Direct and inverse problems for the nonlinear time-harmonic Maxwell equations in Kerr-type media

2017/09/21 by Yernat M. Assylbekov, Ting Zhou, Assylbekov, Yernat M. +1
Engineering · Mathematics · #35Q60 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.1709.07767

openalex publication_date 2017/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of the medium by making electromagnetic measurements on the boundary. We are interested in the case of the time-harmonic Maxwell equations.

Citations

• Nonlinear Properties of Left-Handed Metamaterials
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem
• A note on time-harmonic Maxwell equations on Riemannian manifolds

Cited by

• The DC Kerr Effect in Nonlinear Optics

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