Abstract

The geometric phase of optical beams possessing orbital angular momentum was first predicted by Van Enk [1]. It arises from cyclic transformations in the mode of a high-order Gaussiam beam. In this study we concentrate on the phases in the spaces of first and second order modes. These modes are expressed in terms of Hermite-Gauss and Laguerre-Gauss functions HG_nm and LG_nm, respectively, where the order of the mode is given by N=n+m [2,3]. Modes LG_nm posses orbital angular momentum of lh/2π per photon, where l=n-m. If a cyclic sequence of transformations T=Π T_i, where T_i is represented by a (N+1)x(N+1) matrix in a spinor basis [4], then Tψ=exp(iφ)ψ, with ψ being the initial mode and φ the geometric phase. If the optical path length does not change, throughout this transformation we can ignore any dynamical phase.

© 2003 Optical Society of America