Quantum numbers and spectra of structured light

TL;DR

This paper demonstrates that describing structured light in terms of photon quantum numbers, especially helicity, reveals fundamental properties and links the topology of knotted electromagnetic waves to angular momentum eigenvalues.

Contribution

It introduces a quantum number-based framework for analyzing structured light, connecting knot topology with angular momentum eigenvalues in photon wave functions.

Findings

Helicity quantum number is fundamental in structured light.

Knotted electromagnetic waves' topology is determined by angular momentum eigenvalues.

Photon quantum numbers elucidate properties of twisted and knotted light beams.

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.