Quantum numbers and spectra of structured light

Abstract

It is shown that the description of light beams in terms of the corresponding photon quantum numbers elucidates the properties of these beams. In particular, this description shows that the helicity quantum number plays the fundamental role. This mode of description is applied to twisted and knotted electromagnetic waves. We concentrate on the cases where photon wave functions are eigenfunctions of one component of angular momentum. We discovered that for knotted waves the eigenvalue of the angular momentum determines the topology of knots.