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Updated: May 26, 2026
07:56
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Polarization ellipse and Stokes parameters in geometric algebra
Adler G Santos1, Quirino M Sugon, Daniel J McNamara
1Manila Observatory, Ateneo de Manila University Campus, Loyola Heights, Quezon City, Philippines. adler.g.santos@gmail.com
Summary
This study introduces geometric algebra for describing polarized light, converting complex scalars to vectors to analyze electric and magnetic fields. It establishes new geometric relations for light polarization, linking to the Poincaré sphere equation.
Area of Science:
- Optics and Photonics
- Electromagnetism
- Geometric Algebra
Background:
- The polarization ellipse and Stokes parameters are fundamental in optics.
- Describing polarized light often involves complex mathematical frameworks.
Purpose of the Study:
- To utilize geometric algebra for a novel description of the polarization ellipse and Stokes parameters.
- To explore the relationship between Maxwell's equations and geometric algebra representations of light.
Main Methods:
- Applying geometric algebra to represent polarization states.
- Converting complex scalar quantities to complex vectors.
- Deriving representations in Cartesian and rotated ellipse forms.
- Calculating conversion relations between parameters and Stokes parameters.
Main Results:
- A new method for describing polarized light using geometric algebra.
- Separation of electric and magnetic field vectors through vector conversion.
- Established conversion relations for different polarization representations.
- Proposed geometric relations analogous to the Poincaré sphere equation.
Conclusions:
- Geometric algebra offers a powerful framework for analyzing polarized light.
- The proposed methods provide new insights into the geometric properties of light polarization.
- This work connects fundamental electromagnetism with advanced geometric concepts.
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