Metasurfaces and Optimal transport
Gutiérrez, Cristian E.1 ; Huang, Qingbo2 ; Mérigot, Quentin3 ; Thibert, Boris4
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, Tome 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.

Publié le :
DOI : 10.5802/smai-jcm.84
Classification : 49N45
Mots clés : optimal transport, metasurfaces
Gutiérrez, Cristian E. 1 ; Huang, Qingbo 2 ; Mérigot, Quentin 3 ; Thibert, Boris 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 
@article{SMAI-JCM_2022__8__201_0,
     author = {Guti\'errez, Cristian E. and Huang, Qingbo and M\'erigot, Quentin and Thibert, Boris},
     title = {Metasurfaces and {Optimal} transport},
     journal = {The SMAI Journal of computational mathematics},
     pages = {201--224},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {8},
     year = {2022},
     doi = {10.5802/smai-jcm.84},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/smai-jcm.84/}
}
TY  - JOUR
AU  - Gutiérrez, Cristian E.
AU  - Huang, Qingbo
AU  - Mérigot, Quentin
AU  - Thibert, Boris
TI  - Metasurfaces and Optimal transport
JO  - The SMAI Journal of computational mathematics
PY  - 2022
SP  - 201
EP  - 224
VL  - 8
PB  - Société de Mathématiques Appliquées et Industrielles
UR  - http://www.numdam.org/articles/10.5802/smai-jcm.84/
DO  - 10.5802/smai-jcm.84
LA  - en
ID  - SMAI-JCM_2022__8__201_0
ER  - 
%0 Journal Article
%A Gutiérrez, Cristian E.
%A Huang, Qingbo
%A Mérigot, Quentin
%A Thibert, Boris
%T Metasurfaces and Optimal transport
%J The SMAI Journal of computational mathematics
%D 2022
%P 201-224
%V 8
%I Société de Mathématiques Appliquées et Industrielles
%U http://www.numdam.org/articles/10.5802/smai-jcm.84/
%R 10.5802/smai-jcm.84
%G en
%F SMAI-JCM_2022__8__201_0
Gutiérrez, Cristian E.; Huang, Qingbo; Mérigot, Quentin; Thibert, Boris. Metasurfaces and Optimal transport. The SMAI Journal of computational mathematics, Tome 8 (2022), pp. 201-224. doi : 10.5802/smai-jcm.84. http://www.numdam.org/articles/10.5802/smai-jcm.84/

[1] The runners-up, Science, Volume 354 (2016) no. 6319, pp. 1518-1523 | DOI

[2] Abedin, Farhan; Gutiérrez, Cristian E; Tralli, Giulio C 1,α estimates for the parallel refractor, Nonlinear Anal., Theory Methods Appl., Volume 142 (2016), pp. 1-25 | DOI | Zbl

[3] Chen, Wei Ting; Capasso, Federico Will flat optics appear in everyday life anytime soon?, Appl. Phys. Lett., Volume 118 (2021) no. 10, p. 100503 | DOI

[4] Gutiérrez, Cristian E.; Huang, Qingbo The refractor problem in reshaping light beams, Arch. Ration. Mech. Anal., Volume 193 (2009) no. 2, pp. 423-443 | DOI | MR | Zbl

[5] Gutiérrez, Cristian E.; Huang, Qingbo The near field refractor, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 31 (2014) no. 4, pp. 655-684 | DOI | Numdam | MR | Zbl

[6] Gutiérrez, Cristian E.; Pallucchini, Luca Reflection and refraction problems for metasurfaces related to Monge-Ampère equations, Journal Optical Society of America A, Volume 35 (2018) no. 9, pp. 1523-1531 | DOI

[7] Gutiérrez, Cristian E.; Pallucchini, Luca; Stachura, Eric General refraction problems with phase discontinuities on nonflat metasurfaces, Journal Optical Society of America A, Volume 34 (2017) no. 7, pp. 1160-1172 | DOI

[8] Gutiérrez, Cristian E.; Sabra, Ahmad Aspherical lens design and imaging, SIAM J. Imaging Sci., Volume 9 (2016) no. 1, pp. 386-411 | DOI | MR | Zbl

[9] Gutiérrez, Cristian E.; Sabra, Ahmad Freeform lens design for scattering data with general radiant fields, Arch. Ration. Mech. Anal., Volume 228 (2018), pp. 341-399 | DOI | MR | Zbl

[10] Gutiérrez, Cristian E.; Sabra, Ahmad Chromatic aberration in metalenses, Adv. Appl. Math., Volume 124 (2021), pp. 1090-2074 | DOI | MR | Zbl

[11] Kitagawa, Jun; Mérigot, Quentin; Thibert, Boris Convergence of a Newton algorithm for semi-discrete optimal transport, J. Eur. Math. Soc., Volume 21 (2019) no. 9, pp. 2603-2651 | DOI | MR | Zbl

[12] Lin, Ren Jie; Su, Vin-Cent; Wang, Shuming; Chen, Mu Ku; Chung, Tsung Lin; Chen, Yu Han; Kuo, Hsin Yu; Chen, Jia-Wern; Chen, Ji; Huang, Yi-Teng et al. Achromatic metalens array for full-colour light-field imaging, Nature nanotechnology, Volume 14 (2019) no. 3, pp. 227-231

[13] Merigot, Quentin; Thibert, Boris Optimal transport: discretization and algorithms, Handbook of Numerical Analysis, Volume 22, Elsevier, 2021, pp. 133-212

[14] Meyron, Jocelyn Initialization procedures for discrete and semi-discrete optimal transport, Comput.-Aided Des., Volume 115 (2019), pp. 13-22 | DOI | MR

Cité par Sources :