Work

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

Year: 2026

Type: article

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-Ampère type operator satisfied by the solution of the problem is derived, which is useful to understand this complex optical phenomenon.

Source: Mathematics in Engineering

DOI: 10.3934/mine.2026004

Authors: Haokun Sui, Feida Jiang

Institutions: Southeast University, Shanghai Institute for Mathematics and Interdisciplinary Sciences

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Southeast University

Awards: G283934269, G3044850942