Classical and quantum properties of cylindrically polarized states of light

TL;DR

This paper provides a comprehensive theoretical analysis of cylindrically polarized light beams, detailing their configurations, angular momentum, and a novel hybrid description using two Poincaré spheres, with implications for quantum optics.

Contribution

It introduces a hybrid spatio-polarization framework with dual Poincaré spheres for cylindrically polarized modes, advancing understanding of their structure and transformations.

Findings

All possible CPM configurations identified

Total angular momentum calculated for these modes

Hybrid Poincaré sphere representation developed

Abstract

We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electro-magnetic field, calculate their total angular momentum and highlight the subtleties of their structure. Furthermore, a hybrid spatio-polarization description for such modes is introduced and developed. In particular, two independent Poincar\'e spheres have been introduced to represent simultaneously the polarization and spatial degree of freedom of CPMs. Possible mode-to-mode transformations accomplishable with the help of conventional polarization and spatial phase retarders are shown within this representation. Moreover, the importance of these CPMs in the quantum optics domain due to their classical features is highlighted.