Geometric quantification of photonic 4D spin-orbit states

TL;DR

This paper introduces a geometric method to quantify high-dimensional 4D photonic spin-orbit states using interferometry and Stokes parameters, enabling complete state reconstruction and advancing optical metrology and quantum communication.

Contribution

The authors develop a novel geometric approach to quantify arbitrary 4D spin-orbit states in photonics, using three ellipses and nine Stokes parameters, verified through experiments with fibers and wave plates.

Findings

Successfully quantified 4D spin-orbit states with interferometry.

Reconstructed higher-order modal group evolution in fibers.

Demonstrated potential for advanced optical metrology and quantum communication.

Abstract

High-dimensional photonic states have significantly advanced the fundamentals and applications of light. However, it remains huge challenges to quantify arbitrary states in high-dimensional Hilbert spaces with spin and orbital angular momentum bases. Here we introduce a geometric method to quantify arbitrary states in a 4D Hilbert space by interferometrically mapping them to unified centroid ellipses. Specifically, nine Stokes parameters can be deduced from three ellipses to quantify the 4D spin-orbit states described by SU(4) Poincar\'e hypersphere. We verify its feasibility by detecting these spin-orbit states gotten by both free-space wave plates and few-mode fibers. For the first time, we completely quantify and reconstruct higher-order modal group evolution of a weakly guiding few-mode fiber under twist perturbation. This geometric quantification, beyond the classical Stokes polarimetry, may pave the way to multi-dimensional optical metrology, sensing, and high-dimensional classical or quantum communications.