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Mathematics > Analysis of PDEs

arXiv:2503.04536v2 (math)
[Submitted on 6 Mar 2025 (v1) , last revised 15 Jul 2025 (this version, v2)]

Title: Double metasurfaces and Optimal transport

Title: 双超表面和最优传输

Authors:Irem Altiner, Cristian E. Gutiérrez
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.
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
Subjects: Analysis of PDEs (math.AP) ; Materials Science (cond-mat.mtrl-sci); Optics (physics.optics)
MSC classes: 49Q22, 78A05, 78A46
Cite as: arXiv:2503.04536 [math.AP]
  (or arXiv:2503.04536v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2503.04536

Submission history

From: Cristian Gutierrez [view email]
[v1] Thu, 6 Mar 2025 15:21:53 UTC (446 KB)
[v2] Tue, 15 Jul 2025 15:45:23 UTC (182 KB)
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