The enclosure method for the anisotropic Maxwell system

TL;DR

This paper introduces an enclosure method for reconstructing obstacles in anisotropic electromagnetic media, overcoming the lack of complex geometrical optics solutions by employing oscillating-decaying solutions and Meyers' estimates.

Contribution

It develops a novel reconstruction scheme for anisotropic Maxwell systems using oscillating-decaying solutions, a significant advancement over previous methods.

Findings

Successfully reconstructs obstacles in anisotropic media

Introduces oscillating-decaying solutions for Maxwell's equations

Validates the scheme with Meyers' L^{p} estimates

Abstract

We develop an enclosure-type reconstruction scheme to identify penetrable and impenetrable obstacles in electromagnetic field with anisotropic medium in \mathbb{R}^{3}. The main difficulty in treating this problem lies in the fact that there are so far no complex geometrical optics solutions available for the Maxwell's equation with anisotropic medium in \mathbb{R}^{3}. Instead, we derive and use another type of special solutions called oscillating-decaying solutions. To justify this scheme, we use Meyers' L^{p} estimate, for the Maxwell system, to compare the integrals coming from oscillating-decaying solutions and those from the reflected solutions.