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Codes for electromagnetic scattering by spheres
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<h2 id="solution-techniques">Solution techniques</h2> <p>Majority of existing codes for calculation of electromagnetic scattering by a single sphere is based on <a href="/facts/Mie_theory/5mJc3SrT">Mie theory</a> which is an analytical solution of Maxwell's equations in terms of infinite series. Other approximations to scattering by a single sphere include: Debye series, <a href="/facts/Ray_tracing_(physics)/VKdjk6Sc">ray tracing</a> (<a href="/facts/Geometrical_optics/gIFu84Tm">geometrical optics</a>), ray tracing including the effects of interference between rays, Airy theory, <a href="/facts/Rayleigh_scattering/o0MQtPMM">Rayleigh scattering</a>, diffraction approximation. There are many phenomena related to light scattering by spherical particles such as resonances, surface waves, plasmons, near-field scattering. Even though Mie theory offers convenient and fast way of solving light scattering problem by homogeneous spherical particles, there are other techniques, such as <a href="/facts/Discrete_dipole_approximation/6aNfztC5">discrete dipole approximation</a>, FDTD, T-matrix, which can also be used for such tasks. <a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> </p> <h2 id="classification">Classification</h2> <p>The compilation contains information about the electromagnetic scattering by spherical particles, relevant links, and applications.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> </p> <h3>Codes for electromagnetic scattering by a single homogeneous sphere</h3> <table><tbody><tr><th>Year</th><th>Name</th><th>Authors</th><th>References</th><th>Language</th><th>Short Description</th></tr><tr><td>1983</td><td>BHMIE <a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a></td><td>Craig F. Bohren and Donald R. Huffman</td><td><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></td><td><p><a href="http://scatterlib.wdfiles.com/local--files/codes/bhmie-f.zip">Fortran</a> <a href="http://scatterlib.wdfiles.com/local--files/codes/bhmie-idl.zip">IDL</a><a href="http://scatterlib.wdfiles.com/local--files/codes/bhmie-matlab.zip">Matlab</a> <a href="http://scatterlib.wdfiles.com/local--files/codes/bhmie-c.zip">C</a> <a href="http://scatterlib.wdfiles.com/local--files/codes/bhmie.py">Python</a></p></td><td>"Mie solutions" (infinite series) to scattering, absorption and phase function of electromagnetic waves by a homogeneous sphere.</td></tr><tr><td>2002</td><td>MiePlot <a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a></td><td>Philip Laven</td><td><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></td><td>Visual Basic</td><td>MiePlot offers the following mathematical models for the scattering of light by a sphere: Mie solutions, Debye series, ray tracing (based on geometrical optics), ray tracing including the effects of interference between rays, Airy theory, Rayleigh scattering, diffraction, surface waves. In addition to single-wavelength calculations, MiePlot can also perform calculations for some wavelengths, thus approximating a continuous spectrum (such as sunlight) to produce simulations of atmospheric optical effects such as rainbows, coronas and glories.</td></tr><tr><td>2003</td><td><a href="https://web.archive.org/web/20100702162242/http://www.atm.ox.ac.uk/code/mie/index.html">Mie_Single etc.</a></td><td>Gareth Thomas and Don Grainger</td><td><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></td><td>IDL</td><td>The Sub-Department of Atmospheric Oceanic and Planetary Physics in the University of Oxford maintains an archive of Mie scattering routines for both single spheres and populations of particles in which sizes follow a <a href="/facts/Log-normal/V2RXmmlE">log-normal</a> distribution. The code is also available for calculating the analytical derivatives of Mie scattering (i.e. the derivative of the extinction and scattering coefficients, and the intensity functions with respect to size parameter and complex refractive index). The routines are written in <a href="/facts/IDL_(programming_language)/E6YhA7zY">IDL</a>, but a Fortran-based DLM version (which substantially reduces runtime) of the single-sphere code is also available.</td></tr></tbody></table> <h3>Codes for electromagnetic scattering by a layered sphere</h3> <p>Algorithmic literature includes several contributions <a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> <a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> <a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> <a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> </p> <table><tbody><tr><th>Year</th><th>Name</th><th>Authors</th><th>Ref</th><th>Language</th><th>License</th><th>Short Description</th></tr><tr><td>1981</td><td>DMILAY</td><td>Owen B. Toon and T. P. Ackerman</td><td><a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a></td><td><a href="/facts/Fortran/m1KqjcMU">Fortran</a></td><td>No license specified but open source (public domain)</td><td>Scattering by a stratified sphere (a particle with a spherical core surrounded by a spherical shell).<p>Code dates from 1968 available here:<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a></p></td></tr><tr><td>1983</td><td>BHCOAT</td><td>Craig F. Bohren and Donald R. Huffman</td><td><a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a></td><td><a href="/facts/Fortran/m1KqjcMU">Fortran</a></td><td>No specified but open source (public domain via <a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a>)</td><td>"Mie solutions" (infinite series) to scattering, absorption and phase function of electromagnetic waves by a homogeneous concentring shells.</td></tr><tr><td>1997</td><td>BART <a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a></td><td>A. Quirantes</td><td><a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a></td><td><a href="/facts/Fortran/m1KqjcMU">Fortran</a></td><td>Open source (own license)</td><td>Based on the Aden–Kerker theory to calculate light-scattering properties for coated spherical particles</td></tr><tr><td>2004</td><td>MjcLscCoatSph<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a></td><td>M. Jonasz</td><td></td><td>GUI/Windows</td><td>Proprietary / closed source</td><td>This program calculates the scattering, absorption, and attenuation parameters, as well as the angular scattering patterns of a single coated sphere according to Aden-Kerker theory.</td></tr><tr><td>2007</td><td></td><td>L. Liu, H. Wang, B. Yu, Y. Xu, J. Shen</td><td><a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a></td><td><a href="/facts/C_(programming_language)/Ky2No763">C</a></td><td>Unknown</td><td>Light scattering by a coated sphere (extinction efficiency, scattering efficiency, light scattering intensity)</td><td></td></tr><tr><td>2009-2022</td><td><a href="https://github.com/ovidiopr/scattnlay">Scattnlay</a></td><td>O. Pena, U. Pal, K. Ladutenko</td><td><a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a></td><td><a href="/facts/C%252B%252B/Et0F2qn9">C++</a>, Python, and <a href="/facts/JavaScript/XhhIIEsl">JavaScript</a></td><td>GPLv3</td><td>Light scattering from a multilayered sphere based on the algorithm by W Yang.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> Very robust and stable, slower than Toon and Ackerman. Evaluate integral parameters and angular patterns, near-field and power flow streamlines plotting. Has a compilation option to use <a href="/facts/Boost_(C%252B%252B_libraries)/vGLGG51A">Boost.Multiprecision</a> for higher accuracy.<p><a href="/facts/Web_application/BLkF3BIN">Web application</a> is the part of package, <a href="https://physics.itmo.ru/mie/">available</a> online on the website of Department of Physics and Engineering in ITMO University.</p></td></tr></tbody></table> <h3>Codes for electromagnetic scattering by cluster of spheres</h3> <table><tbody><tr><th>Year</th><th>Name</th><th>Authors</th><th>References</th><th>Language</th><th>Short Description</th></tr><tr><td>1998-2003</td><td>GMM</td><td>Yu-lin Xu and Bo A. S. Gustafson</td><td><a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></td><td>Fortran</td><td>Codes which calculate exactly electromagnetic scattering by an aggregate of spheres in a single orientation or at an average over individual orientations.</td></tr><tr><td>2013</td><td>MSTM</td><td>D. W. Mackowski</td><td><a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a></td><td>Fortran</td><td>Codes which calculate exactly electromagnetic scattering by an aggregate of spheres and spheres within spheres for complex materials. Works in parallel as well.</td></tr><tr><td>2015</td><td>py_gmm</td><td>G. Pellegrini</td><td><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></td><td>Python + Fortran</td><td>A Python + Fortran 90 implementation of the Generalized Multiparticle Mie method, especially suited for plasmonics and near field computation.</td></tr><tr><td>2017</td><td>CELES</td><td>A. Egel, L. Pattelli and G. Mazzamuto</td><td><a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a></td><td>MATLAB + CUDA</td><td>Running on NVIDIA GPUs, with high performance for many spheres.</td></tr><tr><td>2020</td><td>QPMS</td><td>M. Nečada</td><td><a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a></td><td>C, Python</td><td>Many-particle simulations in homogeneous media, supports various particle shapes in finite as well as infinite periodic configurations.</td></tr><tr><td>2021</td><td>SMUTHI</td><td>A. Egel et al.</td><td><a class="footnote-ref" id="fnref:27" href="#fn:27"><sup>27</sup></a><a class="footnote-ref" id="fnref:28" href="#fn:28"><sup>28</sup></a></td><td>Python + Fortran + CUDA</td><td>Many spheres in stratified media, other particle shapes are available.</td></tr></tbody></table> <h2 id="relevant-scattering-codes">Relevant scattering codes</h2> <ul><li><a href="/facts/Discrete_dipole_approximation_codes/6aNfztC5">Discrete dipole approximation codes</a></li> <li><a href="/facts/Codes_for_electromagnetic_scattering_by_cylinders/rXa5DDQV">Codes for electromagnetic scattering by cylinders</a></li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Computational_electromagnetics/uJKnwCar">Computational electromagnetics</a></li> <li><a href="/facts/Light_scattering_by_particles/pyNaTyrj">Light scattering by particles</a></li> <li><a href="/facts/List_of_atmospheric_radiative_transfer_codes/Mmtgr1hK">List of atmospheric radiative transfer codes</a></li> <li><a href="/facts/Optical_properties_of_water_and_ice/qkkfvufC">Optical properties of water and ice</a></li> <li><a href="/facts/Mie_theory/5mJc3SrT">Mie theory</a></li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="http://scatterlib.wikidot.com">SCATTERLIB: Collection of light scattering codes</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Bohren, Craig F. and Donald R. Huffman, Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., ISBN 0-471-29340-7, ISBN 978-0-471-29340-8 (second edition) <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Wriedt, T. (2009). "Light scattering theories and computer codes". Journal of Quantitative Spectroscopy and Radiative Transfer. 110 (11): 833–843. Bibcode:2009JQSRT.110..833W. doi:10.1016/j.jqsrt.2009.02.023. S2CID 33734719. <a href="https://zenodo.org/record/896157" target="_blank">https://zenodo.org/record/896157</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>This code is maintained as part of scatterlib, and can be downloaded from http://scatterlib.wikidot.com/mie <a href="http://scatterlib.wikidot.com/mie" target="_blank">http://scatterlib.wikidot.com/mie</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Bohren, Craig F. and Donald R. Huffman, Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., ISBN 0-471-29340-7, ISBN 978-0-471-29340-8 (second edition) <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>The MiePlot program can be downloaded from http://www.philiplaven.com/mieplot.htm <a href="http://www.philiplaven.com/mieplot.htm" target="_blank">http://www.philiplaven.com/mieplot.htm</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Philip Laven, "Simulation of Rainbows, Coronas, and Glories by use of Mie Theory", Applied Optics Vol. 42, 3, 436-444 (January 2003) plus various other published papers (all available at http://www.philiplaven.com/Publications.html). <a href="http://www.philiplaven.com/Publications.html" target="_blank">http://www.philiplaven.com/Publications.html</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Grainger, R.G.; Lucas, J.; Thomas, G.E.; Ewan, G. (2004). "The Calculation of Mie Derivatives". Appl. Opt. 43 (28): 5386–5393. Bibcode:2004ApOpt..43.5386G. doi:10.1364/AO.43.005386. PMID 15495430. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Mackowski, D.W.; Altenkirch, R. A.; Menguc, M. P. (1990). "Internal absorption cross sections in a stratified sphere". Applied Optics. 29 (10): 1551–1559. Bibcode:1990ApOpt..29.1551M. doi:10.1364/ao.29.001551. PMID 20563039. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Yang, W (2003). "Improved recursive algorithm for light scattering by a multilayered sphere". Applied Optics. 42 (9): 1710–1720. Bibcode:2003ApOpt..42.1710Y. doi:10.1364/ao.42.001710. PMID 12665102. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Toon, O. B.; Ackerman, T. P. (1981). "Algorithms for the calculation of scattering by stratified spheres". Applied Optics. 20 (20): 3657–3660. Bibcode:1981ApOpt..20.3657T. doi:10.1364/ao.20.003657. PMID 20372235. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Liu, L.; Wang, H.; Yu, B.; Xua, Y.; Shen, J. (2007). "Improved algorithm of light scattering by a coated sphere". China Particuology. 5 (3): 230–236. doi:10.1016/j.cpart.2007.03.003. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Toon, O. B.; Ackerman, T. P. (1981). "Algorithms for the calculation of scattering by stratified spheres". Applied Optics. 20 (20): 3657–3660. Bibcode:1981ApOpt..20.3657T. doi:10.1364/ao.20.003657. PMID 20372235. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Toon, Owen B.; Ackerman, T. P. (15 October 1981). "Algorithms for the calculation of scattering by stratified spheres". Applied Optics. 20 (20): 3657. Bibcode:1981ApOpt..20.3657T. doi:10.1364/AO.20.003657. <a href="https://atmos.uw.edu/~ackerman/Mie_code/rtpmie.ackerman.dmiess.f" target="_blank">https://atmos.uw.edu/~ackerman/Mie_code/rtpmie.ackerman.dmiess.f</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Bohren, Craig F. and Donald R. Huffman, Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., ISBN 0-471-29340-7, ISBN 978-0-471-29340-8 (second edition) <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Bohren, Craig F. and Donald R. Huffman, Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., ISBN 0-471-29340-7, ISBN 978-0-471-29340-8 (second edition) <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>/http://www.ugr.es/~aquiran/ciencia/codigos/bart.f <a href="http://www.ugr.es/~aquiran/ciencia/codigos/bart.f" target="_blank">http://www.ugr.es/~aquiran/ciencia/codigos/bart.f</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>A Quirantes and A V Delgado, The scattering of light by a suspension of coated spherical particles: effects of polydispersity on cross sections, J. Phys. D: Appl. Phys. 30 (1997) 2123–2131. <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>"||". <a href="http://www.mjcopticaltech.com/Products/LscCoatSphHelp.htm" target="_blank">http://www.mjcopticaltech.com/Products/LscCoatSphHelp.htm</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>Liu, L.; Wang, H.; Yu, B.; Xu, Y.; Shen, J. (2007). "Improved algorithm of light scattering by a coated sphere". China Particuology. 5 (3): 230–236. doi:10.1016/j.cpart.2007.03.003. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>O Pena and U Pal, Scattering of EM radiation by a multilayer sphere, Computer Physics Communications, 180, 2348-2354, 2009 <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>W Yang, Improved recursive algorithm for light scattering by a multilayered sphere, Applied Optics, Vol. 42, No. 9, 2003 <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> <li id="fn:22"><p>Yu-lin Xu, Bo A.S. Gustafson, A generalized multiparticle Mie-solution: further experimental verification, Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 395–419 <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li> <li id="fn:23"><p>"Scatcodes". <a href="http://www.eng.auburn.edu/users/dmckwski/scatcodes/" target="_blank">http://www.eng.auburn.edu/users/dmckwski/scatcodes/</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li> <li id="fn:24"><p>"A Generalized Multiparticle Mie code, especially suited for plasmonics: Gevero/py_gmm". GitHub. 2019-02-11. <a href="https://github.com/gevero/py_gmm" target="_blank">https://github.com/gevero/py_gmm</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li> <li id="fn:25"><p>"CELES: CUDA-accelerated electromagnetic scattering by large ensembles of spheres: Disordered-photonics/celes". GitHub. 2019-02-14. <a href="https://github.com/disordered-photonics/celes" target="_blank">https://github.com/disordered-photonics/celes</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></p></li> <li id="fn:26"><p>"QPMS: Electromagnetic multiple scattering library and toolkit". QPMS. 2022. <a href="https://qpms.necada.org" target="_blank">https://qpms.necada.org</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></p></li> <li id="fn:27"><p>"SMUTHI: Scattering by multiple particles in thin-film systems". 2022-01-21. <a href="https://smuthi.readthedocs.io/en/latest/_source/01%20about/about_smuthi.html" target="_blank">https://smuthi.readthedocs.io/en/latest/_source/01%20about/about_smuthi.html</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></p></li> <li id="fn:28"><p>Amos Egel, Krzysztof M. Czajkowski, Dominik Theobald, Konstantin Ladutenko, Alexey S. Kuznetsov, Lorenzo Pattelli, SMUTHI: A python package for the simulation of light scattering by multiple particles near or between planar interfaces, Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 273, p. 107846 (2021) DOI <a href="https://doi.org/10.1016/j.jqsrt.2021.107846" target="_blank">https://doi.org/10.1016/j.jqsrt.2021.107846</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></p></li> </ol>