Calculating the extinction cross section of a nanodisk with a removed wedge

fdtd
cross-section
array
extinction

#1

Dear all,

I am trying to reproduce the result of this nanodisk with the wedge (120degree) shown in Figure 1 of this paper. I would like to observe the fano resonance.

I have attached my simulation fsp. Can anyone help me, thanks.
extinction_unit cell.fsp (343.1 KB)

Also, i would like to ask how can i calculate the extinction cross section for arrays with different period.


#2

Hi @wxlim1,

I checked your simulation file and there are a couple of changes to improve it (modified simulation file: extinction_unit cell_modFG.fsp (292.1 KB)):

  • We recommended using a uniform mesh in the directions perpendicular to the propagation direction inside the TFSF source, as explained here. Therefore, I used the mesh override region to cover the entire TFSF source.
  • You can bring the boundaries of the cross-section analysis groups and the TFSF source closer to the structure, so that the mesh override region is as small as possible to save simulation time and memory. The size of the simulation region can be also reduced while making sure you leave a distance of at least half the maximum wavelength between the structure and the PML (in order to reduce evanescent fields at the PML).
  • I suggest using stretched-coordinate PML.
  • You can also take advantage of anti-symmetric boundary conditions.
  • For calculating the extinction cross section of a single nanodisk you can use this script: extinction_sigma.lsf (406 Bytes). See this KX post:

The extinction cross section seems quite sensitive to the mesh step in the mesh override region so you need to run a convergence test by refining the mesh. However, for dx=dy=1nm and dz=2nm, you can see two clear peaks near the expected wavelengths:

Not only the mesh will affect the peaks, the material fit can also play a role in causing discrepancies with respect to the results in the paper.

For periodic structures you can find the extinction cross section from 1 - (transmission measured inside the substrate). In this case you should use periodic boundary conditions and a plane wave source; the TFSF source it is not necessary as explained here.


#3

Dear @fgomez,

Thank you very much for helping me to check with my simulation. This has been bothering me for days.

Am i right to assume that using a simulation region with more than a wavelength or larger will not affect the overall results since it is used to reduce the evanescent fields at the PML? This is because i may increase the size of my structure and i do not want to keep expanding the simulation region along with the analysis group.

I didn’t know that the mesh override region should cover the entire TFSF source because for simulations related to transmission/reflection, mesh override region is only used to cover the structures.

Thank you again for the kind help. :slight_smile:


#4

Hi @fgomez,

May i ask how does the number of frequency points affect the simulation results?

E.g. if i want to monitor the source from 350 to 650 nm, why did you use 101 freq points? Isn’t the larger the better the accuracy, meaning more data points are gathered across the wavelength range.
Why does my results deviate even more?

Thanks.


#5

Hi @wxlim1,

See some comments and suggestions below:

If you increase the size of the structure significantly while keeping the same size of the simulation region, it can be an issue because you might get evanescent fields near the surface of the structure. It is a good idea to keep the same simulation region when comparing different structures, so you can probably use the simulation region size that works for the largest structure.

The number of frequency points does not have an impact on the simulation itself, it just affects the resolution of the frequency-domain results. FDTD is a time-domain method so it is necessary to Fourier transform the results to get frequency-domain data. The number of frequency points just controls how many points we take, it does not affect the time domain data.

I reduced the number of frequency points because this lowers the memory requirements. If you increase this number, you will get data for additional frequencies and your plot will look smoother.


#6

Thank you once again. :grin:


#7

2 posts were split to a new topic: Calculating the extinction cross section of a dual-disk ring plasmonic nanostructure


#8

Hello,

I would like to confirm one thing: can we or cannot we just sum up the absorption and scattering spectra together to get the extinction spectrum like shown in the script “extinction_sigma.lsf” from answer of @fgomez? Do we need to do different normalization for the two spectra before adding them up?

Thank you.


#9

Hi @wendu.ding,

I don’t think you need to use different normalizations for the the two spectra. To be consistent they should be normalized in the same way. In the cross-section calculations we normalize using the source intensity as explained here.