Source in Maxwell equation


I have a question about the implementation of the source term from the Maxwell equation in FDTD Solution. If I choose a electric dipole source, then we can have the following equation:

Now, in FDTD, is the dipole time signal the P_ex term on the right hand side of the equation, or double partial derivative of the P_ex? Also, how does FDTD define the electric dipole? From positive charge to negative or the reverse?

Thank you very much.

Dear @wendu.ding

In FDTD, we don’t solve the wave equations rather we calculate E and H field by alternatively in time domain over mesh grids. If we have a source in our simulation region (dipole source in this case), the effect of the source field will be added to the simulation region as a function of time. This E filed is very similar to as what you see in the signal vs time panel for the dipole source. As a result the polarization of the dipole source is defined by the direction of the electric field.

I hope this could clarify the problem.