reflection at a flat silicon surface

fdtd

#1

I calculated the reflected intensity for a flat silicon surface and wavelengths between 1µm and 15µm using simple fresnel reflection formula (vertical beam).

I compared this result with fdtd simulations and to my suprise there are big differences between fdtd results and analytical results. These differences seem to depend on the chosen bandwidth of the plane wave source. See the fsp-file attached 21_Si_Quader_2D.fsp (274.8 KB)

If the numerical calculation is done with a source bandwith from 2,5 µm to 15 µm, the results are close to the analytical solution in the range between 7 µm and 15 µm.
If the numerical calculation is done with a source bandwith from 5 µm to 15 µm, the results are close to the analytical solution in the range between 13 µm and 15 µm.
If the numerical calculation is done with a source bandwith from 7 µm to 15 µm, the results are completey different compared with the analytical solution.

Adapting the material fit or expanding or minimizing the region do not change the numerical results. I used a 2D simulation and PML conditions.

Does somebody my mistake? I would expect that all grahps show the same course.


#2

Hi,
I just used finer mesh.
simulation file :21_Si_Quader_2D.fsp (874.1 KB)
Best regards.
Dezyani


#3

Thanks @m.dezyani . You are right, refining the grid quickly gets you closer to the analytical result.

You can use the stackrt script function for getting the analytical result using the transfer matrix method: compare_analytical_reflection.lsf (465 Bytes).