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Global aspects of polarization optics and coset space geometry

Arvind,S. Chaturvedi,N. Mukunda

Published 2017 in Physics Letters A

ABSTRACT

Abstract We use group theoretic ideas and coset space methods to deal with problems in polarization optics of a global nature. The well-known impossibility of a globally smooth phase convention for electric fields for all points on the Poincare sphere, and the equally well-known impossibility of real bases for transverse electric vectors for all propagation directions, are expressed in terms of coset spaces S U ( 2 ) / U ( 1 ) , S O ( 3 ) / S O ( 2 ) respectively. Combining these two negative results in a judicious manner, by making the singularities in coset representatives in the two cases cancel one another, the known possibility of a globally smooth complex basis for transverse electric vectors, and its essential uniqueness, are shown. We find that apart from the groups S U ( 2 ) and S O ( 3 ) which occur naturally in these problems, the group S U ( 3 ) also plays an important role.

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