  A simple non-interferometric approach for probing the geometric phase of a
structured Gaussian beam is proposed. Both the Gouy and Pancharatnam-Berry
phases can be determined from the intensity distribution following a mode
transformation if a part of the beam is covered at the initial plane. Moreover,
the trajectories described by the centroid of the resulting intensity
distributions following these transformations resemble those of ray optics,
revealing an optical analogue of Ehrenfest's theorem associated with changes in
geometric phase.
