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

Abstract

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

Light Spins of Cylindrical Electromagnetic Waves and their Jumps across Material Interfaces in the Presence of Energy Exchange

“…Therefore, the specific transverse light spin z σ (to be henceforth shortened as "specific spin") in the axial z -direction is defined with respect to energy density of electromagnetic waves [3,12]. …”

“…This jump is related to spin-orbital interactions (SOIs) [3,9,12]. See in particular equation (3) of Ref.…”

“…They are Poynting vector, angular momentum, and chirality (or helicity) for instance [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Polarizations and polarization ellipses are in between scalars and vectors, depending on their definitions [3,10,14]. The angular momentum (AM) of EM waves can be separated into its orbital and spin parts [12, 15,16].…”

“…The orbital AM is extrinsic, since it depends on the distance vector between a coordinate center and the point of application. In contrast, the spin AM is intrinsic, since it is not required to specify such a distance vector [3].…”

“…Traditionally, light spin has been suitably normalized by taking the energy density as a reference [3,10]. This light spin per energy density will be henceforth called the "specific spin" for short [9,17].…”