This package provides a comprehensive suite of tools to study the reflective properties of hyperbolic materials and anisotropic structures using the 4×4 transfer matrix method. It enables easy configuration of multilayer systems, calculation of reflection coefficients, and analysis using Mueller matrices.

• Features
• Installation
• Quick Start
• Usage Examples
• Advanced Features
• Contributing
• Citation
• Known Issues / Limitations
• Papers & Further Reading
• License
• Getting Help

• Simulation of Reflective Properties: Analyze how hyperbolic materials and anisotropic structures reflect light
• Multilayer Configuration: Configure multilayer systems with customizable materials and layer properties
• 4×4 Transfer Matrix Method: Compute reflection coefficients accurately for anisotropic media
• Mueller Matrix Analysis: Convert reflection coefficients into Mueller matrices and simulate optical component interactions
• Built-in Materials Library: Pre-configured materials including Quartz, Calcite, Sapphire, Gallium Oxide
• Arbitrary Material Support: Define custom materials with arbitrary permittivity tensor
• Multiple Scenario Types: Support for incident angle sweeps, azimuthal rotations, dispersion analysis, and single-point calculations
• Visualization: Publication-quality plotting functionality for results analysis
• Extensible Architecture: Modular design for easy extension with new materials and optical components

The package is now available on PyPI and can be installed using pip or uv:

pip install hyperbolic-optics

uv add hyperbolic-optics

For development or to get the latest features:

git clone https://github.com/MarkCunningham0410/hyperbolic_optics.git
cd hyperbolic_optics
pip install -e .

Here's a simple example to get you started:

import json
from hyperbolic_optics.structure import Structure
from hyperbolic_optics.mueller import Mueller

# Define a simple multilayer structure
payload = {
    "ScenarioData": {
        "type": "Simple",
        "incidentAngle": 45.0,  # degrees
        "azimuthal_angle": 0.0,  # degrees
        "frequency": 1460.0      # cm^-1
    },
    "Layers": [
        {
            "type": "Ambient Incident Layer",
            "permittivity": 50.0
        },
        {
            "type": "Semi Infinite Anisotropic Layer",
            "material": "Calcite",
            "rotationX": 0,
            "rotationY": 90,
            "rotationZ": 0
        }
    ]
}

# Create and execute the simulation
structure = Structure()
structure.execute(payload)

# Calculate reflectivities
R_pp = abs(structure.r_pp)**2
R_ss = abs(structure.r_ss)**2
print(f"p-polarized reflectivity: {R_pp}")
print(f"s-polarized reflectivity: {R_ss}")

# Perform Mueller matrix analysis
mueller = Mueller(structure)
mueller.set_incident_polarization('linear', angle=45)
mueller.add_optical_component('anisotropic_sample')

# Get Stokes parameters and polarization properties
all_params = mueller.get_all_parameters()
print(f"Reflectance (S0): {all_params['S0']}")
print(f"Degree of polarization: {all_params['DOP']}")

The examples/ folder contains simple scripts demonstrating various capabilities.

Run any example with:

python examples/basic_calcite_example.py

Define materials with arbitrary permittivity and permeability tensors:

custom_material = {
    "eps_xx": {"real": 2.27, "imag": 0.001},
    "eps_yy": {"real": -4.84, "imag": 0.755}, 
    "eps_zz": {"real": -4.84, "imag": 0.755},
    "eps_xy": {"real": 0.0, "imag": 0.0},
    "eps_xz": {"real": 0.0, "imag": 0.0},
    "eps_yz": {"real": 0.0, "imag": 0.0},
}

• Incident: Frequency vs incident angle analysis
• Azimuthal: Frequency vs azimuthal rotation analysis
• Dispersion: k-space dispersion at fixed frequency
• Simple: Single-point calculation for specific conditions

from hyperbolic_optics.plots import plot_mueller_dispersion, plot_kx_frequency

# Generate publication-quality plots
plot_kx_frequency(structure, reflectivity, save_name="my_plot")

We welcome contributions! Please see our contributing guidelines for details on:

• Reporting bugs and requesting features
• Setting up a development environment
• Code style and testing requirements
• Submitting pull requests

If you use this package in your research, please cite:

@software{cunningham2025hyperbolic,
  title={Hyperbolic Optics Simulation Package},
  author={Mark Cunningham},
  year={2025},
  version={0.2.3},
  doi={10.5281/zenodo.14946556},
  url={https://pypi.org/project/hyperbolic-optics/},
  howpublished={PyPI},
  note={Python package for 4×4 transfer matrix method simulations}
}

This package was used to generate results in:

M. Cunningham et al., "Optical footprint of ghost and leaky hyperbolic polaritons," Photonics Research, vol. 13, no. 8, pp. 2291-2305 (2025). DOI: 10.1364/PRJ.558334

• Transmission Coefficients: Currently, transmission coefficients are not fully supported
• Multiple Optical Components: While you can place multiple Mueller matrix components in series, matching incident angles between them isn't yet implemented

This package includes a comprehensive test suite with 93+ tests covering all major functionality. Run tests locally with:

pytest
pytest --cov=hyperbolic_optics --cov-report=html  # With coverage report

*Please open an [issue](https://github.com/MarkCunningham0410/hyperbolic_optics/issues) if you encounter any bugs or have suggestions for improvements.*

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## Papers & Further Reading

For background on the physics and mathematical methods, see:

**Key References:**
- N. C. Passler and A. Paarmann, "Generalized 4 × 4 matrix formalism for light propagation in anisotropic stratified media," *J. Opt. Soc. Am. B* **34**, 2128-2139 (2017)
- P. Yeh, "Electromagnetic propagation in birefringent layered media," *J. Opt. Soc. Am.* **69**, 742-756 (1979)
- N. C. Passler et al., "Layer-resolved resonance intensity of evanescent polariton modes in anisotropic multilayers," *Phys. Rev. B* **107**, 235426 (2023)
- M. Cunningham et al., "Optical footprint of ghost and leaky hyperbolic polaritons," *Photonics Research* **13**, 2291-2305 (2025)

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## License

This project is licensed under the MIT License – see the [LICENSE](LICENSE) file for details.

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## Getting Help

- **Documentation:** Check the [examples/](examples/) folder and docstrings
- **Issues:** Report bugs or request features via [GitHub Issues](https://github.com/MarkCunningham0410/hyperbolic_optics/issues)
- **Discussions:** Start a discussion for usage questions or feature ideas

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**Thank you for your interest in the Hyperbolic Optics Simulation Package!** 

*Happy simulating! 🔬✨*