Plasmonic lattice band diagram



I am interested in calculating the band diagrams of a 2D plasmonic lattice. as usual I am using the dipole cloud combined with the proper sweep along edges of IRBZ. Although the final result after processing gives me an idea about the map however as you can see a lot is going on there. Some of the straight lines with linear dispersion could be recognized as folded light lines but there are some discontinuities which I am not sure about. (e.g. please check the X-point)
Your feedback to resolve the issue would be really appreciated.

Thank you!

plasmonic_lattice_alumina_Lumerical.fsp (286.1 KB)


Dear @hadiseh.alaeian

Can you please provide a reference for this structure? One thing that concerns me is the geometry that contains metal. This object will trap the light, and I am not sure about the application example of periodic array of these cavities.

I was not also quite clear about discontinuances that you mentioned at X-point. Do you mean that band diagrams are discontinuous? Can you please elaborate more and point out the point in the plot?

Regardless of them, I ran the simulations for different meshes, number and location of point monitors, and apodization time. The strength of the peak might vary a bit, but the band diagrams are the same.

Please keep me updated with your thoughts and I will be glad to be of a help.



Dear @bkhanaliloo
This is the device I have designed and fabricated for my experiment and it supposed to have a resonance at 795nm at Gamma point (kx = ky = 0) The metallic particles indeed trap the light and this is the thing I’m using to have a long cavity ring down (or large Q-factor).
In the attached figure I saturated the scale to show the discontinuity better. As you can see at X-point the band structure is discontinuous. I highlighted this with the white box there and I am referring to the sudden jump at that point from f~4e14 along gamma-X to f ~3.3e14 along X-M.
yes, you’re absolutely right about the dependency of the peak intensities on the simulation features but I also noticed that the main trend is the same so I assumed that the current features are OK. However in all of them I got that features at X-point.
Please let me know if further info is needed.


Dear @hadiseh.alaeian

Thank you very much for additional information. I think I have a better understanding of the geometry and application of interest. I also could see the resonance at at ~795 nm at kx=ky=0 point.

Unfortunately I was not still clear what you are referring to as the jump. To be more specific, are you referring to the jump at point A. point B, or from point A to point B in the plot below?

To me this is a complicated band diagram with lots of bands and multiple band crossings. While its complicated, I didn’t find anything out of ordinary at this moment.

At point X, the direction on the Brillouin zone is changing. This might results in a big shift in the direction of each individual band. Also, I think the point A and B belong to two different bands and the gap between these two bands is normal.

Thank you for your patience.


Dear @bkhanaliloo

Thank you for the response!
Yes, I was referring to the jump from point A to point B. You’re right that the directions from Gamma-X and X-M are different but at point X they should lead to same frequency since kx=0.5 and ky=0 on both directions. At the moment it’s not clear for me that why X-M bands doesn’t start from A. In fact we can see a faint continuous band at A in X-M direction but then it suddenly disappears.

Thank you for all the help!


Dear @hadiseh.alaeian

Thanks again for additional information.

I discussed this with my colleagues but we still could not find a problem in the bandstructure diagram. For example, if you look at the badnstructure in this KB example (an screen shot is provided below), you can see that bands do not necessarily converge to the same point at X point.

You mentioned that you have fabricated these results. Do you have a theory or reference that explains why the bands should meet? Since my physics background in plasmonic/bandstructure calculations is short, there might be something that I am missing. Simulation wise, everything looks normal.

Thank you for your patience.


Dear @bkhanaliloo

Thank you for the message!
Maybe I have to clarify myself better - by meeting the bands I didn’t want to imply that all the bands should meet at Gamma,X, or K points. In fact there might be bandgaps which are indeed very interesting. However even if two bands can can be completely separated by the gap each band should be continuous. For example in your example while we have very different separated bands each one is continuous.
In my case I have a continuous branch along Gamma-X with maximum point A. After that when changing the direction along X-M you can see the very faint band continuous at A but it suddenly disappears. The same happens for the branch along X-M where point B is on it. You can see that there is no branch for this part along Gamma-X.
I hope I’m clear now but please let me know if I need to clarify better.

Thank you for your kind help and the time!


Dear @hadiseh.alaeian

Thank you for clarification and sorry for the confusion.

In your first plot to this post, you can see that discussed bands are continuous and they become discontinous when you saturated/scaled the plots. Please note that the strength/intensity of these peaks can vary depending on the source and monitor locations. To get a stronger peak, you need to locate sources where the resonances are at their maximum as well as monitors to record the field.

While you can try to improve the plot by repositioning dipole sources and time monitors, the behavior of band diagram will not change. For demonstration purposes, you can use the script in the KB page (the link is provided in my earlier post) to obtain plots like the one above.

Please let me know if this answered your question.