JOURNAL OF COMPUTATIONAL MATHEMATICS

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Metasurfaces and Optimal transport
Cristian E. Gutiérrez1; Qingbo Huang2; Quentin Mérigot3; Boris Thibert4
1 Department of Mathematics Temple University Philadelphia, PA 19122
2 Department of Mathematics and Statistics Wright State University Dayton, OH 45435
3 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France & Institut universitaire de France (IUF)
4 Université Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 201-224.

This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for the numerical solution we study and implement a damped Newton algorithm to solve the semi discrete problem. A detailed analysis is carried out to solve the near field one source refraction problem and extensions to the far field are also mentioned.

Published online:
DOI: 10.5802/smai-jcm.84
Classification: 49N45
Keywords: optimal transport, metasurfaces

Cristian E. Gutiérrez 1; Qingbo Huang 2; Quentin Mérigot 3; Boris Thibert 4

1 Department of Mathematics Temple University Philadelphia, PA 19122
2 Department of Mathematics and Statistics Wright State University Dayton, OH 45435
3 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France & Institut universitaire de France (IUF)
4 Université Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Metasurfaces and {Optimal} transport},
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Cristian E. Gutiérrez; Qingbo Huang; Quentin Mérigot; Boris Thibert. Metasurfaces and Optimal transport. The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 201-224. doi : 10.5802/smai-jcm.84. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.84/

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