Solving the multi-frequency electromagnetic inverse source problem by the Fourier method

TL;DR

This paper introduces a Fourier-based method for reconstructing current sources in Maxwell's equations from multi-frequency data, supported by rigorous proofs and numerical validation.

Contribution

It presents a novel Fourier method for the inverse source problem in Maxwell's equations, extending techniques from scalar Helmholtz problems to vector systems.

Findings

Method is mathematically justified.

Numerical examples confirm feasibility.

Effective in reconstructing sources.

Abstract

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method.