POLARIZATION OF LIGHT AND TOPOLOGICAL PHASES

The phase shifts experienced by a polarized light wave when it propaga tes through media with arbitrary birefringence, dichroism and depolari zing properties, while on the one hand provide the basis for a variety of optical devices and experiments, on the other provide a powerful m eans of understanding unitary evolution, nonunitary evolution and deco herence of two-state quantum systems by virtue of a mathematical isomo rphism of the two systems. These also help understand aspects of evolu tion of classical systems under the group of rotations in three-dimens ional space, namely the SO(3) group, by virtue of its homomorphism wit h the group SU(2) governing unitary evolution of polarized light waves . In this review we present a survey and analysis of recent work on to pological phases with polarization of light which has revealed several counterintuitive features of such phase shifts such as 2n pi anholono mies, nonlinear and discontinuous behaviour originating in singulariti es, peculiar spectral dependence, etc. We point out several areas wher e these results may find practical application, for example endless ph ase correction in interferometric sensors, fast switching spatial ligh t modulators, phase shifters with unusual chromatic properties, phasin g of antenna arrays, etc. Several useful theoretical insights relevant to polarization optics, quantum mechanics, classical mechanics and ot her areas of physics, obtained from the work on polarization states ar e described and some directions for future work are indicated.