On the distribution of Born transmission eigenvalues in the complex plane

2023/04/19 by Narek Hovsepyan, Hovsepyan, Narek
Materials Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Metamaterials and Metasurfaces Applications #Orbital Angular Momentum in Optics

paper · pdf · doi:10.48550/arxiv.2304.09470

openalex publication_date 2023/04/19 · openalex created_date 2023/04/22 · openalex updated_date 2026/07/28

Abstract

We analyze an approximate interior transmission eigenvalue problem in \mathbb R^d for d=2 or d=3, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index with its first order approximation, which is an unbounded function. We show the discreteness of transmission eigenvalues in the complex plane. Moreover, using the radial symmetry we show the existence of (infinitely many) complex transmission eigenvalues and prove that there exists a horizontal strip in the complex plane around the real axis, that does not contain any transmission eigenvalues.

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