Why is the Scattering Cross Section negative?

fdtd

#1

Dear all,

I have a question regarding the simulation of Gold nanosphere on TiO2 substrate,
when I calculate the Scattering Cross Section I get negative results at some wavelengths!

Here is the structure:

Here is the result:

I also have a question, I feel it is little bit arbitrary to choose the position of the scattering cross section analysis group, What I mean is: wouldn’t the results differ if I moved it a little bit? (Then the results are not unique and random ? ).

Thank you.


#2

Dear Ahmed,

I think the main issue in your simulation is the proximity of the PML to the structure. It is a good practice to leave a distance of at least half the maximum wavelength between the structure and the PML; the reason is that we want to avoid evanescent fields at the PML, which can be difficult to absorb. After increasing the simulation size I got a scattering cross section positive everywhere:

The simulation I used is attached: D=9nm_simplified.fsp (259.1 KB). For simplicity I centered the sphere at the origin. Some additional changes that helped with the simulation are:

  • Used smaller mesh accuracy (level 2) and used the mesh override “mesh_particles” to refine the region of the TFSF source and the cross-section monitor (dx = dy = dz = 0.5 nm).
  • Used symmetric and antisymmetric boundary conditions to speed up the simulation.

If the results for the cross section have converged (if the mesh is fine enough, etc.), they should not depend on the position of the analysis group as long as it encloses the sphere and part of the substrate. The reason is that the cross section is calculated from the transmission through the box monitor, which should be independent of the size of the box (note that the substrate is lossless).


#3

Thank you for your great reply , I have some questions :

How can I choose this number? (is it because resonance happens at around 520nm ?)

Does that mean it’s dependent on the position in case of lossy materials?

Thank you again.


#4

Hi Ahmed,

You are welcome!

The proposed values for the mesh step dx=dy=dz=0.5nm were motivated by the size of the sphere. I just wanted to find a coarse mesh that gives you something that resembles a sphere. You can look at an index preview of the structure using an index monitor. This is what you get for the file I modified:

Note that this is probably too coarse for accurate results but it is not too bad for a starting point if you want a quick initial simulation.

Regarding the situation when the substrate is absorbing (or if you have a multilayer array), there are some subtleties about the absorption and scattering cross section, as explained in the last section of this KB page.