On the transformations generated by the electromagnetic spin and orbital angular momentum operators

TL;DR

This paper investigates the properties and transformations generated by electromagnetic spin and orbital angular momentum operators, revealing their roles in translations, rotations, and light-matter interactions, with implications for symmetry and mode structures.

Contribution

It provides a detailed analysis of the electromagnetic spin and orbital angular momentum operators, linking them to symmetry transformations and mode structures in light-matter interactions.

Findings

Spin operators generate helicity-dependent translations.

Orbital angular momentum operators generate combined translations and rotations.

Eigenstates of spin operators relate to standing modes in chiral molecule interactions.

Abstract

We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and frequency and that the "orbital angular momentum" operators generate transformations which are a sequence of this kind of translations and rotations. We give some examples of the use of these operators in light matter interaction problems. Their relationship with the helicity operator allows to involve the electromagnetic duality symmetry in the analysis. We also find that simultaneous eigenstates of the three "spin" operators and parity define a type of standing modes which has been recently singled out for the interaction of light with chiral molecules. With respect to the relationship between "spin angular momentum", polarization, and total angular momentum, we show that, except for the case of a single plane wave, the total angular momentum of the field is decoupled from its vectorial degrees of freedom even in the regime where the paraxial approximation holds. Finally, we point out a relationship between the three "spin" operators and the spatial part of the Pauli-Lubanski four vector.