Finding Symmetric modes in MIM Plasmon Waveguide

I am trying to find the dispersion curves for the antisymmetric and symmetric modes of a metal-insulator-metal (MIM) plasmonic slab wave guide. I was able to find the correct dispersion curves for the asymmetric mode in Mode Solutions, using a antisymmetric boundary condition, finding the modes, and sweeping the frequency to find the effective index. However, when I changed the x boundary condition to symmetric, I was unable to find the symmetric modes with the expected dispersion curves. The effective index of these symmetric mode are not correct, so I am not finding the correct modes (I expect an index somewhere around 1.4, give or take, but I am instead getting results with the n_eff around 0.2). What can I do to calculate the correct symmetric mode?

(For reference for the expected dispersion, I am currently trying to replicate the dispersion curves in figure 3 of the following paper: J. A. Dionne, L. A. Sweatlock, and H. A. Atwater and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization”, Phys. Rev. B 73, 035407 (2006).)

My Lumerical file is attached for reference. The waveguide has an SiO2 core of 35nm, and a silver cladding. I set up a mesh over the center of the waveguide. Since the plasmon should decay away from the interface, I used a wide simulation area with metal boundary conditions in x. The slab waveguide is infinite in y, so I used a periodic condition in +/- y. The modes I am looking for would propagate in z.

plasmon_WG_modes.lms (297.1 KB)

Dear @alan2914

Can you please explain what did you expect for the symmetric modes of the MIM structure? and how you want to use dispersion data to extract the energy vs ky data?

I am working on this case with another user in the link below, but our approach on that post is to calculate band-structure:


The modes have a large imaginary part in index (really lossy). so you have to use a large number of trial modes or guess and index with a larger imaginary part. I wrote a script that just uses a large number of trial modes and picks the mode with the largest k.
plasmonscript_sym_2.lsf (789 Bytes)

Dear @michael.grayson

I ran your script, but I am not still quite sure if this is what you were looking. Does this plot match with the results of the paper?


I’ve tried a few different things with this script, and have not been able to find the modes I’m looking for.

In order to plot the mode as seen in the paper, I use the effective index to find k = n 2pi/(wavelength), and plot f vs k. I would expect it to reach a k of about 0.05. The modes that the script is finding are still an order of magnitude less than that.

The expected shape of the index vs frequency should look similar to the plot below (data from an antisymmetric waveguide of 20nm thickness).

This would give a f vs k curve of the following:

The primary issue is that the symmetric mode pushes more power into the metal, so they have higher loss. But the general shape of the plot should look similar. Maybe with a k of about half of that in the above chart.

Dear @alan2914 and @michael.grayson

Since device geometry does not change along y direction, and you were using periodic BCs along y, I started using a 1D FDE simulations. It was a great help to run faster simulations with finer mesh and higher number of trail modes for trouble shooting purposes.

The gap of 12 nm was the hardest one to reproduce as software had a hard time finding the proper modes:

and here is the result for 35nm oxide layer:

You can run the simulations for different oxide layers, and the trend matches very well with the results of the paper, I think. I was also able to find the modes for different oxide thickness at different wavelength (I changed the FDE x-span to 50nm to find the mode for 12 nm thick oxide layer):

For oxide thickness of 12nm, at lambda=350 nm:

and for oxide thickness of 50nm, at lambda=1550 nm:

Here is my simulation file:
plasmon_WG_modes_1D.lms (301.8 KB)

Please let me know if you had further questions.