# Abs and scattering cross sections of periodic structure

#1

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

#2

You can still use TFSF source with periodic BCs:
https://kb.lumerical.com/en/index.html?ref_sim_obj_tfsf_source_in_periodic_boundaries.html

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:
https://kb.lumerical.com/en/index.html?particle_scattering_mie_3d.html

For periodic structures you can also define reflection cross section as is explained in the link below:
https://kb.lumerical.com/en/index.html?ref_sim_obj_tfsf_cross_section_and_normalization.html

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.

#3

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 image. 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?
f=getdata(“T”,“f”);
lambda=c/f;
sigma_scattered =(Reflection(f)+Transmission (f))sourcepower(f)/ source intensity(f));
plot(lambda
1e9,sigma_scattered,“wavelength (nm)”,“scattering”);Questions_scattering.fsp (308.4 KB)

#4