“…Numerical formulation of FDTD is achieved by considering the transient current , which can be calculated by using (8), (9), and (4) to yield (25) where (26) (27) (28) Source current at th timestep can be rewritten in terms of electrostatic field and time-dependent conductivity, and , respectively, as (29) Then, transient current is introduced in discrete form of Ampere's equation 7as (30) which enables a split formulation of Ampere-Maxwell and Faraday laws, of the form ( It also bears remarking that proposed procedure is prone to instabilities in the numerical solution. To avoid this, the Courant stability condition still holds for the solution of the combined drift-diffusion and FDTD scheme, but other challenging issues appear in this case which differ from the usual electromagnetic case: on one hand, the complete system of equations is nonlinear, because of the recombination function (12) appearing in (10) and (11) and, on the other hand, terms related to distribution of carriers and act as diffusive sources of the electromagnetic field.…”