Analysis of the Pancharatnam-Berry phase of vector vortex states using the Hamiltonian based on the Maxwell-Schr\"odinger equation

TL;DR

This paper derives and experimentally measures the Pancharatnam-Berry phase of vector vortex states using a Hamiltonian from the Maxwell-Schrödinger equation, revealing new insights into optical spin-orbital angular momentum conversion.

Contribution

It introduces a Hamiltonian-based approach to analyze the PB phase of VVSs and experimentally demonstrates the first observation of homogeneous PB phase.

Findings

Homogeneous PB phase observed for the first time.

Inhomogeneous PB phase linked to gauge dependence of hybrid-order Poincaré sphere.

Provides new understanding of optical spin-orbital angular momentum conversion.

Abstract

We derived the Berry connection of vector vortex states (VVSs) from the "true" Hamiltonian obtained through the Maxwell--Schr\"odinger equation for an inhomogeneous anisotropic (IA) medium, and we experimentally demonstrated measurement of the corresponding Pancharatnam--Berry (PB) geometrical phase of VVSs. The PB phase (PBP) of VVSs can be divided into two phases: homogeneous and inhomogeneous PBPs. Homogeneous and inhomogeneous PBPs are related to the conventional PBP and the spatially-dependent geometric phase given by an IA medium such as a polarization converter, respectively. We theoretically detected that inhomogeneous PBP accumulation originates from the gauge dependence of the index of the hybrid-order Poincar\'e sphere, which provides an alternate method for understanding optical spin--orbital angular momentum conversion. The homogeneous PBP, which is explicitly observed for the first time, has implications for quantum state manipulation and information processing.