Section 2. SPIN AND ORBITAL ANGULAR MOMENTUM
The modern study of optical angular momentum can be said to have started with the paper of Allen et al. (2.1, Paper 2.1). This work showed that any beam with the amplitude distribution uðr; ; zÞ ¼ u0ðr; zÞ exp il, carried angular momentum about the beam axis. Moreover, this angular momentum could be separated into orbital and spin components. The orbital contribution is determined solely by the azimuthal phase dependence and is equivalent to lh per photon. The spin angular momentum is determined by the polarisation and has the value zh per photon, where 1 z 1, with the extremal values corresponding to pure circular polarisation. A physically realisable example of light with this phase distribution is a Laguerre-Gaussian beam, familiar from paraxial optics (2.2).