Geometric Phases in Optics: Polarization of Light Propagating in Helical Optical Fibers

TL;DR

This paper explores how the geometric phase in optics, related to light polarization, is affected by the geometry of helical optical fibers, providing analytical formulas and analyzing the influence of fiber parameters on the phase.

Contribution

It derives analytic expressions for polarization and geometric phase in helical fibers, linking phase behavior to fiber geometry and material properties, including stress effects.

Findings

Derived formulas for polarization and GPIO as functions of fiber parameters

Established relationship between GPIO and solid angle on Poincaré sphere

Analyzed effects of fiber geometry fluctuations on GPIO

Abstract

The geometric phase in optics (GPIO) is directly associated with the polarization of light. We investigate the physical principles underlying the occurrence of the GPIO for a single-mode light beam propagating in a single-mode optical fiber wound into a circular helix configuration, with and without stress-induced birefringence. The effects of the curvature and torsion of the helical fiber on the rotation of the polarization vector and the associated GPIO are discussed. Analytic expressions are derived for the polarization vector and Stokes parameters for any initial polarization state of the light entering the helical fiber, as well as for the GPIO of the light as a function of helix arc-length. Additionally, the intensity of a superposition of the initial and final beams, which depends on the final GPIO, is derived. Furthermore, the relationship between the GPIO and the solid angle subtended by the tangent vector of the helix plotted on the Poincar\'{e} sphere is analyzed, and the effects of fluctuations of the parameters specifying the geometry and the material characteristics of the helical fiber on the GPIO are considered.