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Published on: August 30, 2013
Geometric phase: two triangles on the Poincaré sphere
Piotr Kurzynowski1, Władysław A Woźniak, Małgorzata Szarycz
1Institute of Physics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
Summary
This study presents a novel method for separating the dynamic and geometric phase shifts in birefringent media using Poincaré sphere visualizations. The findings offer a clearer understanding of phase division in optical experiments.
Area of Science:
- Optics and Photonics
- Mathematical Physics
Background:
- Birefringent media introduce phase shifts in light, which can be decomposed into dynamic and geometric components.
- Understanding this phase division is crucial for various interferometric and polariscopic applications.
Purpose of the Study:
- To present a method for obtaining the dynamic and geometric parts of the phase shift introduced by a birefringent medium.
- To visualize these phase components using graphical constructions on the Poincaré sphere.
Main Methods:
- Utilized Jones formalism to derive mathematical formulas for phase calculations.
- Employed graphical constructions on the Poincaré sphere, adapted from Pancharatnam's geometric phase concept.
- Represented birefringent medium eigenvectors on the Poincaré sphere for intuitive visualization.
Main Results:
- Successfully visualized the division of the total phase shift into dynamical and geometrical parts.
- Demonstrated the applicability of the method in Mach-Zehnder interferometer and polariscopic setups.
- Provided theoretical predictions for experimental verification.
Conclusions:
- The presented graphical method offers an intuitive explanation for the phase division mechanism in birefringent media.
- The model is validated through descriptions of two experimental setups.
- Experimental verification is expected to confirm the theoretical predictions and the model's correctness.
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