Beltrami Herglotz functions for electromagnetic scattering theory in chiral media

Abstract

In this article, Herglotz functions of electromagnetic fields in a chiral medium are considered. The left-circularly polarized and the right-circularly polarized Beltrami Herglotz functions are defined by an integral representation over the unit sphere where the corresponding kernels are exactly the Beltrami far-field patterns. Herglotz condition holds true for these Beltrami Herglotz functions and a density theorem is proved. It is shown that Beltrami Herglotz kernels can be obtained from the Beltrami fields without the need to expand them in eigenvectors. Using the Beltrami Herglotz functions, an electromagnetic Herglotz pair in a chiral medium is defined and it is proved that it satisfies the Herglotz condition. The corresponding far-field patterns are considered and a density theorem is obtained.

Keywords:

• Herglotz functions
• Chiral media
• AMS Subject Classifications: 35Q60
• 78A45