Time-Domain Direct Sampling Method for Inverse Electromagnetic Scattering with a Single Incident Source

In this paper, we consider an inverse electromagnetic medium scattering problem of reconstructing unknown objects from time-dependent boundary measurements. A novel time-domain direct sampling method is developed for determining the locations of unknown scatterers by using only a single incident source. Notably, our method imposes no restrictions on the waveform of the incident wave. Based on the Fourier--Laplace transform, we first establish the connection between the frequency-domain and the time-domain direct sampling method. Furthermore, we elucidate the mathematical mechanism of the imaging functional through the properties of modified Bessel functions. Theoretical justifications and stability analyses are provided to demonstrate the effectiveness of the proposed method. Finally, several numerical experiments are presented to illustrate the feasibility of our approach.