FDTD 1D with scattered field /total field boundary

How to implement total/ scattered field boundary so that there is no reflection on the TF SF boundary due to numerical dispersion ? The TFSF total/ scattered field boundary should work away from the magic step perfectly. Here m=2, c*dt = 1/2dx;

I am trying to match the numerical dispersion by propagating the incident field in its own grid. Seems it is incorrect as the field is canceling entering the scattered field region on its way back.

If I define continuous H and E (phase shifted )incoming field as plane wave, There is some reflection on the TS TF boundary. Is it possible to remove.

Mur absorption boundary | SF 1/3 of the grid | Total field 2/3 | Mur absorption boundary

Update equations at TFSF boundary

H at (L-1/2),(t+1/2) = H at (L-1/2),(t+1/2) + const*Eincident at (L),(t)

E at (L),(t+1) = H at (L),(t+1) + const*Hincident at (L-1/2),(t+1/2)