Pancharatnam-Berry phase in electromagnetic double-pinhole interference

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.