Transmission Vs Periodicity


#1

Hi everyone,

I am trying to simulate the transmission of nano bar array on a glass substrate. The results show that the peak of transmission, which corresponds to localized surface plasmon resonance, depends on the periodicity. I assume that the coupling of nano bar between neighbouring cells is negligible, so resonance just relies on the geometry of nano bar, not the periodicity. The setup of simulation is referred to https://kb.lumerical.com/en/sp_periodic_structures.html

Hope you guys can help me about it. Thanks!


#2

Dear @jmz5364

I guess, as long as the peak of transmission is changing with periodocity, there is a coupling between the neighbouring nano bars. You can increase the number of periodicity to find out when the results are fixed/stabilized. On the other hand, scattering from neighbouring bars can effect the near field emission, which will affect the farfield emission.

If you are interested to see the results for a single nano bar, you can set boundary conditions to PML and run simulations.

I hope this was helpful.

Thanks


#3

Hey Dear bkhanaliloo,

Thanks for your reply!

You mentioned increasing the number of periodicity. I guess that you mean to increase the number of unit cell in the FDTD simulation region, but I don’t see the merit of doing so. Do you mean that I can increase the number of unit cell in the FDTD simulation region and use PML boundary condition on 6 faces in order to check if the results are fixed?

Yes. I can use PML and TFSFsource to investigate the LSPR of a single bar. However, this simulation setup can not be realized easily in experiments because of the difficulty of locating a single bar. What I want to do instead is to study the bar array with large periodicity length in order to get rid of coupling effect. In this process, Anti-symmetry and symmetry boundary condition will be used on the 4 side faces.

Hope to continue the discussion!

Good day you guys!


#4

Dear @jmz5364

Sorry for being confusing.

Yes, I meant to say that you can increase the number of periods inside a simulation region with PML boundary conditions (BCs) until results remain unchanged. The idea is to check and see how transmission changes with the number of bars (or periods). I think this will be the only way to say if coupling between bars, beyond some period, is negligible. If results are still changing, it means that there is still some coupling between neighbour bars. Does this make sense to you?

On the other hand, I am not quite sure how you define “coupling between bars”. Generally speaking, transmission is affected by the light scattered from each bar. Once you increase the number of bars, transmission plot will be modified. I think the part that I don’t understand is how you relate change in transmission with “coupling between the bars”. Maybe we are saying the same thing but from different aspects?

Yes, I understand the challenge. I think what you are planning is reasonable. Please keep me updated with your results and I will be happy to be of a help.

Thanks


#5

Good day @bkhanaliloo

Yes, I meant to say that you can increase the number of periods inside a simulation region with PML boundary conditions (BCs) until results remain unchanged. The idea is to check and see how transmission changes with the number of bars (or periods). I think this will be the only way to say if coupling between bars, beyond some period, is negligible. If results are still changing, it means that there is still some coupling between neighbour bars. Does this make sense to you?

On the other hand, I am not quite sure how you define “coupling between bars”. Generally speaking, transmission is affected by the light scattered from each bar. Once you increase the number of bars, transmission plot will be modified. I think the part that I don’t understand is how you relate change in transmission with “coupling between the bars”. Maybe we are saying the same thing but from different aspects?

I guess the coupling you mentioned origins from the scatter electromagnetic filed by each bar which may couple with neighboring bars. The strategy you mentioned seems a way to examine the longest distance that the scattering field can reach? Am I right?

The coupling effect I mentioned refers to the dipole coupling between neighboring bars. As you know, electromagnetic field induces the electric dipole in the bar. The coupling between the dipoles may introduce a damping effect (i. e., the oscillation of charges in a bar may be affected by that of the neighboring bars)

Thanks very much!


#6

Dear @jmz5364

Thank you very much for clarification, it was very helpful.

I think I understand the nature of coupling that you are discussing. However, I am not quite sure how you want to study this effect by looking at transmission? As we discussed, transmission plot is affected by scattering from all the bars located in simulation region and I am afraid we can not separate them from the light coming from a single bar. In other words, as you are including more periods, transmission results will include scattering from added periods.

I was thinking if you could directly study the filed intensity inside the bar. For example, you can add a pabs analysis group and study absorbed power in the central bar (object of interest) as you increase the number of periods. Please take a look at the example in the link that shows how to use pabs analysis group, and let me know if this is useful:

https://kb.lumerical.com/en/layout_analysis_pabs_adv.html

We can discuss it further if you think the approach makes sense.

Thanks