Spin and orbital angular momentum of a class of nonparaxial light beams havinga globally defined polarization

摘要

It is shown that the momentum density of free electromagnetic field splits into two parts. One has nocontribution to the net momentum due to the transversality condition. The other yields all the momentum. Theangular momentum that originates from the former part is spin. and the angular momentum that originates fromthe latter part is orbital angular momentum. Expressions for the spin and orbital angular momentum are givenin terms of the electric vector in reciprocal space. The spin and orbital angular momentum defined this way areused to investigate the angular momentum of nonparaxial beams that are described in a recently publishedpaper [Phys. Rev. A 78. 063831 (2008)]. It is found that the orbital angular momentum depends, apart from an/-dependent term, on two global quantities, the polarization represented by a generalized Jones vector andanother characteristic represented by a unit vector I. though the spin depends only on the polarization. Thepolarization dependence of orbital angular momentum through the effect of I is obtained and discussed. Someapplications of the result obtained here are also made. The fact that the spin originates from the part ofmomentum density that has no contribution to the net momentum is used to show that there does not exist theparadox on the spin of circularly polarized plane wave. The polarization dependence of both spin and orbitalangular momentum is shown to be the origin of conversion from the spin of a paraxial Laguerre-Gaussianbeam into the orbital angular momentum of the focused beam through a high numerical aperture.