Formulation of the twisted-light–matter interaction at the phase singularity: The twisted-light gauge

Abstract

Twisted light is light carrying orbital angular momentum. The profile of such a beam is a ringlike structure with a node at the beam axis, where a phase singularity exists. Due to the strong spatial inhomogeneity the mathematical description of twisted-light--matter interaction is nontrivial, in particular close to the phase singularity, where the commonly used dipole-moment approximation cannot be applied. In this paper we show that, if the handedness of circular polarization and the orbital angular momentum of the twisted-light beam have the same sign, a specific gauge---the twisted-light gauge---can be used where the Hamiltonian takes a form similar to the dipole-moment approximation. However, if the signs differ, no such gauge can be found. Here in general the magnetic parts of the light beam become of significant importance and an interaction Hamiltonian which only accounts for electric fields is inappropriate. We discuss the consequences of these findings for twisted-light excitation of a semiconductor nanostructure, e.g., a quantum dot, placed at the phase singularity.