This paper presents a transient electromagnetic Maxwell solver (MS), a transient semiconductor Poisson-Drift-Diffusion (PDD) solver, and their numerical coupling. The proposed numerical solution schemes are based on Finite Element Method (FEM). Due to the solvers complexity it is important to carefully examine the obtained initial results. Therefore, a simple 1D pnjunction diode illuminated by an external electromagnetic plane wave is considered, as the stationary solutions of this structure such as the depletion width, built-in voltage, and carrier concentration distribution can be analytically obtained. The presented initially obtained transient results converge well to the analytic stationary solutions. The electromagnetic waves reflected from a diode with zero bias and 0.8 V bias structure reveal a small signal difference within a wide frequency range, which is an encouraging initial step towards more realistic simulations of scanning microwave microscopy structures and arrangements. The extension of the presented field formulations and numerical methods to 2D and 3D problems is straightforward.