# MPB (software)

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**MPB** (**M**IT **P**hotonic **B**ands) is a [free and open-source](/source/Open-source_software)[1] software package for [electromagnetic analysis](/source/Computational_electromagnetics) of [periodic](/source/Periodic_boundary_conditions) structures with an emphasis on [photonic crystals](/source/Photonic_crystal). It was developed by [Steven G. Johnson](/source/Steven_G._Johnson) and collaborators at *ab initio* research group at [Massachusetts Institute of Technology](/source/Massachusetts_Institute_of_Technology) in 1999.[2] Operating under [Unix-like](/source/Unix-like) systems and being scriptable in [Python](/source/Python_(programming_language)), it uses the [frequency domain](/source/Frequency_domain) [plane wave expansion method](/source/Plane_wave_expansion_method) with [block-iterative algorithms](/source/Eigenvalue_algorithm) and [Fast Fourier transform](/source/Fast_Fourier_transform) for [modal analysis](/source/Modal_analysis).[3] The solver is able to analyze lossless and [dispersionless](/source/Dispersion_(optics)) [anisotropic](/source/Anisotropy) materials, including [birefringent](/source/Birefringence) and [gyrotropic](/source/Magneto-optic_effect) media.[4]

MPB is widely used by [band diagram](/source/Band_diagram) analysis of photonic crystals by the [photonics](/source/Photonics) community,[5][6] with uses in the studies on [optical waveguides](/source/Waveguide_(optics)),[7][8][9] [photonic-crystal fibers](/source/Photonic-crystal_fiber),[10] [negative refraction](/source/Negative_refraction)[11] and [photonic topological insulators](/source/Photonic_topological_insulator).[12][13] The software also serves as a complimentary module to the general-purpose electromagnetic simulation software [Meep](/source/Meep_(software)), also developed by the *ab initio* research group.[4]

## See also

- [Comparison of EM simulation software](/source/Comparison_of_EM_simulation_software)
- [List of computer simulation software](/source/List_of_computer_simulation_software)

## References

1. ["Meep: License and Copyright"](https://mpb.readthedocs.io/en/latest/License_and_Copyright/). *mpb.readthedocs.io*. Retrieved December 19, 2025.

1. ["MIT Photonic-Bands"](http://ab-initio.mit.edu/mpb/). *ab-initio.mit.edu*. [Archived](https://web.archive.org/web/20000815211405/http://ab-initio.mit.edu/mpb/) August 15, 2000 at the Wayback Machine. Retrieved December 19, 2025.

1. Johnson, Steven G. & Joannopoulos, J. D. (2001). "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis". *[Optics Express](/source/Optics_Express)*. **8** (3): 173-190. [doi:10.1364/OE.8.000173](https://doi.org/10.1364/OE.8.000173)

1. ["MPB"](https://mpb.readthedocs.io/en/latest/). *mpb.readthedocs.io*. Retrieved December 19, 2025.

1. Cersonsky, Rose K.; Antonaglia, James; Dice, Bradley D.; Glotzer, Sharon C. (2021). "The diversity of three-dimensional photonic crystals". *[Nature Communications](/source/Nature_Communications)*. [doi:10.1038/s41467-021-22809-6](https://doi.org/10.1038/s41467-021-22809-6). [PMC 8100142](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8100142)

1. John D. Joannopoulos; S. G. Johnson; J. N. Winn; R. D. Meade (2008), [*Photonic Crystals: Molding the Flow of Light*](http://ab-initio.mit.edu/book/photonic-crystals-book.pdf), 2nd ed., Princeton University Press, p. 264, [Bibcode:2008pcmf.book.....J](https://ui.adsabs.harvard.edu/abs/2008pcmf.book.....J). ISBN 978-0-691-12456-8

1. Kuchinsky, S.; Golyatin, V. Y.; Kutikov, A. Y.; Pearsall, T. R.; Nedelikovic, D. (2002). "Coupling between photonic crystal waveguides". *[IEEE Journal of Quantum Electronics](/source/IEEE_Journal_of_Quantum_Electronics)*. **38** (10): 1349-1352.

1. Safavi-Naeini, Amir H.; Hill, Jeff T.; Meenehan, Seán; Chan, Jasper; Gröblacher, Simon; Painter, Oskar (2014). "Two-dimensional phononic-photonic band gap optomechanical crystal cavity". *[Physical Review Letters](/source/Physical_Review_Letters)*. **112**. [arXiv:1401.1493](https://arxiv.org/abs/1401.1493). [doi:10.1103/PhysRevLett.112.153603](https://doi.org/10.1103/PhysRevLett.112.153603)

1. Tiecke, T. G.; Nayak, K. P.; Thompson, J. D.; Peyronel, T.; de Leon, N. P.; Vuletić, V.; Lukin, M. D. (2015). "Efficient fiber-optical interface for nanophotonic devices". *[Optica](/source/Optica_(journal))*. **2** (2). [doi:10.1364/OPTICA.2.000070](https://doi.org/10.1364/OPTICA.2.000070). [hdl:1721.1/98467](https://hdl.handle.net/1721.1/98467)

1. Limpert, J.; Schreiber, T.; Nolte, S.; Zellmer, H.; Tünnermann, A.; Iliew, R.; Lederer, F.; Broeng, J.; Vienne, G.; Petersson, A.; Jakobsen, C. (2003). "High-power air-clad large-mode-area photonic crystal fiber laser". *[Optics Express](/source/Optics_Express)*. **11** (7): 818-823. [doi:10.1364/OE.11.000818](https://doi.org/10.1364/OE.11.000818)

1. Luo, Chiyan; Johnson, Steven G.; Joannopoulos, J. D.; Pendry, J. B. (2002). "All-angle negative refraction without negative effective index". *[Physical Review B](/source/Physical_Review_B)*. **65**. [doi:10.1103/PhysRevB.65.201104](https://doi.org/10.1103/PhysRevB.65.201104)

1. Wu, Long-Hua & Hu, Xiao (2015). "Scheme for achieving a topological photonic crystal by using dielectric material". *[Physical Review Letters](/source/Physical_Review_Letters)*. **114**. [arXiv:1503.00416](https://arxiv.org/abs/1503.00416). [doi:10.1103/PhysRevLett.114.223901](https://doi.org/10.1103/PhysRevLett.114.223901)

1. Christensen, Thomas; Po, Hoi Chun; Joannopoulos, John D.; Soljačić, Marin (2022). "Location and topology of the fundamental gap in photonic crystals". *[Physical Review X](/source/Physical_Review_X)*. **12**. [arXiv:2106.10267](https://arxiv.org/abs/2106.10267). [doi:10.1103/PhysRevX.12.021066](https://doi.org/10.1103/PhysRevX.12.021066)

## External links

- [Official website](https://mpb.readthedocs.io/en/latest/)

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Adapted from the Wikipedia article [MPB (software)](https://en.wikipedia.org/wiki/MPB_(software)) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/MPB_(software)?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.