Geometric phase, transformations of gaussian light beams and angular momentum transfer

When a beam of light undergoes a cycle of transformations, then both the electric field component and the quantum state acquire, in addition to a dynamical phase, a geometric phase. The latter depends only on geometric properties such as the enclosed area [ 1 ], or the distance and length [2 ] of the curve that represents the sequence of transformations in an appropriate parameter space. So far three manifestations of the geometric phase in optics have been reported on. Historically the first example is Pancharatnam's phase [ 3 ]. This phase originates from cyclic changes of the polarization vector of a plane wave propagating in a fixed direction. Its existence has been experimentally demonstrated both for macroscopic light beams [4] and for a single photon [5 ]. The second manifestation arises when the direction of the wave vector of a plane wave is slowly rotated around a closed circuit [6]. In this case the polarization of the beam does not change. Also the mutual influence of these two phases has been investigated [7]. The third example that has been proposed concerns a geometric phase due to cyclic changes in squeezed states of light [8 ]. These changes represent a cycle of Lorentz transformations, whereas in the former two examples the transformations are rotations. Here we propose a fourth optical manifestation of