# Sectoral Multipole Focused Beams

## TL;DR

This paper characterizes sectoral multipole focused beams with well-defined angular momentum and helicity, revealing their unique properties and potential applications in light-matter interaction modeling.

## Contribution

It introduces the concept of sectoral multipole beams, providing exact Maxwell solutions and analyzing their angular momentum and energy flow characteristics.

## Key findings

- Sectoral multipole beams are the only propagating beams under hemispherical illumination.
- The sectoral dipole beam is equivalent to a time-reversed Huygens' source.
- Higher order multipolar beams are vortex beams with specific properties.

## Abstract

We discuss the properties of pure multipole beams with well-defined handedness or helicity, with the beam field a simultaneous eigenvector of the squared total angular momentum and its projection along the propagation axis. Under the condition of hemispherical illumination, we show that the only possible propagating multipole beams are `sectoral' multipoles. The sectoral dipole beam is shown to be equivalent to the non-singular time-reversed field of an electric and a magnetic point dipole Huygens' source located at the beam focus. Higher order multipolar beams are vortex beams vanishing on the propagation axis. The simple analytical expressions of the electric field of sectoral multipole beams, exact solutions of Maxwell's equations, and the peculiar behaviour of the Poynting vector and spin and orbital angular momenta in the focal volume could help to understand and model light-matter interactions under strongly focused beams.