Geometric phase evolution

TL;DR

This paper proposes a generalized definition of geometric phase for polarized waves, allowing continuous phase tracking along any path, which offers deeper insights into wave behavior and clarifies the use of geodesic paths in the Poincare sphere.

Contribution

It introduces a wave model-based approach to define geometric phase more broadly, moving beyond traditional closed-cycle and differential geometry methods.

Findings

Provides a continuous geometric phase evolution framework.

Offers new insights into wave behavior in optical systems.

Explains the use of geodesic paths in the Poincare sphere.

Abstract

Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is better to define geometric phase more generally, allowing every polarized wave to have a well-defined value at any point in its path. Using several example systems, we show how this approach provides more insight into the wave's behavior. Moreover, by tracking the continuous evolution of geometric phase as a wave propagates through an optical system, we encounter a natural explanation of why the conventional Poincare sphere solid angle method uses geodesic paths rather than physical paths of the polarization state.