@article{Sui2026, 
author = {Haokun Sui and Feida Jiang},
title = {Far field refraction problem with loss of energy in negative refractive index material},
year = {2026},
journal = {Mathematics in Engineering},
volume = {8},
number = {1},
pages = {98-139},
keywords = {negative refraction, far field, weak solution, loss of energy, Monge-Ampère type operator},
url = {https://www.sciopen.com/article/10.3934/mine.2026004},
doi = {10.3934/mine.2026004},
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    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.}
}