# Classical Emergence of Intrinsic Spin-Orbit Interaction of Light at the Nanoscale

## TL;DR

This paper provides a theoretical analysis of the classical emergence of spin-orbit interaction of light at the nanoscale, revealing the conditions under which it appears and offering insights for experimental enhancement.

## Contribution

It introduces a full-vector theoretical framework that explains the emergence of intrinsic spin-orbit interaction of light at the nanoscale, especially distinguishing near-field and far-field behaviors.

## Key findings

- Spin-orbit factorizability holds only in the far-field.
- Near-field introduces additional phase hindering factorization.
- Framework captures key features of classical SOI emergence.

## Abstract

Traditionally, in macroscopic geometrical optics intrinsic polarization and spatial degrees of freedom of light can be treated independently. However, at the subwavelength scale these properties appear to be coupled together, giving rise to the spin-orbit interaction (SOI) of light. In this work we address theoretically the classical emergence of the optical SOI at the nanoscale. By means of a full-vector analysis involving spherical vector waves we show that the spin-orbit factorizability condition, accounting the mutual influence between the amplitude (spin) and phase (orbit), is fulfilled only in the far-field limit. On the other side, in the near-field region, an additional relative phase introduces an extra term that hinders the factorization and reveals an intricate dynamical behavior according to the SOI regime. As a result, we find a suitable theoretical framework able to capture analytically the main features of intrinsic SOI of light. Besides allowing for a better understanding into the mechanism leading to its classical emergence at the nanoscale, our approach may be useful in order to design experimental setups that enhance the response of SOI-based effects.