Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Advertisement

Scientific Reports
  • View all journals
  • Search
  • My Account Login
  • Content Explore content
  • About the journal
  • Publish with us
  • Sign up for alerts
  • RSS feed
  1. nature
  2. scientific reports
  3. articles
  4. article
ZenBand: a numerical solver of photonic crystals with a graphical user interface
Download PDF
Download PDF
  • Article
  • Open access
  • Published: 04 February 2026

ZenBand: a numerical solver of photonic crystals with a graphical user interface

  • Andrius Zinkevičius1,
  • Ignas Lukošiūnas1 &
  • Darius Gailevičius1 

Scientific Reports , Article number:  (2026) Cite this article

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Optics and photonics
  • Physics

Abstract

We developed an open-source Plane Wave Expansion Method solver using Python and a custom Tkinter library to solve a design oriented problem of photonic crystal dispersion for known classical examples, custom geometries, and symmetries. Such structures are capable of light confinement, omnidirectional reflection, beam collimation and negative refraction. We dive deeper into the diagonally anisotropic photonic crystals, whose Plane Wave Expansion algorithm is directly embedded in the application. The user interface is present in the developer’s repository link: https://github.com/ZenTunturi/ZenBand.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Tang, Y. et al. Optical neural engine for solving scientific partial differential equations. Nat. Commun. 16, 4603 (2025).

    Google Scholar 

  2. Vial, B. & Hao, Y. Open-source computational photonics with auto differentiable topology optimization. Mathematics 10, 3912 (2022).

    Google Scholar 

  3. Jiang, X. et al. Physics-informed neural network for nonlinear dynamics in fiber optics. Laser Photon. Rev. 16, 2100483 (2022).

    Google Scholar 

  4. Su, Y. & Zhang, Q. Glare: A free and open-source software for generation and assessment of digital speckle pattern. Opt. Lasers Eng. 148, 106766 (2022).

    Google Scholar 

  5. Neese, F. Software update: The orca program system—version 5.0. Wiley Interdiscip. Rev. Comput. Mol. Sci. 12, e1606 (2022).

  6. Erdem, S. et al. Rayx—An optics simulation software for synchrotron applications. Rev. Sci. Instrum. 96 (2025).

  7. Woodhams, L. G. et al. Virtual Blebbistatin: A robust and rapid software approach to motion artifact removal in optical mapping of cardiomyocytes. Proc. Natl. Acad. Sci. 120, e2212949120 (2023).

    Google Scholar 

  8. Lamb, J. R., Ward, E. N. & Kaminski, C. F. Open-source software package for on-the-fly deskewing and live viewing of volumetric lightsheet microscopy data. Biomed. Opt. Exp. 14, 834–845 (2023).

    Google Scholar 

  9. Gröhl, J. et al. Simpa: An open-source toolkit for simulation and image processing for photonics and acoustics. J. Biomed. Opt. 27, 083010–083010 (2022).

    Google Scholar 

  10. Oskooi, A. F. et al. MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method. Comput. Phys. Commun. 181, 687–702. https://doi.org/10.1016/j.cpc.2009.11.008 (2010).

    Google Scholar 

  11. Kim, C. & Lee, B. Torcwa: GPU-accelerated Fourier modal method and gradient-based optimization for metasurface design. Comput. Phys. Commun. 282, 108552. https://doi.org/10.1016/j.cpc.2022.108552 (2023).

    Google Scholar 

  12. Yoon, G. & Rho, J. Maxim: Metasurfaces-oriented electromagnetic wave simulation software with intuitive graphical user interfaces. Comput. Phys. Commun. 264, 107846. https://doi.org/10.1016/j.cpc.2021.107846 (2021).

    Google Scholar 

  13. Sanchez-Brea, L. M. et al. Diffraction: An open-source library for diffraction and interference calculations. In Optics and Photonics for Advanced Dimensional Metrology III (de Groot, P. J., Guzman, F. & Picart, P. eds.) . Vol. 12997. 129971B. https://doi.org/10.1117/12.3021879. (International Society for Optics and Photonics, SPIE, 2024).

  14. Dharmavarapu, R., Ng, S. H., Eftekhari, F., Juodkazis, S. & Bhattacharya, S. Metaoptics: Opensource software for designing metasurface optical element GDSII layouts. Opt. Exp. 28, 3505–3516. https://doi.org/10.1364/OE.384057 (2020).

    Google Scholar 

  15. Dharmavarapu, R., Bhattacharya, S. & Juodkazis, S. GDOESII: Software for design of diffractive optical elements and phase mask conversion to GDSII lithography files. SoftwareX 9, 126–131. https://doi.org/10.1016/j.softx.2019.01.012 (2019).

    Google Scholar 

  16. Veettikazhy, M. et al. Bpm-Matlab: An open-source optical propagation simulation tool in Matlab. Opt. Exp. 29, 11819–11832. https://doi.org/10.1364/OE.420493 (2021).

    Google Scholar 

  17. Magalhães, T. E. & Rebordão, J. M. Pywolf: A pyopencl implementation for simulating the propagation of partially coherent light. Comput. Phys. Commun. 276, 108336. https://doi.org/10.1016/j.cpc.2022.108336 (2022).

    Google Scholar 

  18. Loetgering, L. et al. Ptylab.m/py/jl: A cross-platform, open-source inverse modeling toolbox for conventional and Fourier ptychography. Opt. Exp. 31, 13763–13797. https://doi.org/10.1364/OE.485370 (2023).

  19. Hugonin, J. P. & Lalanne, P. Reticolo software for grating analysis. arXiv preprint arXiv:2101.00901 (2021).

  20. Zuo, S., Doñoro, D. G., Zhang, Y., Bai, Y. & Zhao, X. Simulation of challenging electromagnetic problems using a massively parallel finite element method solver. IEEE Access 7, 20346–20362 (2019).

    Google Scholar 

  21. Yavich, N. & Zhdanov, M. S. Finite-element EM modelling on hexahedral grids with an FD solver as a pre-conditioner. Geophys. J. Int. 223, 840–850 (2020).

    Google Scholar 

  22. Liu, V. & Fan, S. S4: A free electromagnetic solver for layered periodic structures. Comput. Phys. Commun. 183, 2233–2244 (2012).

    Google Scholar 

  23. Tang, G.-J. et al. Broadband and fabrication-tolerant 3-db couplers with topological valley edge modes. Light Sci. Appl. 13, 166 (2024).

  24. Huang, H., Yang, C., Li, H. & Zhang, Z. Unveiling the potential of photonic crystal surface emitting lasers: A concise review. In Semiconductor Science and Technology (2025).

  25. Han, C. et al. Generating first-order optical vortex beams by photonic crystal slabs. Opt. Exp. 32, 27591–27598 (2024).

    Google Scholar 

  26. Deng, R. et al. Broadband complete polarization control via inverse-designed photonic crystal slabs. Adv. Opt. Mater. 12, 2303218 (2024).

    Google Scholar 

  27. Ho, K., Chan, C. T. & Soukoulis, C. M. Existence of a photonic gap in periodic dielectric structures. Phys. Rev. Lett. 65, 3152 (1990).

    Google Scholar 

  28. Rumpf, R., Garcia, C., Berry, E. & Barton, J. Finite-difference frequency-domain algorithm for modeling electromagnetic scattering from general anisotropic objects. Prog. Electromagnet. Res. B 61, 55–67. https://doi.org/10.2528/PIERB14071606 (2014).

    Google Scholar 

  29. Rumpf, R. C. Engineering the dispersion and anisotropy of periodic electromagnetic structures. In Solid State Physics. Vol. 66. 213–300 (Elsevier, 2015).

  30. Zanotti, S. et al. Legume: A free implementation of the guided-mode expansion method for photonic crystal slabs. Comput. Phys. Commun. 304, 109286 (2024).

    Google Scholar 

  31. Yang, Y., Jiang, H. & Hang, Z. H. Topological valley transport in two-dimensional honeycomb photonic crystals. Sci. Rep. 8, 1588 (2018).

    Google Scholar 

  32. Shi, B. et al. Efficient coupling of topological photonic crystal waveguides based on transverse spin matching mechanism. Nat. Commun. 16. https://doi.org/10.1038/s41467-025-59941-6 (2025).

  33. Li, M. et al. Ultrabroadband valley transmission and corner states in valley photonic crystals with dendritic structure. Commun. Phys. 7, 214 (2024).

    Google Scholar 

  34. Xu, Z.-H. et al. Quantitative terahertz communication evaluation of compact valley topological photonic crystal waveguides. ACS Photon. 12, 1822–1828 (2025).

    Google Scholar 

  35. Xu, X. et al. Polymer valley photonic crystals with honeycomb structures for terahertz waveguides. Opt. Commun. 538, 129446 (2023).

    Google Scholar 

  36. Moniem, T. A. All optical active high decoder using integrated 2D square lattice photonic crystals. J. Mod. Opt. 62, 1643–1649 (2015).

    Google Scholar 

  37. Jamois, C. et al. Silicon-based two-dimensional photonic crystal waveguides. Photon. Nanostruct.-Fundam. Appl. 1, 1–13 (2003).

  38. Yuksel, Z. M. et al. Enhanced self-collimation effect by low rotational symmetry in hexagonal lattice photonic crystals. Phys. Scr. 99, 065017 (2024).

    Google Scholar 

  39. Qiu, P. et al. Investigation of beam splitter in a zero-refractive-index photonic crystal at the frequency of Dirac-like point. Sci. Rep. 7. https://doi.org/10.1038/s41598-017-10056-z (2017).

  40. Meade, R. D. V., Johnson, S. G. & Winn, J. N. Photonic crystals: Molding the flow of light (2008).

  41. Oppenheim, A. V. & Schafer, R. W. Discrete-Time Signal Processing. Prentice-Hall Signal Processing Series (Pearson, 2010).

  42. Arik, K. & Akbari, M. Polynomial expansion method for full wave three-dimensional analysis of dielectric waveguides and periodic structures. Opt. Exp. 32, 16115–16131. https://doi.org/10.1364/OE.519283 (2024).

    Google Scholar 

  43. Fay, T. H. & Kloppers, P. H. The Gibbs’ phenomenon. Int. J. Math. Educ. Sci. Technol. 32, 73–89. https://doi.org/10.1080/00207390117151 (2001).

    Google Scholar 

  44. Lou, B. & Fan, S. Rcwa4d: Electromagnetic solver for layered structures with incommensurate periodicities. Comput. Phys. Commun. 306, 109356. https://doi.org/10.1016/j.cpc.2024.109356 (2025).

    Google Scholar 

  45. Götz, P., Schuster, T., Frenner, K., Rafler, S. & Osten, W. Normal vector method for the RCWA with automated vector field generation. Opt. Exp. 16, 17295–17301. https://doi.org/10.1364/OE.16.017295 (2008).

    Google Scholar 

Download references

Funding

D.G. acknowledges funding from the Research Council of Lithuania (LMTLT), grant No. S-MIP-23-49. A.Z. and I.L. acknowledge the “Universities’ Excellence Initiative” programme by the Ministry of Education, Science and Sports of the Republic of Lithuania under the agreement with the Research Council of Lithuania (project No. S-A-UEI-23–6).

Author information

Authors and Affiliations

  1. Laser Research Center, Faculty of Physics, Vilnius University, Saulėtekio Ave. 10, Vilnius, Lithuania

    Andrius Zinkevičius, Ignas Lukošiūnas & Darius Gailevičius

Authors
  1. Andrius Zinkevičius
    View author publications

    Search author on:PubMed Google Scholar

  2. Ignas Lukošiūnas
    View author publications

    Search author on:PubMed Google Scholar

  3. Darius Gailevičius
    View author publications

    Search author on:PubMed Google Scholar

Contributions

I.L. and A.Z. developed ZenBand academic and commercial software, D.G. is the leader of the technical project. All authors contributed equally to this paper. I.L. and A.Z. have made equal contributions to the ZenBand software.

Corresponding author

Correspondence to Andrius Zinkevičius.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zinkevičius, A., Lukošiūnas, I. & Gailevičius, D. ZenBand: a numerical solver of photonic crystals with a graphical user interface. Sci Rep (2026). https://doi.org/10.1038/s41598-026-37129-2

Download citation

  • Received: 26 September 2025

  • Accepted: 20 January 2026

  • Published: 04 February 2026

  • DOI: https://doi.org/10.1038/s41598-026-37129-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Download PDF

Associated content

Collection

Photonic crystals

Advertisement

Explore content

  • Research articles
  • News & Comment
  • Collections
  • Subjects
  • Follow us on Facebook
  • Follow us on Twitter
  • Sign up for alerts
  • RSS feed

About the journal

  • About Scientific Reports
  • Contact
  • Journal policies
  • Guide to referees
  • Calls for Papers
  • Editor's Choice
  • Journal highlights
  • Open Access Fees and Funding

Publish with us

  • For authors
  • Language editing services
  • Open access funding
  • Submit manuscript

Search

Advanced search

Quick links

  • Explore articles by subject
  • Find a job
  • Guide to authors
  • Editorial policies

Scientific Reports (Sci Rep)

ISSN 2045-2322 (online)

nature.com sitemap

About Nature Portfolio

  • About us
  • Press releases
  • Press office
  • Contact us

Discover content

  • Journals A-Z
  • Articles by subject
  • protocols.io
  • Nature Index

Publishing policies

  • Nature portfolio policies
  • Open access

Author & Researcher services

  • Reprints & permissions
  • Research data
  • Language editing
  • Scientific editing
  • Nature Masterclasses
  • Research Solutions

Libraries & institutions

  • Librarian service & tools
  • Librarian portal
  • Open research
  • Recommend to library

Advertising & partnerships

  • Advertising
  • Partnerships & Services
  • Media kits
  • Branded content

Professional development

  • Nature Awards
  • Nature Careers
  • Nature Conferences

Regional websites

  • Nature Africa
  • Nature China
  • Nature India
  • Nature Japan
  • Nature Middle East
  • Privacy Policy
  • Use of cookies
  • Legal notice
  • Accessibility statement
  • Terms & Conditions
  • Your US state privacy rights
Springer Nature

© 2026 Springer Nature Limited

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing