. Differences between the methods used and results obtained with those of earlier workers are noted and where possible resolved. Several optical effects predicted to exist by earlier workers are shown to be forbidden, and vice versa. In particular the Jones birefringence should appear in E1/M1 coupling for all fluids, irrespective of the centrosymmetric or non-magnetic character of the system, and there exist field-dependent refractive index contributions which reverse with the direction of the light beam and are detectable by a ring laser.