The reconstruction of a time-dependent source from a surface measurement for full Maxwell's equations by means of the potential field method

This paper is devoted to the study of an inverse source problem governed by full Maxwell's equations by means of the potential field method (the A-ϕ method). The source term is assumed to be separable in time and space, in which the unknown part is solely time-dependent and is recovered from a surface measurement. We prove that the solution to the inverse problem based on the A-ϕ formulation is existing and unique. We suggest a constructive scheme for approximating the solution and discuss its convergence. Finally, a few examples are presented to verify the theoretical results.