Credits

The development of the TMMax library has been influenced and supported by a number of exceptional tools, libraries, and publications in the field of optical multilayer thin films. We would like to acknowledge these contributions and provide references for further exploration.

Third-Party Libraries

This repository occasionally utilizes approaches inspired by Steven Byrnes’ [tmm](https://github.com/sbyrnes321/tmm) library. We sincerely thank Dr. Byrnes for developing this comprehensive and widely used resource, which has provided valuable insights for simulating multilayer optical systems.

In addition, for alternative implementations of multilayer thin-film simulations, we recommend the following libraries:

These libraries provide excellent reference points and are particularly useful when GPU acceleration is available. We encourage users to explore them alongside TMMax to evaluate computational efficiency and performance under different conditions.

Key Publications

For calculating the optical properties of incoherent multilayer thin films, we follow the methodology introduced by:

  • _Charalambos C. Katsidis and Dimitrios I. Siapkas_, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Applied Optics, 41(19):3978, 2002. [doi:10.1364/AO.41.003978](https://doi.org/10.1364/AO.41.003978)

This paper provides a rigorous framework for handling coherent, partially coherent, and incoherent interference, forming a foundational reference for the calculations implemented in TMMax.

GPU Acceleration Considerations

Certain transfer matrix method (TMM) implementations leverage GPU acceleration to enhance computational efficiency. For example:

  • vtmm uses TensorFlow with GPU support.

  • tmm-fast uses PyTorch with multi-threading and GPU compatibility.

As a result, benchmark comparisons may vary significantly depending on hardware availability. Users with access to GPUs are encouraged to perform their own benchmarks to compare the performance of TMMax, vtmm, and tmm-fast in GPU-accelerated conditions. Detailed benchmark results and implementation notes are provided in the benchmark directory of this repository.

Citing TMMax

If you find the TMMax library useful in your work, we kindly ask that you consider citing it.

The current version is available as an arXiv preprint. A submission to the Journal of Open Source Software (JOSS) is currently under review, and we will update the reference once it is published.

Here is the recommended citation in BibTeX format:

@misc{danis2025tmmaxhighperformancemodelingmultilayer,
      title={TMMax: High-performance modeling of multilayer thin-film structures using transfer matrix method with JAX},
      author={Bahrem Serhat Danis and Esra Zayim},
      year={2025},
      eprint={2507.11341},
      archivePrefix={arXiv},
      primaryClass={physics.comp-ph},
      url={https://arxiv.org/abs/2507.11341},
}