arXiv subjects

Haokun Sui

Publications and source records attributed to Haokun Sui.

3 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2026

Near Field Refraction Problem With Loss of Energy in Negative Refractive Index Material

This paper studies the near field refraction problem with loss of energy in negative refractive index material. Based on the relative refractive index $κ$, the analysis is categorized into two cases, namely $κ< -1$ and $-1 < κ< 0$. For each case, we give the definition of the refractor and discuss some crucial properties of it. The properties of Fresnel coefficients are also discussed. Based on these properties, the existence of the weak solution when the target measure is either discrete or a finite Radon measure are proved. Besides, the critical case $κ= -1$ is also discussed briefly at the end of this paper.

math.AP↗

arXiv2026

Far field refraction problem with loss of energy in negative refractive index material

This paper studies the far field refraction problem in negative refractive index material with loss of energy, which is a remaining problem in E. Stachura, Nonlinear Anal. 2017;157:76-103. The analysis is divided into two cases according to the relative refractive index $κ$, that is, $κ<-1$ and $-1<κ<0$. For each case, we use the Minkowski method to establish the existence of the weak solution when the target measure is either discrete or a finite Radon measure. Eventually, the inequality involving a Monge-Ampère type operator satisfied by the solution of the problem is derived, which is useful to understand this complex optical phenomenon.

math.AP↗