Magneto-Optic Rotation in Birefringent Media—Application of the Poincaré Sphere

It is pointed out that the concept of the Poincaré sphere appreciably simplifies the mathematical treatment of phenomena accompanying the passage of polarized light through a medium which exhibits birefringence, optical activity or both simultaneously. This is exemplified by using the Poincaré sphere to evolve techniques which could be used for determining the true Faraday rotation in the presence of birefringence. When birefringence is present, measurements made with the half-shade at the polarizer and analyzer ends are not equivalent. In either arrangement, the errors introduced as a result of birefringence are largely reduced by taking the mean of two measurements for opposite directions of the field. Formulae are also derived by which the magnitudes of the error can be calculated for the particular experimental set up, knowing the value of the birefringence. In certain cases, even this need not be known, and the true rotation can be determined purely from measurements of the apparent rotations for two different azimuths of the incident plane of polarization.