Measurement of Berry Phase Associated with Higher Dimensional Orbital Angular Momentum of Light by Interference Method

Berry phase of higher-dimensional orbital angular momentum of light is studied. When an N^th order orbital state, described by a vector in (N+1)-dimensional space, evolves through a closed path in space of orbital states, there will exist a higher order orbital Berry phase. We calculate this phase by using the matrix transformation theory. A direct measurement of the higher-order orbital Berry phase is also carried out by the interference method. The experimental results are in good agreement with the theoretical description, which shows that the Berry phase is proportional to the orbital angular momentum of light.