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

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.

References in corpus (7)

• Dual electromagnetism: Helicity, spin, momentum, and angular momentum
• Angular Momenta and Spin-Orbit Interaction of Nonparaxial Light in Free Space
• Characterizing optical chirality
• Electromagnetic duality symmetry and helicity conservation for the macroscopic Maxwell's equations (previously "Experimental demonstration of electromagnetic duality symmetry breaking")
• Helicity and Angular Momentum. A Symmetry based framework for the study of Light-Matter Interactions
• Duality constrained meta atoms for transformation optics
• Dual and anti-dual modes in dielectric spheres

Cited by in corpus (9)

• Transverse and longitudinal angular momenta of light
• Relativistic Spin-Orbit Interactions of Photons and Electrons
• Unified theory to describe and engineer conservation laws in light-matter interactions
• Far-field measurements of vortex beams interacting with nanoholes
• Helicity is a topological invariant of massless particles: C=-2h
• Achiral nanostructures: perturbative harmonic generation and dichroism under vortex and vector beams illumination
• Lorentz-boosted evanescent waves
• Unified treatment of the total angular momentum of single photons via generalized quantum observables
• Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons