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

Haokun Sui; Feida Jiang

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arXiv · 2603.11092

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

Haokun Sui·Feida Jiang

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Abstract

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 $\kappa$, that is, $\kappa<-1$ and $-1<\kappa<0$. 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-Amp\`ere type operator satisfied by the solution of the problem is derived, which is useful to understand this complex optical phenomenon.

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Haokun Sui, Feida Jiang. 2026-03-11. Far field refraction problem with loss of energy in negative refractive index material. https://arxiv.org/abs/2603.11092

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