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PreprintCC BY 4.0arXiv

A Critical Case for the Near Field Refraction Problem in Negative Refractive Index Material

  • Yi He
  • Feida Jiang
  • Haokun Sui
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Abstract

This paper studies the near field refraction problem for the critical case in negative refractive index material. Snell law in vector form is first reviewed, and the physical constraint governing refraction is discussed. We then define the refractor for the critical case and analyze several of its key properties. Building on these properties, we introduce the notion of a weak solution to this problem and prove the existence of the weak solution when the target measure is either discrete or a finite Radon measure. The proof relies on the Minkowski method, an iterative approach to refraction and reflection problems in geometric optics.

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Cite

BibTeXRIS
BibTeX
@misc{he2026critical,
  title = {{A Critical Case for the Near Field Refraction Problem in Negative Refractive Index Material}},
  author = {Yi He and Feida Jiang and Haokun Sui},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26998},
  eprint = {2610.26998},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26998},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Critical Case for the Near Field Refraction Problem in Negative Refractive Index Material
AU  - Yi He
AU  - Feida Jiang
AU  - Haokun Sui
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26998
UR  - https://arxiv.org/abs/2610.26998
AB  - This paper studies the near field refraction problem for the critical case in negative refractive index material. Snell law in vector form is first reviewed, and the physical constraint governing refraction is discussed. We then define the refractor for the critical case and analyze several of its key properties. Building on these properties, we introduce the notion of a weak solution to this problem and prove the existence of the weak solution when the target measure is either discrete or a finite Radon measure. The proof relies on the Minkowski method, an iterative approach to refraction and reflection problems in geometric optics.
ER  -