Abs and scattering cross sections of periodic structure



Questions_scattering.fsp (309.5 KB)

I would like to calculate the absorption and scattering cross sections from a periodic structure.
I found on the lumerical website that I should use plane wave not TFSF , T and R monitors to calculate the scattering cross sections.
My questions is:
how can I get the abs and scattering cross sections from the T and R monitors ?

I found this sentence written in lumerical community “for a certain wavelength that means that 20% percent of the light coming in gets transmitted so you can interpret the transmission cross section to be 20% of the unit cell area”

it is confusing because scattering might be in air and in the substrate which means we need to consider (R +T) to calculate the scattering cross sections.
secondly, for calculation of scattering cross sections is that correct?
sigma_scattered = (Reflection (f)+Transmission (f))/ source intensity


Hi @maisaad

You can still use TFSF source with periodic BCs:

Since the structure is periodic, any light that leaves the simulation region from one side will be injected from other side. That’s why you need only T and R monitors rather than 6 monitors encompassing the TFSF source.

You can use T and R monitors inside and outside the TFSF source to calculate the absorption and scattering cross sections, respectively as we have done in the mie scattering example:

For periodic structures you can also define reflection cross section as is explained in the link below:

and we have:

sigma_scattered = (Reflection (f)+Transmission (f))*sourcepower(f)/ source intensity(f)

where T and R monitors are located outside the TFSF source region.


Thank for your reply.
I modified the simulation source and monitors as you mentioned.
However, I have two problems first , the Reflection is more than one as indicated in that imageReflection. is there some thing wrong with monitors locations
Second, I used this script to plot the sigma scattering is there something wrong in line three?
sigma_scattered =(Reflection(f)+Transmission (f))sourcepower(f)/ source intensity(f));
1e9,sigma_scattered,“wavelength (nm)”,“scattering”);Questions_scattering.fsp (308.4 KB)


Hi @maisaad

I spent quite a lot of time to understand transmission/reflection larger than 1 but I was not quite sure if the problem is due to post processing done internally within TFSF source or due to normalization. I guess a good approach here would be to remove substrate and study the periodic scatterer using plane wave source. The effect of substrate may be ignored as it has a relatively flat contribution on the reflection, and may be only red shifting the spectra compared to no-substrate case. Please let me know of your thoughts.

Once you are using plane wave source, you will have transmission and reflection results. I am not quite sure how we can extract the scattering cross section with these results. If you have any references that show how they interpret the reflection and transmission results to obtain scattering cross section, maybe you can share them with me.