A new optical geometric phase

Has been directly measured. Geometric phase arises when a system is carried around a closed path in some parameter or state space. For example, parallel-transporting a vector around a loop on the surface of a sphere will change the vector’s orientation when it returns to its starting point. Physicists at Colgate University used a laser beam and “mode space,” with modes characterized by the surfaces of constant phase within the beam. They sent a Gaussian beam of laser light in a zero-order mode—with planar phase surfaces—through a special diffraction grating. The beam then contained high-order “doughnut” modes with helical phase surfaces that carry orbital angular momentum. The researchers combined a zero-order and a higher-order mode from the same beam and sent them together along the same path to avoid any dynamical phase changes that would swamp the desired signal. They used cylindrical lenses to alter the doughnut mode and trace out a closed path in mode space, and monitored the interference with the unaltered zero-order mode. The group’s result agreed well with theory and supports the conjecture that the geometric phase arises from the exchange of angular momentum between the light and the optical system. (E. J. Galvez et al., Phys. Rev. Lett. 90 , 203901, 2003 http://dx.doi.org/10.1103/PhysRevLett.90.203901 .)