---
abstract: 'We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.'
author:
- 'Konstantin Y. Bliokh'
- 'Miguel A. Alonso'
- 'Elena A. Ostrovskaya'
- Andrea Aiello
title: 'Angular Momenta and Spin-Orbit Interaction of Nonparaxial Light in Free Space'
---

Introduction
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The problem of the identification of the spin and orbital parts of the angular momentum (AM) of an electromagnetic wave has a long history and has posed fundamental difficulties in both quantum electrodynamics and classical optics [@AB; @EN; @BA; @B].

It is known that the photon AM operator in the momentum (plane-wave) representation has the form [@AB]: $$\label{eqn:1}
\mathbf{\hat J} =  - i\left( {\mathbf{k} \times \partial _\mathbf{k} } \right) + \mathbf{\hat S} \equiv \mathbf{\hat L} + \mathbf{\hat S}~.$$ Here the orbital part is $\mathbf{\hat L}=\mathbf{\hat r} \times \mathbf{\hat p}$ ($\mathbf{\hat 