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{{Short description|Open-source software for electromagnetic scattering calculations}}
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{{Draft topics|computing|physics}}
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{{Infobox software
| name = ''treams''
| author = Dominik Beutel
| developer = Dominik Beutel, Ivan Fernandez-Corbaton, [[Carsten Rockstuhl]]
| programming_language = [[Python (programming language)|Python]], [[Cython]]
| license = [[MIT License]]
| website = {{URL|https://tfp-photonics.github.io/treams/}}
}}

'''treams''' is an [[open-source software]] package for calculations of [[electromagnetic scattering]] based on the [[T-matrix method]]. It can be used for finite and periodic arrangements of scatterers of different schapes.<ref name="Beutel2024">{{cite journal
| last1 = Beutel
| first1 = Dominik
| last2 = Fernandez-Corbaton
| first2 = Ivan
| last3 = Rockstuhl
| first3 = Carsten
| title = treams – a T-matrix-based scattering code for nanophotonics
| journal = Computer Physics Communications
| volume = 297
| article-number = 109076
| year = 2024
| doi = 10.1016/j.cpc.2023.109076
}}</ref>

== Capabilities ==

treams computes T-matrices analyticalaly for spheres and for infinitely long cylinders, including multilayered spheres and cylinders. It can also import external T-matrices, e.g. from T-matrix database<ref name="Asadova2026">{{cite arXiv
| last1 = Asadova
| first1 = Nigar
| last2 = Boussaoud
| first2 = Kaoutar
| last3 = Meyer
| first3 = Jörg
| last4 = Tristram
| first4 = Frank
| last5 = Rockstuhl
| first5 = Carsten
| title = A T-matrix database to promote information-driven research in nanophotonics
| eprint = 2602.02101
| class = physics.optics
| year = 2026
}}</ref>. If the T-matrices of single scatterers are known, T-matrices of corresponding clusters and periodic arrays of these scatterers can be also calculated. Then the quantities such as fields outside the structures, scattering, extinction and absorption cross-sections, multipolar decompositions may be extracted. <ref name="Beutel2024" />

Periodic systems can be considered in different dimensions. Particle arrays can be placed near multilayered substrates, for which transmission and reflection can be calculated. Fore some geometries, the package can be also used to compute band structures.<ref name="Beutel2024" /><ref name="Beutel2023" />

Isotropic chiral media are implemented directly, and scatterers from anisotropic material can be introduced through externally calculated T-matrices.<ref name="Beutel2024" />

== Method ==

In the [[T-matrix method]], incident and scattered fields are expanded into a set of basis functions. Fields expanded into [[vector spherical harmonics]] can be represented in helicity or parity (TE/TM) bases, also cylindrical harmonics basis and plane wave basis are available. The T-matrix of a nanostructure connects the coefficients of the incident field with those of the scattered field. For clusters and arrays, the fields scattered by one particle act as incident fields for the others, and the basis change is performed using translation addition theorems<ref>{{cite journal|first1=R. C.|last1=Wittmann|doi=10.1109/8.7220|title=Spherical wave operators and the translation formulas|journal=IEEE Transactions on Antennas and Propagation|volume=36|number=8|pages=1078–1087|year=1988|bibcode=1988ITAP...36.1078W |url=https://zenodo.org/record/1262852 }}</ref><ref name="Beutel2024" />

For periodic systems, the same interaction has to be summed over the repeated lattice. treams evaluates these sums using the [[Ewald summation|Ewald method]]. <ref name="Beutel2023">{{cite journal
| last1 = Beutel
| first1 = Dominik
| last2 = Fernandez-Corbaton
| first2 = Ivan
| last3 = Rockstuhl
| first3 = Carsten
| title = Unified lattice sums accommodating multiple sublattices for solutions of the Helmholtz equation in two and three dimensions
| journal = Physical Review A
| volume = 107
| issue = 1
| article-number = 013508
| year = 2023
| doi = 10.1103/PhysRevA.107.013508
}}</ref>

== Applications ==
treams has been used for dispersion and band-structure calculations in periodic plasmonic lattices,<ref>N. de Gaay Fortman, D. Pal, P. Schall, A. F. Koenderink, ''ACS Photonics'' '''12''', 1163–1173 (2025), {{doi|10.1021/acsphotonics.4c02323}}.</ref> for the electromagnetic response of metasurfaces coupled to quantum-emitter arrays,<ref>F. Lindel, C. J. Sánchez Martínez, J. Feist, F. J. García-Vidal, ''Phys. Rev. Lett.'' '''137''', 103802 (2026), {{doi|10.1103/71nx-b83j}}.</ref> and for reflectance calculations of transition-metal dichalcogenide nanosphere arrays.<ref>I. J. Bundgaard, C. G. Ferreira, Y. Lebsir, C. Tserkezis, ''ACS Appl. Nano Mater.'' '''9''', 16632–16642 (2026), {{doi|10.1021/acsanm.6c01961}}.</ref> It has also been discussed in comparison with other multiple-scattering codes such as ''Multem 3''.<ref>A. Shalev, K. Ladutenko, I. Lobanov, V. Yannopapas, A. Moroz, ''Comput. Phys. Commun.'' '''301''', 109218 (2024), {{doi|10.1016/j.cpc.2024.109218}}.</ref> An acoustic implementation, ''acoustotreams'', was introduced in 2026.<ref>N. Ustimenko, C. Rockstuhl, ''acoustotreams – A Python package for acoustic-wave scattering based on the T-matrix method'', arXiv:2606.22573 (2026).</ref>


== See also ==
* [[T-matrix method]]
* [[Mie scattering]]
* [[Computational electromagnetics]]
* [[Multiple scattering]]
* [[Ewald summation]]

== References ==

{{Reflist}}