The Anatomy of Geometric Phase for an Optical Vortex Transiting a Lens

TL;DR

This paper introduces an analytical method to quantify the fractional geometric phase accumulated by an optical vortex passing through a cylindrical lens, accounting for beam waist and position changes.

Contribution

It provides a novel analytical framework for tracking geometric phase accumulation in optical vortices during lens transit, including multiple lens configurations.

Findings

Quantifies geometric phase as a function of initial state and lens position

Applicable to multiple lenses and complex optical setups

Enhances understanding of phase evolution in optical vortex systems

Abstract

We present an analytical means of quantifying the fractional accumulation of geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a Sphere of Modes is endowed with a Supplementary Product Space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of geometric phase across a single lens as a function of initial state and lens position within the beam. It can be readily applied to a series of lenses as well.