# Near-Field Directionality Beyond the Dipole Approximation: Electric Quadrupole and Higher-Order Multipole Angular Spectra

## TL;DR

This paper extends the understanding of near-field directionality beyond dipole sources by analytically addressing higher-order multipoles, especially electric quadrupoles, which could enhance nanoscale light-matter interaction engineering.

## Contribution

It provides a general analytical framework for analyzing near-field directionality of any multipole source, focusing on electric quadrupoles, advancing current spin-dependent directionality models.

## Key findings

- Analytical treatment for multipole near-field directionality.
- Extension of spin-dependent directionality to higher-order multipoles.
- Potential applications in nanoscale light-matter coupling.

## Abstract

Within the context of spin-related optical phenomena, the near-field directionality is generally understood from the quantum spin Hall effect of light, according to which the transverse spin of surface or guided modes is locked to the propagation direction. So far, most previous works have been focused on the spin properties of circularly polarized dipolar sources. However, in near-field optics, higher-order multipole sources (e.g., quadrupole, octupole, and so on) might become relevant, so a more in-depth formulation would be highly valuable. Building on the angular spectrum representation, we provide a general, analytical, and ready-to-use treatment in order to address the near-field directionality of any multipole field, particularizing to the electric quadrupole case. Besides underpinning and upgrading the current framework on spin-dependent directionality, our results may open up new perspectives for engineering light-matter coupling at the nanoscale.