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Electric field control of Berry phase in an optical interferometer

J. H. Woo, E. Y. Choi, Jeong Weon Wu

Published Aug 1, 2009• 0 citations
Publisher

Abstract

We observed a Pancharatnam's phase of light using liquid crystal cell. Changes in the interference pattern are analyzed in terms of the geometric phase change. The electric field dependence of the interference pattern change exhibits the occurrence of geometric phase jump.
DOI
10.1109/cleopr.2009.5292498

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Young's two-beam interference and the Pancharatnam-Berry geometric phase constitute two landmark results in optical physics. Employing the spectral interference law of electromagnetic waves, we establish a general expression for the Pancharatnam-Berry phase in Young's two-pinhole setup. We show that the phase is elegantly specified by the electric field Stokes parameters at the openings. The geometric phase can also be deduced from the interference pattern using Pancharatnam's definition of the generalized phase, as we demonstrate both numerically and experimentally. Our results imply a way to control the phase differences in two-beam electromagnetic interference by adjusting the input-field intensities and polarization states.
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The geometric phase was first anticipated 1956 by Pancharatnam, in the context of polarised light. Much later, in 1984, Berry made an analogue discovery, but this time in the context of quantum mechanics. It turns our that the geometric phase, or Berry's phase, or the Pancharatnam phase, is a very general phenomenon. It is a phase shift that can be acquired by a system, when it has undergone a adiabatic process, bringing it back to its original initial conditions. If the parameter space of the involved Hamiltonian is curved, the final condition may involve a phase change. This effect has been demonstrated in a range of different interferometry experiments. Although the Pancharatnam phase has been seen, this has always been in studies involving the first order correlation, g(1), this is in the intereferogramm of two or more wave amplitudes. Here, we demonstrate experimental proofs of the effect of the Pancharatnam phase in intensity interferometry, or in other words, where the second order correlation factor g(2) is the relevant description of the interference.
In crystal optics the concept of the geometric phases can be demonstrated to the naked eye with comparatively simple apparatus. Pancharatnam's phase is described by an area on the Poincaré sphere which is enclosed by geodesic lines (great circles) while the concept of the Berry phase does not restrict the nature of the contour. With a simple experiment we demonstrate that Pancharatnam's phase is accompanied by a second phase which compensates the pure area effect for areas enclosed by small circles. This compensating phase changes sign at time reversal and, thus, exhibits the features of a geometric phase.