Uniqueness and increasing stability in electromagnetic inverse source problems

TL;DR

This paper investigates the uniqueness and stability of electromagnetic source identification from boundary measurements across multiple frequencies, employing Fourier analysis and unique continuation principles to enhance understanding of inverse problems.

Contribution

It introduces new methods for proving uniqueness and increasing stability in electromagnetic inverse source problems using boundary data and Fourier transform techniques.

Findings

Established uniqueness of source determination in inhomogeneous media.

Derived increasing stability estimates with larger wave number intervals.

Provided explicit bounds for analytic continuation and boundary data analysis.

Abstract

In this paper we study the uniqueness and the increasing stability in the inverse source problem for electromagnetic waves in homogeneous and inhomogeneous media from boundary data at multiple wave numbers. For the unique determination of sources, we consider inhomogeneous media and use tangential components of the electric field and magnetic field at the boundary of the reference domain. The proof relies on the Fourier transform with respect to the wave numbers and the unique continuation theorems. To study the increasing stability in the source identification, we consider homogeneous media and measure the absorbing data or the tangential component of the electric field at the boundary of the reference domain as additional data. By using the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, Huygens' principle and bounds for initial boundary value problems, increasing (with larger wave numbers intervals) stability estimate is obtained.