Hybrid-order Poincar\'e sphere

TL;DR

This paper introduces a hybrid-order Poincaré sphere to effectively describe polarization evolution in complex anisotropic media, extending existing models and linking Berry curvature and phase to angular momentum.

Contribution

It develops a generalized hybrid-order Poincaré sphere that unifies and extends previous models for polarization states in inhomogeneous anisotropic media.

Findings

Polarization evolution can be represented along the longitude of the sphere.

Berry curvature acts as an effective magnetic field with a monopole at the center.

Berry phase is proportional to the total angular momentum.

Abstract

In this work, we develop a hybrid-order Poincar\'{e} sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincar\'{e} sphere and high-order Poincar\'{e} sphere to a more general form. Polarization evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by state evolution along the longitude line on the hybrid-order Poincar\'{e} sphere. Similar to that in previously proposed Poincar\'{e} spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the origin of sphere and Berry connection can be interpreted as the vector potential. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincar\'{e} sphere are demonstrated to be proportional to the total angular momentum. Our scheme provides a convenient method to describe the spin-orbit interaction in inhomogeneous anisotropic media.