Some results on electromagnetic transmission eigenvalues

Authors

Fang Zeng, Chongqing University
Tiara Turner, University of Maryland Eastern Shore
Jiguang Sun, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

1-15-2015

Department

Department of Mathematical Sciences

Abstract

The electromagnetic interior transmission problem is a boundary value problem, which is neither elliptic nor self-adjoint. The associated transmission eigenvalue problem has important applications in the inverse electromagnetic scattering theory for inhomogeneousmedia. In this paper, we show that, in general, there do not exist purely imaginary electromagnetic transmission eigenvalues. For constant index of refraction, we prove that it is uniquely determined by the smallest (real) transmission eigenvalue. Finally, we show that complex transmission eigenvalues must lie in a certain region in the complex plane. The result is verified by examples.

Publisher's Statement

Copyright © 2014 John Wiley & Sons, Ltd. Publisher’s version of record: https://doi.org/10.1002/mma.3058

Publication Title

Mathematical Methods in the Applied Sciences

Recommended Citation

Zeng, F., Turner, T., & Sun, J. (2015). Some results on electromagnetic transmission eigenvalues. Mathematical Methods in the Applied Sciences, 38(1), 155-163. http://doi.org/10.1002/mma.3058
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3773