Double metasurfaces and Optimal transport
Analysis of PDEs
2025-07-16 v2 Materials Science
Optics
Abstract
This paper constructs metalenses that separate homogeneous media with different refractive indices, refracting one domain into another while conserving a prescribed energy distribution. Using optimal transport theory, we design singlet and doublet metalenses satisfying energy conservation by refraction, and obtain partial regularity of the optimal maps involved.
Cite
@article{arxiv.2503.04536,
title = {Double metasurfaces and Optimal transport},
author = {Irem Altiner and Cristian E. Gutiérrez},
journal= {arXiv preprint arXiv:2503.04536},
year = {2025}
}
Comments
35 pages, 2 figures. This replaces Version 1, where the results were demonstrated using flows. Additionally, the multimarginal Monge problem and its application discussed in Version 1 are not included in this version and will be addressed in a separate paper