paper.bib

@Article{Wilkinson2016,
  author={Wilkinson, Mark D.
  and Dumontier, Michel
  and Aalbersberg, IJsbrand Jan
  and Appleton, Gabrielle
  and Axton, Myles
  and Baak, Arie
  and Blomberg, Niklas
  and Boiten, Jan-Willem
  and da Silva Santos, Luiz Bonino
  and Bourne, Philip E.
  and Bouwman, Jildau
  and Brookes, Anthony J.
  and Clark, Tim
  and Crosas, Merc{\`e}
  and Dillo, Ingrid
  and Dumon, Olivier
  and Edmunds, Scott
  and Evelo, Chris T.
  and Finkers, Richard
  and Gonzalez-Beltran, Alejandra
  and Gray, Alasdair J.G.
  and Groth, Paul
  and Goble, Carole
  and Grethe, Jeffrey S.
  and Heringa, Jaap
  and 't Hoen, Peter A.C
  and Hooft, Rob
  and Kuhn, Tobias
  and Kok, Ruben
  and Kok, Joost
  and Lusher, Scott J.
  and Martone, Maryann E.
  and Mons, Albert
  and Packer, Abel L.
  and Persson, Bengt
  and Rocca-Serra, Philippe
  and Roos, Marco
  and van Schaik, Rene
  and Sansone, Susanna-Assunta
  and Schultes, Erik
  and Sengstag, Thierry
  and Slater, Ted
  and Strawn, George
  and Swertz, Morris A.
  and Thompson, Mark
  and van der Lei, Johan
  and van Mulligen, Erik
  and Velterop, Jan
  and Waagmeester, Andra
  and Wittenburg, Peter
  and Wolstencroft, Katherine
  and Zhao, Jun
  and Mons, Barend},
  title={The FAIR Guiding Principles for scientific data management and stewardship},
  journal={Scientific Data},
  year={2016},
  month={Mar},
  day={15},
  volume={3},
  number={1},
  pages={160018},
  abstract={There is an urgent need to improve the infrastructure supporting the reuse of scholarly data. A diverse set of stakeholders---representing academia, industry, funding agencies, and scholarly publishers---have come together to design and jointly endorse a concise and measureable set of principles that we refer to as the FAIR Data Principles. The intent is that these may act as a guideline for those wishing to enhance the reusability of their data holdings. Distinct from peer initiatives that focus on the human scholar, the FAIR Principles put specific emphasis on enhancing the ability of machines to automatically find and use the data, in addition to supporting its reuse by individuals. This Comment is the first formal publication of the FAIR Principles, and includes the rationale behind them, and some exemplar implementations in the community.},
  issn={2052-4463},
  doi={10.1038/sdata.2016.18},
  url={https://doi.org/10.1038/sdata.2016.18}
}

@Article{Barker2022,
  author={Barker, Michelle
  and Chue Hong, Neil P.
  and Katz, Daniel S.
  and Lamprecht, Anna-Lena
  and Martinez-Ortiz, Carlos
  and Psomopoulos, Fotis
  and Harrow, Jennifer
  and Castro, Leyla Jael
  and Gruenpeter, Morane
  and Martinez, Paula Andrea
  and Honeyman, Tom},
  title={Introducing the FAIR Principles for research software},
  journal={Scientific Data},
  year={2022},
  month={Oct},
  day={14},
  volume={9},
  number={1},
  pages={622},
  abstract={Research software is a fundamental and vital part of research, yet significant challenges to discoverability, productivity, quality, reproducibility, and sustainability exist. Improving the practice of scholarship is a common goal of the open science, open source, and FAIR (Findable, Accessible, Interoperable and Reusable) communities and research software is now being understood as a type of digital object to which FAIR should be applied. This emergence reflects a maturation of the research community to better understand the crucial role of FAIR research software in maximising research value. The FAIR for Research Software (FAIR4RS) Working Group has adapted the FAIR Guiding Principles to create the FAIR Principles for Research Software (FAIR4RS Principles). The contents and context of the FAIR4RS Principles are summarised here to provide the basis for discussion of their adoption. Examples of implementation by organisations are provided to share information on how to maximise the value of research outputs, and to encourage others to amplify the importance and impact of this work.},
  issn={2052-4463},
  doi={10.1038/s41597-022-01710-x},
  url={https://doi.org/10.1038/s41597-022-01710-x}
}

@article{Konnecke2015,
  author = "K{\"{o}}nnecke, Mark and Akeroyd, Frederick A. and Bernstein, Herbert J. and Brewster, Aaron S. and Campbell, Stuart I. and Clausen, Bj{\"{o}}rn and Cottrell, Stephen and Hoffmann, Jens Uwe and Jemian, Pete R. and M{\"{a}}nnicke, David and Osborn, Raymond and Peterson, Peter F. and Richter, Tobias and Suzuki, Jiro and Watts, Benjamin and Wintersberger, Eugen and Wuttke, Joachim",
  title = "{The NeXus data format}",
  journal = "Journal of Applied Crystallography",
  year = "2015",
  volume = "48",
  number = "1",
  pages = "301--305",
  month = "Feb",
  doi = {10.1107/S1600576714027575},
  url = {https://doi.org/10.1107/S1600576714027575},
  abstract = {NeXus is an effort by an international group of scientists to define a common data exchange and archival format for neutron, X-ray and muon experiments. NeXus is built on top of the scientific data format HDF5 and adds domain-specific rules for organizing data within HDF5 files, in addition to a dictionary of well defined domain-specific field names. The NeXus data format has two purposes. First, it defines a format that can serve as a container for all relevant data associated with a beamline. This is a very important use case. Second, it defines standards in the form of application definitions for the exchange of data between applications. NeXus provides structures for raw experimental data as well as for processed data.},
  keywords = {NeXus data format, data exchange, data archiving, platform-independent, HDF5},
}

@article{rii,
  author = {Mikhail N. Polyanskiy},
  title = {Refractiveindex.info database of optical constants},
  journal = "Scientific Data",
  year = "2024",
  volume = "11",
  number = "1",
  pages = "94",
  month = "Jan",
  day = "18",
  issn={2052-4463},
  doi = {10.1038/s41597-023-02898-2},
  url = {https://doi.org/10.1038/s41597-023-02898-2},
  abstract = {We introduce the refractiveindex.info database, a comprehensive open-source repository containing optical constants for a wide array of materials, and describe in detail the underlying dataset. This collection, derived from a meticulous compilation of data sourced from peer-reviewed publications, manufacturers’ datasheets, and authoritative texts, aims to advance research in optics and photonics. The data is stored using a YAML-based format, ensuring integrity, consistency, and ease of access. Each record is accompanied by detailed metadata, facilitating a comprehensive understanding and efficient utilization of the data. In this descriptor, we outline the data curation protocols and the file format used for data records, and briefly demonstrate how the data can be organized in a user-friendly fashion akin to the books in a traditional library.},
}

@software{berreman4x4_software,
  author = {Olivier Castany and Céline Molinaro},
  title = {Berreman4x4},
  url = {https://github.com/Berreman4x4/Berreman4x4},
  urldate = {2024-07-02},
  year = {2021}
}

@manual{berreman4x4_doku,
  author = {Olivier Castany},
  title = {Berreman4x4},
  url = {https://sourceforge.net/projects/berreman4x4/files/documentation.pdf},
  year = {2021},
  month = oct,
  day = {31},
}

@Article{         harris2020array,
  title         = {Array programming with {NumPy}},
  author        = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J.
                  van der Walt and Ralf Gommers and Pauli Virtanen and David
                  Cournapeau and Eric Wieser and Julian Taylor and Sebastian
                  Berg and Nathaniel J. Smith and Robert Kern and Matti Picus
                  and Stephan Hoyer and Marten H. van Kerkwijk and Matthew
                  Brett and Allan Haldane and Jaime Fern{\'{a}}ndez del
                  R{\'{i}}o and Mark Wiebe and Pearu Peterson and Pierre
                  G{\'{e}}rard-Marchant and Kevin Sheppard and Tyler Reddy and
                  Warren Weckesser and Hameer Abbasi and Christoph Gohlke and
                  Travis E. Oliphant},
  year          = {2020},
  month         = sep,
  journal       = {Nature},
  volume        = {585},
  number        = {7825},
  pages         = {357--362},
  doi           = {10.1038/s41586-020-2649-2},
  publisher     = {Springer Science and Business Media {LLC}},
  url           = {https://doi.org/10.1038/s41586-020-2649-2}
}

@ARTICLE{2020SciPy-NMeth,
  author  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and
              Haberland, Matt and Reddy, Tyler and Cournapeau, David and
              Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and
              Bright, Jonathan and {van der Walt}, St{\'e}fan J. and
              Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and
              Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and
              Kern, Robert and Larson, Eric and Carey, C J and
              Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and
              {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and
              Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and
              Harris, Charles R. and Archibald, Anne M. and
              Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and
              {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},
  title   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific Computing in Python}},
  journal = {Nature Methods},
  year    = {2020},
  volume  = {17},
  pages   = {261--272},
  adsurl  = {https://rdcu.be/b08Wh},
  doi     = {10.1038/s41592-019-0686-2},
}

@article{Berreman72,
  author = {Dwight W. Berreman},
  journal = {J. Opt. Soc. Am.},
  keywords = {Cholesteric liquid crystals; Faraday effect; Liquid crystals; Magnetic fields; Nonlinear effects; Optical activity},
  number = {4},
  pages = {502--510},
  publisher = {Optica Publishing Group},
  title = {Optics in Stratified and Anisotropic Media: 4{\texttimes}4-Matrix Formulation},
  volume = {62},
  month = {Apr},
  year = {1972},
  url = {https://opg.optica.org/abstract.cfm?URI=josa-62-4-502},
  doi = {10.1364/JOSA.62.000502},
  abstract = {A 4{\texttimes}4-matrix technique was recently introduced by Teitler and Henvis for finding propagation and reflection by stratified anisotropic media. It is more general than the 2{\texttimes}2-matrix technique developed by Jones and by Abel\`{e}s and is applicable to problems involving media of low optical symmetry. A little later, we developed a 4{\texttimes}4 differential-matrix technique in order to solve the problem of reflection and transmission by cholesteric liquid crystals and other liquid crystals with continuously varying but planar ordering. Our technique is mathematically equivalent to that of Teitler and Henvis, but we used a somewhat different approach. We start with a 6{\texttimes}6-matrix representation of Maxwell's equations that can include Faraday rotation and optical activity. From this, we derive expressions for 16 differential-matrix elements so that a wide variety of specific problems can be attacked without repeating a large amount of tedious algebra. The 4{\texttimes}4-matrix technique is particularly well suited for solving complicated reflection and transmission problems on a computer. It also serves as an illuminating alternative way to rederive closed solutions to a number of less-complicated classical problems. Teitler and Henvis described a method of solving some of these problems, briefly in their paper. We give solutions to several such problems and add a solution to the Oseen--DeVries optical model of a cholesteric liquid crystal, to illustrate the power and simplicity of the 4{\texttimes}4-matrix technique.},
}

@misc{byrnes2020multilayer,
  title={Multilayer optical calculations},
  author={Steven J. Byrnes},
  doi={10.48550/arXiv.1603.02720},
  url={https://doi.org/10.48550/arXiv.1603.02720},
  year={2020},
  eprint={1603.02720},
  archivePrefix={arXiv},
  primaryClass={physics.comp-ph}
}

@article{Scheidgen2023,
  doi = {10.21105/joss.05388},
  url = {https://doi.org/10.21105/joss.05388},
  year = {2023},
  publisher = {The Open Journal},
  volume = {8},
  number = {90},
  pages = {5388},
  author = {Markus Scheidgen
    and Lauri Himanen
    and Alvin Noe Ladines
    and David Sikter
    and Mohammad Nakhaee
    and Ádám Fekete
    and Theodore Chang
    and Amir Golparvar
    and José A. Márquez
    and Sandor Brockhauser
    and Sebastian Brückner
    and Luca M. Ghiringhelli
    and Felix Dietrich
    and Daniel Lehmberg
    and Thea Denell
    and Andrea Albino
    and Hampus Näsström
    and Sherjeel Shabih
    and Florian Dobener
    and Markus Kühbach
    and Rubel Mozumder
    and Joseph F. Rudzinski
    and Nathan Daelman
    and José M. Pizarro
    and Martin Kuban
    and Cuauhtemoc Salazar
    and Pavel Ondračka
    and Hans-Joachim Bungartz
    and Claudia Draxl},
  title = {NOMAD: A distributed web-based platform for managing materials science research data},
  journal = {Journal of Open Source Software}
}

@Inbook{Hilfiker2018,
  author="Hilfiker, James N.
  and Tiwald, Tom",
  editor="Fujiwara, Hiroyuki
  and Collins, Robert W.",
  title="Dielectric Function Modeling",
  bookTitle="Spectroscopic Ellipsometry for Photovoltaics: Volume 1: Fundamental Principles and Solar Cell Characterization",
  year="2018",
  publisher="Springer International Publishing",
  address="Cham",
  pages="115--153",
  abstract="Spectroscopic ellipsometry (SE) is commonly used to measure the optical constants of thin films and bulk materials. The optical constants vary with wavelength, which is referred to as dispersion. Rather than independently determine the optical constants at each wavelength, it is convenient to use an equation to describe their dispersion. A dispersion equation simplifies the description of the optical constants and improves the efficiency of data analysis. We begin this chapter by describing the optical constants, optical resonance, and the Kramers-Kronig relations. Different absorption phenomena are also briefly described. Many dispersion equations relate an optical resonance or absorption in terms of the complex dielectric function. Multiple resonance and absorption features can be summed to describe the overall dielectric function for the material. Finally, we review the common dispersion equations used for photovoltaic materials. The Cauchy and Sellmeier equations are used to describe transparent materials. The Lorentz, Harmonic, and Gaussian equations describe a resonant absorption. The Tauc-Lorentz and Cody-Lorentz were developed for amorphous semiconductors with dispersion features necessary to describe the optical functions near the bandgap energy. Additional dispersion equations are designed to describe the critical points in semiconductor band structure. We conclude this review with a description of polynomials, splines, and basis-splines, which are used to empirically match the optical functions of many materials.",
  isbn="978-3-319-75377-5",
  doi="10.1007/978-3-319-75377-5_5",
  url="https://doi.org/10.1007/978-3-319-75377-5_5"
}

@software{matt_newville_2024_12785036,
  author       = {Matt Newville and
                  Renee Otten and
                  Andrew Nelson and
                  Till Stensitzki and
                  Antonino Ingargiola and
                  Dan Allan and
                  Austin Fox and
                  Faustin Carter and
                  Michał and
                  Ray Osborn and
                  Dima Pustakhod and
                  Sebastian Weigand and
                  lneuhaus and
                  Andrey Aristov and
                  Glenn and
                  Mark and
                  mgunyho and
                  Christoph Deil and
                  Allan L. R. Hansen and
                  Gustavo Pasquevich and
                  Leon Foks and
                  Nicholas Zobrist and
                  Oliver Frost and
                  Stuermer and
                  Jean-Christophe Jaskula and
                  Shane Caldwell and
                  Pieter Eendebak and
                  Matteo Pompili and
                  Jens Hedegaard Nielsen and
                  Arun Persaud},
  title        = {lmfit/lmfit-py: 1.3.2},
  month        = jul,
  year         = 2024,
  publisher    = {Zenodo},
  version      = {1.3.2},
  doi          = {10.5281/zenodo.12785036},
  url          = {https://doi.org/10.5281/zenodo.12785036},
}

@article{eberheim2022,
  author = {Eberheim, Kevin and Dues, Christof and Attaccalite, Claudio and Müller, Marius J. and Schwan, Sebastian and Mollenhauer, Doreen and Chatterjee, Sangam and Sanna, Simone},
  title = {Tetraphenyl Tetrel Molecules and Molecular Crystals: From Structural Properties to Nonlinear Optics},
  journal = {The Journal of Physical Chemistry C},
  volume = {126},
  number = {7},
  pages = {3713-3726},
  year = {2022},
  doi = {10.1021/acs.jpcc.1c10107},
  url = {https://doi.org/10.1021/acs.jpcc.1c10107},
  eprint = { https://doi.org/10.1021/acs.jpcc.1c10107}
}

@article{Passler17,
  author = {Nikolai Christian Passler and Alexander Paarmann},
  journal = {J. Opt. Soc. Am. B},
  keywords = {Anisotropic optical materials; Multilayers; Spectroscopy, infrared; Thin films, optical properties; Nanophotonics and photonic crystals ; Light matter interactions; Light propagation; Material properties; Stratified media; Thin films; Total internal reflection},
  number = {10},
  pages = {2128--2139},
  publisher = {Optica Publishing Group},
  title = {Generalized 4 {\texttimes} 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures},
  volume = {34},
  month = {Oct},
  year = {2017},
  url = {https://opg.optica.org/josab/abstract.cfm?URI=josab-34-10-2128},
  doi = {10.1364/JOSAB.34.002128},
  abstract = {We present a generalized 4{\texttimes}4 matrix formalism for the description of light propagation in birefringent stratified media. In contrast to previous work, our algorithm is capable of treating arbitrarily anisotropic or isotropic, absorbing or non-absorbing materials and is free of discontinuous solutions. We calculate the reflection and transmission coefficients and derive equations for the electric field distribution for any number of layers. The algorithm is easily comprehensible and can be straightforwardly implemented in a computer program. To demonstrate the capabilities of the approach, we calculate the reflectivities, electric field distributions, and dispersion curves for surface phonon polaritons excited in the Otto geometry for selected model systems, where we observe several distinct phenomena ranging from critical coupling to mode splitting, and surface phonon polaritons in hyperbolic media.},
}

@article{Passler19,
  author = {Nikolai Christian Passler and Alexander Paarmann},
  journal = {J. Opt. Soc. Am. B},
  keywords = {Electric fields; Evanescent waves; Light propagation; Polaritons; Stratified media; Transmission coefficient},
  number = {11},
  pages = {3246--3248},
  publisher = {Optica Publishing Group},
  title = {Generalized 4 {\texttimes} 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures: erratum},
  volume = {36},
  month = {Nov},
  year = {2019},
  url = {https://opg.optica.org/josab/abstract.cfm?URI=josab-36-11-3246},
  doi = {10.1364/JOSAB.36.003246},
  abstract = {In our paper J. Opt. Soc. Am. B34, 2128 (2017)JOBPDE0740-322410.1364/JOSAB.34.002128 in Section 2.C, the calculation of the layer-dependent electric field distribution is only valid for media with permittivity tensors that are diagonal in the lab frame, i.e., non-birefringent media. This erratum corrects Section 2.C such that the electric field distribution in birefringent media is calculated correctly. Further, Eqs. (20) and (33)--(36) are corrected. The associated MATLAB implementation has been updated.},
}

@article{Pearce2021,
  doi = {10.21105/joss.03460},
  url = {https://doi.org/10.21105/joss.03460},
  year = {2021},
  publisher = {The Open Journal},
  volume = {6},
  number = {65},
  pages = {3460},
  author = {Phoebe M. Pearce},
  title = {RayFlare: flexible optical modelling of solar cells},
  journal = {Journal of Open Source Software}
}

@article{Luce22,
  author = {Alexander Luce and Ali Mahdavi and Florian Marquardt and Heribert Wankerl},
  journal = {J. Opt. Soc. Am. A},
  keywords = {Matrix methods; Neural networks; Refractive index; Thin film design; Thin film optical properties; Thin films},
  number = {6},
  pages = {1007--1013},
  publisher = {Optica Publishing Group},
  title = {TMM-Fast, a transfer matrix computation package for multilayer thin-film optimization: tutorial},
  volume = {39},
  month = {Jun},
  year = {2022},
  url = {https://opg.optica.org/josaa/abstract.cfm?URI=josaa-39-6-1007},
  doi = {10.1364/JOSAA.450928},
  abstract = {Achieving the desired optical response from a multilayer thin-film structure over a broad range of wavelengths and angles of incidence can be challenging. An advanced thin-film structure can consist of multiple materials with different thicknesses and numerous layers. Design and optimization of complex thin-film structures with multiple variables is a computationally heavy problem that is still under active research. To enable fast and easy experimentation with new optimization techniques, we propose the Python package Transfer Matrix Method - Fast (TMM-Fast), which enables parallelized computation of reflection and transmission of light at different angles of incidence and wavelengths through the multilayer thin film. By decreasing computational time, generating datasets for machine learning becomes feasible, and evolutionary optimization can be used effectively. Additionally, the subpackage TMM-Torch allows us to directly compute analytical gradients for local optimization by using PyTorch Autograd functionality. Finally, an OpenAI Gym environment is presented, which allows the user to train new reinforcement learning agents on the problem of finding multilayer thin-film configurations.},
}

@article{Bay2022,
  title = {PyLlama: A stable and versatile Python toolkit for the electromagnetic modelling of multilayered anisotropic media},
  journal = {Computer Physics Communications},
  volume = {273},
  pages = {108256},
  year = {2022},
  issn = {0010-4655},
  doi = {10.1016/j.cpc.2021.108256},
  url = {https://www.sciencedirect.com/science/article/pii/S0010465521003684},
  author = {Mélanie M. Bay and Silvia Vignolini and Kevin Vynck},
  keywords = {Multilayers, Anisotropic optical materials, Optical modelling, Photonic crystals, Cholesterics, Surface phonon polaritons},
  abstract = {PyLlama is a handy Python toolkit to compute the electromagnetic reflection and transmission properties of arbitrary multilayered linear media, including the case of anisotropy. Relying on a 4×4-matrix formalism, PyLlama implements not only the transfer matrix method, that is the most popular choice in existing codes, but also the scattering matrix method, which is numerically stable in all situations (e.g., thick, highly birefringent cholesteric structures at grazing incident angles). PyLlama is also designed to suit the practical needs by allowing the user to create, edit and assemble layers or multilayered domains with great ease. In this article, we present the electromagnetic theory underlying the transfer matrix and scattering matrix methods and outline the architecture and main features of PyLlama. Finally, we validate the code by comparison with available analytical solutions and demonstrate its versatility and numerical stability by modelling cholesteric media of varying complexity. A detailed documentation and tutorial are provided in a separate user manual. Applications of PyLlama range from the design of optical components to the modelling of polaritonic effects in polar crystals, to the study of structurally coloured materials in the living world.
  Program summary
  Program Title: PyLlama – Python Toolkit for the Electromagnetic Modelling of Multilayered Anisotropic Media CPC Library link to program files: https://doi.org/10.17632/dzw8x5vyrv.1 Developer's repository link: https://github.com/VignoliniLab/PyLlama Licensing provisions: GPLv3 Programming language: Python Supplementary material: User guide and tutorials at https://pyllama.readthedocs.io/ Nature of problem: Computation of the optical reflection and transmission coefficients of arbitrary multilayered linear media, composed of an arbitrary number of layers, possibly mixing isotropic and anisotropic, absorbing and non-absorbing materials, for linearly or circularly polarised light. Solution method: Implementation of both the transfer matrix method (faster) and the scattering matrix method (more robust) relying on a 4×4 matrix formalism. Additional comments including restrictions and unusual features: Integration of a physical model to handle cholesteric structures, blueprint for the integration of user-created custom systems, hassle-free export of spectra for non-programmers even for complex and/or custom systems. External routines include: Numpy [1], Scipy [2], as well as Sympy [3] (optional).
  References
  [1]Numpy, https://numpy.org/.[2]Scipy, https://www.scipy.org/.[3]Sympy, https://www.sympy.org/.}
}

@book{tompkins2005,
  title={Handbook of Ellipsometry},
  author={Tompkins, H. and Irene, E.A.},
  isbn={9780815517474},
  year={2005},
  publisher={William Andrew},
  address={Norwich}
}

@manual{WVASEguide,
  title={Guide to Using WVASE},
  organization={J. A. Woollam Co., Inc.},
  address={Lincoln, NE},
  year={2012}
}

@article{tmmax, 
  doi = {10.21105/joss.09088}, 
  url = {https://doi.org/10.21105/joss.09088}, 
  year = {2025}, publisher = {The Open Journal}, 
  volume = {10}, number = {114}, pages = {9088}, 
  author = {Danis, Bahrem Serhat and Zayim, Esra}, 
  title = {TMMax: High-performance modeling of multilayer thin-film structures using transfer matrix method with JAX}, 
  journal = {Journal of Open Source Software} 
} 

@article{Langevin:24,
  author = {Denis Langevin and Pauline Bennet and Abdourahman Khaireh-Walieh and Peter Wiecha and Olivier Teytaud and Antoine Moreau},
  journal = {J. Opt. Soc. Am. B},
  keywords = {Deep learning; Optical computing; Optical filters; Optical properties; Resonant modes; Wavelength division multiplexing},
  number = {2},
  pages = {A67--A78},
  publisher = {Optica Publishing Group},
  title = {PyMoosh: a comprehensive numerical toolkit for computing the optical properties of multilayered structures},
  volume = {41},
  month = {Feb},
  year = {2024},
  url = {https://opg.optica.org/josab/abstract.cfm?URI=josab-41-2-A67},
  doi = {10.1364/JOSAB.506175},
  abstract = {We present PyMoosh, a Python-based simulation library designed to provide a comprehensive set of numerical tools allowing the computation of essentially all optical characteristics of multilayered structures, ranging from reflectance and transmittance to guided modes and photovoltaic efficiency. PyMoosh is designed not just for research purposes, but also for use cases in education. To this end, we have invested significant effort in ensuring the user-friendliness and simplicity of the interface. PyMoosh has been developed in line with the principles of open science and considering the fact that multilayered structures are increasingly being used as a testing ground for optimization and deep learning approaches. We provide in this paper the theoretical basis at the core of PyMoosh, an overview of its capabilities, as well as a comparison between the different numerical methods implemented in terms of speed and stability. We are convinced such a versatile tool will be useful for the community in many ways.},
}