Perturbative Waveguide Toolkit

A lightweight Python toolkit for perturbative effective-index calculations in integrated photonic waveguides.

This repository implements perturbative modal analysis methods inspired by the treatment presented in:

Coldren, Corzine, and Mašanović,
Diode Lasers and Photonic Integrated Circuits,
2nd Edition, Wiley.

The current implementation focuses on approximate effective-index calculations for silicon nitride (Si₃N₄) waveguides on silicon dioxide (SiO₂) substrates, including asymmetric slab-waveguide analysis, TE/TM modal fields, and perturbative corrections.

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Features

• Effective-index calculations for slab waveguides
• Asymmetric TE/TM mode analysis
• Modal field calculations
• Perturbative effective-index corrections
• Validation examples against Lumerical MODE simulations
• Lightweight and easily extensible Python implementation

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Repository Structure

perturbative-waveguide-toolkit/
│
├── src/
│   └── perturbative_waveguides/
│ 
|── docs/
│   └── images/
|       └── lumerical_comparison.png
|
├── examples/
│
├── tests/
│
├── docs/
│
├── pyproject.toml
├── README.md
└── LICENSE

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Installation

Clone the repository and install it in editable mode:

git clone https://github.com/fdominguezserna/perturbative-waveguide-toolkit.git

cd perturbative-waveguide-toolkit

pip install -e .

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Example Usage

from perturbative_waveguides import neffPerturb

neff = neffPerturb(...)
print(neff)

Additional examples are available in:

examples/

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Minimal example

from perturbative_waveguides import effective_index_perturbative

result = effective_index_perturbative(
    n1=1.44,
    n2=2.00,
    n3=1.00,
    lambda0=1.55,
    width=0.8,
    height=0.7,
    mode="TE",
    l=1,
    m=1,
    nps=3500,
)

print(result.neff_mode)
print(result.neffs)

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Validation Example

The repository includes comparison examples between perturbative calculations and full-vectorial simulations performed with Ansys Lumerical MODE Solutions.

Example comparison between:

• perturbative effective-index calculations, and
• Lumerical MODE simulations

for a Si₃N₄/SiO₂ waveguide geometry.

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Validation Disclaimer

The validation examples use identical material-dispersion models for both the perturbative calculations and the corresponding Lumerical MODE simulations. Additional implementation details are documented directly in the example scripts.

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References

L. A. Coldren, S. W. Corzine, and M. Mašanović,
Diode Lasers and Photonic Integrated Circuits,
2nd Edition, Wiley.

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Citation

If you use this repository in academic work, please cite the corresponding Zenodo release.

Example:

Domínguez-Serna, Francisco A.,
Aguayo-Alvarado, Ana,
Barboza Tello, Norma,
De La Cruz Hernández, Wencel,
and Garay Palmett, Karina

Perturbative Waveguide Toolkit (v0.1.1).
Zenodo (2026).

https://doi.org/10.5281/zenodo.20360060

DOI: https://doi.org/10.5281/zenodo.20360060

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Acknowledgements

This work was partially supported by Secretaría de Ciencia, Humanidades, Tecnología e Innovación (SECIHTI). Ciencia de Frontera CF-2023-G-687, IIXM (709/2018); MADTEC-2025-M-193; A. L. Aguayo-Alavarado thanks SECIHTI for the postdoctoral scholarship.

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License

This project is released under the MIT License.