Spin angular momentum of light

The spin angular momentum of light (SAM) is the component of angular momentum of light that is associated with the quantum spin and the rotation between the polarization degrees of freedom of the photon. Spin is the fundamental property that distinguishes the two types of elementary particles: fermions with half-integer spins and bosons with integer spins. Photons, which are the quanta of light, have been long recognized as spin-1 gauge bosons. The polarization of the light is commonly accepted as its “intrinsic” spin degree of freedom. However, in free space, only two transverse polarizations are allowed. Thus, the photon spin is always only connected to the two circular polarizations. To construct the full quantum spin operator of light, longitudinal polarized photon modes have to be introduced. An electromagnetic wave is said to have circular polarization when its electric and magnetic fields rotate continuously around the beam axis during propagation. The circular polarization is left () or right () depending on the field rotation direction and, according to the convention used: either from the point of view of the source, or the receiver. Both conventions are used in science depending on the context. When a light beam is circularly polarized, each of its photons carries a spin angular momentum (SAM) of , where is the reduced Planck constant and the sign is positive for left and negative for right circular polarizations (this is adopting the convention from the point of view of the receiver most commonly used in optics). This SAM is directed along the beam axis (parallel if positive, antiparallel if negative). The above figure shows the instantaneous structure of the electric field of left () and right () circularly polarized light in space. The green arrows indicate the propagation direction. The mathematical expressions reported under the figures give the three electric-field components of a circularly polarized plane wave propagating in the direction, in complex notation.