pypolar 1.1.0

Routines for analysis of polarization

pypolar

pypolar is a Python library for simulating, analyzing, and visualizing the polarization state of light as it propagates through optical systems. The package supports modeling with both Jones and Mueller calculus frameworks and includes functionality relevant to education, research, ellipsometry, and polarimetric system design.

The library provides computational tools, visualization utilities, and symbolic analysis support, making it suitable for laboratory instruction, computational optics coursework, and applied research in polarization optics.

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Modules

pypolar is organized into several computational and symbolic components:

Numerical computation modules

• pypolar.fresnel — Fresnel reflection and transmission calculations

• pypolar.jones — Analysis of polarization using Jones calculus

• pypolar.mueller — Polarization modeling using the Mueller calculus

• pypolar.ellipsometry — Ellipsometry modeling tools

Visualization support

• pypolar.visualization — Poincaré sphere and vector-based visualization routines

Symbolic computation

• pypolar.sym_fresnel — Symbolic Fresnel reflection and transmission expressions

• pypolar.sym_jones — Symbolic polarization modeling using Jones calculus

• pypolar.sym_mueller — Symbolic Mueller matrix manipulation

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Installation

pypolar may be installed via pip:

pip install pypolar

or using conda:

conda install -c conda-forge pypolar

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Documentation and Examples

Comprehensive user documentation, theory notes, and executable Jupyter examples are available at:

📄 https://pypolar.readthedocs.io

or use immediately in your browser via the JupyterLite button below

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Example Usage

The following example demonstrates modeling an optical isolator using the Jones formalism.

Jones Matrix Example

import numpy as np
import matplotlib.pyplot as plt
import pypolar.jones as jones
import pypolar.visualization as vis

J1 = jones.field_elliptical(np.pi/6, np.pi/6)
J2 = jones.op_linear_polarizer(0) @ J1
J3 = jones.op_quarter_wave_plate(np.pi/4) @ J2
J4 = jones.op_mirror() @ J3
J5 = jones.op_quarter_wave_plate(-np.pi/4) @ J4

fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111, projection='3d')
vis.draw_empty_sphere(ax)

vis.draw_jones_poincare(J1, ax, label='  start', color='red')
vis.draw_jones_poincare(J2, ax, label='  after polarizer', color='blue')
vis.draw_jones_poincare(J3, ax, label='  after QWP', color='blue')
vis.draw_jones_poincare(J4, ax, label='  after mirror', color='blue')
vis.draw_jones_poincare(J5, ax, label='  final', color='red')

plt.show()

Mueller Matrix Example

import numpy as np
import pypolar.mueller as mueller

A = mueller.stokes_right_circular()
B = mueller.op_linear_polarizer(np.pi/4)
C = mueller.op_quarter_wave_plate(0)
D = mueller.op_mirror()
E = mueller.op_quarter_wave_plate(0)
F = mueller.op_linear_polarizer(-np.pi/4)
F @ E @ D @ C @ B @ A

produces:

array([0., 0., 0., 0.])

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Citation

If you use pypolar in academic, instructional, or applied technical work, please cite:

Prahl, S. (2026). pypolar: A Python module for polarization using Jones and Mueller calculus (Version 1.0.2) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.8358111

BibTeX

@software{pypolar_prahl_2026,
  author    = {Scott Prahl},
  title     = {pypolar: A Python module for polarization using Jones and Mueller calculus},
  year      = {2026},
  version   = {1.0.2},
  doi       = {10.5281/zenodo.8358111},
  url       = {https://github.com/scottprahl/pypolar},
  publisher = {Zenodo}
}

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License

pypolar is distributed under the terms of the MIT License.