Shape identification of anisotropic diffraction gratings for TM-polarized electromagnetic waves

Abstract

This paper concerns the shape identification problem of anisotropic periodic structures which are known as diffraction gratings. We study the so-called Factorization method as a tool for reconstructing the anisotropic periodic media from measured spectral data involving scattered electromagnetic waves in TM modes. This sampling method provides a simple criterion to compute a picture of shape of diffraction gratings in a rapid way. We propose a rigorous analysis for the method as well as numerical experiments to examine its performance.

Keywords:

• diffraction gratings
• factorization method
• inverse scattering
• TM modes

AMS Subject Classifications:

• 78A46
• 35R30

Acknowledgments

We would like to thank Houssem Haddar and Armin Lechleiter for useful discussions, as well as the anonymous referees for valuable comments.