On the inverse scattering from anisotropic periodic layers and transmission eigenvalues

ABSTRACT

This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from near field scattering data. This method provides a fast numerical algorithm as well as a unique determination for the shape reconstruction of the scatterer. We present a rigorous justification and numerical examples for the factorization method. The transmission eigenvalue problem in scattering have recently attracted a lot of attentions. Transmission eigenvalues can be determined from scattering data and they can provide information about the material parameters of the scatterers. In this paper, we formulate the interior transmission eigenvalue problem and prove the existence of infinitely many transmission eigenvalues for the scattering from anisotropic periodic layers.

Keywords:

• Inverse scattering
• Factorization method
• transmission eigenvalues
• anisotropic periodic structure
• TM polarization

AMS Subject Classifications:

• 35R30
• 78A46
• 65C20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the NSF [grant number DMS-1812693] and the Faculty Enhancement Program Award from Kansas State University