On Geometric Phase from Pure Projections

Abstract

The geometric phase is usually treated as a quantity modulo 2π, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present author (reviewed in R.Bhandari, Phys. Rep. 281 (1997) p.1) question the usefulness of such a definition of the geometric phase in that it throws away useful and measurable information about the system, for example strengths of singularities giving rise to the geometric phase. Such singularities have been directly demonstrated by phase-shift measurement in interference experiments. In this paper, two recent polarization experiments (Hariharan et.al., J.Mod.Opt. 44 (1997)p.707 and Berry and Klein, J.Mod.Opt. 43 (1996)p.165) are analysed and compared with previous experiments and potentially detectible singularities in these experiments pointed out.