On finding a penetrable obstacle using a single electromagnetic wave in the time domain

TL;DR

This paper develops a time domain enclosure method for inverse obstacle problems governed by Maxwell's equations, enabling detection of penetrable obstacles using a single electromagnetic wave in the time domain.

Contribution

It establishes the theoretical foundation for applying the time domain enclosure method to Maxwell systems with a single wave, including asymptotic inequalities for the indicator function.

Findings

Established the base of the method for Maxwell's equations in inhomogeneous media.

Realized the method for homogeneous and isotropic background media.

Provided a framework for detecting penetrable obstacles with a single electromagnetic wave.

Abstract

The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell system and consists of two parts. The first part establishes the base of the time domain enclosure method for the Maxwell system using a single set of the solutions over a finite time interval for a general (isotropic) inhomogeneous medium in the whole space. It is a system of asymptotic inequalities for the indicator function which may enable us to apply the time domain enclosure method to the problem of finding unknown penetrable obstacles embedded in various background media. As a first step of its expected applications, the case when the background medium is homogeneous and isotropic, is considered and the time domain enclosure method is realized. This is the second part.