Geometric phase in phasing of antenna arrays

The response of a pair of differently polarized antennas is determined by their polarization states AND a phase between them which has a geometric part which becomes discontinuous at singular points in the parameter space. Such phase singularities have been observed in optical polarization experiments [R.Bhandari, Physics Reports 281 (1997) 1]. It is pointed out that such a phase is implicit in an equation for the response derived in the sixties [Morris et al Ap.J. 139 (1964) 551]. When a source emitting partially polarized radiation is observed with a correlation interferometer consisting of two antennas with different polarizations, curiously, fringes can be made to vanish for an appropriate choice of the polarization states, in general non orthogonal [V Radhakrishnan, Current Science 67 (1994) 257]. The result follows by considering the interference as a superposition of two patterns due to the two orthogonal polarization components of the radiation, which have a phase difference of magnitude \pi, a geometric phase.