# Extinction, scattering and absorption cross-sections for a periodic array

#1

Hi,

I am trying to obtain extinction, scattering and absorption cross-sections for a periodic array of metal nanorings.

In the mie scattering example, there are two analysis monitors, ‘Total’ and ‘scat’ enclosing the metal structure, and the whole system is inside the FDTD simulation region. And the TFSF source is sandiwiched between the ‘Total’ and ‘scat’ monitors.
For a periodic array, I changed the FDTD region to include only the unit cell and changed the input source to a plane wave source, but here is where I get confused with the set up for the monitors. How do I construct the monitors in this case to obtain the scattering and absorption cross-sections if the FDTD region is not enclosing the whole system but just the unit cell? Could you have to look at my .fsp file and explain how I should modify it to make it work?

Sorry for the inconvenience,

Sean Park

MNR_Array_extinction.fsp (318.1 KB)

#2

Hi, @hc.park !

Because of the structure geometry, you can’t get a unit cell with no elements touching the boundary ( in the framework of the Cartesian coordinate system). In turn, the requirement for usage of the TFSF source is the uniform index profile along the boundary, so that it is of no use in your case.

I suggest using pre-written scripts from the optical power analysis group:
https://kb.lumerical.com/en/layout_analysis_optical_power.html

Also, you might be interested in calculating s-parameters, for which there is corresponding script in the advanced analysis category: https://kb.lumerical.com/en/layout_analysis_advanced_tool.html

If having problems with your simulation, don’t hesitate to write.

#3

Hi @hc.park and @msaygin,

For periodic structures the TFSF source is usually not required, unless you are interested in scattering in the specular direction, which requires removing the specular reflection from the substrate. In most cases a regular plane wave source is appropriate.

In your setup, the monitor above the source (“Reflection”) gives you the fraction of the source power reflected by the structure. Since the source power is integrated over one unit cell, the fraction you get can be interpreted as a cross section relative to the area of the unit cell. For example, if the reflected power is 10%, this means that the reflection cross section is 10% of the unit cell area. The same applies to other quantities like absorption. You just need to measure it as you would normally do, and interpret the fraction as a fraction of the unit cell area.

Hope this helps!

#4

Hello, @fgomez and @msaygin thank you for the comment. I will assume the setup is correct and see what I can obtain from it.