Glass-Silver-Air Divergence


#1

Hello,
I’m studing the Surface Plasmon Resonance in a thin metallic layer and I started with the example given in the database:
https://kb.lumerical.com/en/sp_spr_2d.html
However, I would like to study it with gold at 1.55 um. The problem I encountered is that changing the wavelength to 1.55 um (and keeping the silver layer) the simulation does not converge. Instead, the autoshutoff level reaches 0.0001 (for example) and start to rise again.
I tried a smaller grid and still occurs. The problem must be the boundary conditions because I turned them into metallic and the simulation converged.

Why does a wavelength change affect this way and how can I solve it?


General tips to solve divergence problem in metal-insulator-metal (MIM) structures
#2

Hi,

Once obvious change due to the change in wavelength is the auto meshing. The mesh size is automatically calculated based on the min lambda. In your case, the mesh size dx can be increased by a factor of 3 (from 0.5um to 1.55um). This will not affect the region where mesh override is applied, but will affect the rest of the region. The other change is that gold has a different refractive index value at different wavelength, ie dispersion.

I am able to reproduce the divergence problem you described. That being said, it might be not entirely obviously the exact reason why it is diverging. Like what we suggested on the divergence simulation page, the simulation is able to converge when I switch to the “stabilized pml” profile. It seems to solve the probem. If you have follow up questions, please reply the post.

sp_film_resonance (4).fsp (250.9 KB)


#3

Thanks for your reply!

Now the simulation converges, but it gives an unusual result. Varying the incidence angle the reflectivity should be almost 1 until the SPR occurs on the other side of the gold film, but is not like this. Here I have the results, and it seems to be some Fabry-Perot resonance in the reflectivity. On the other hand, I can see in the E^2 field plot the angle when the surface plasmon resonates at the correct angle.
Is it a problem with the monitors or with the length of the glass substrate?
sp_film_resonance.fsp (269.6 KB)sp_film_resonance.lsf (1.2 KB)


#4

Switching the PML profile to stabilized can help the unstability in your first case but it will trade off the performance of the PML at the same time. In some situations, it could cause some reflection off from the PML surface and thus creating some FP like resonance. The default normalization to the sourcepower command is screwed up as a result. This is clearly unphysical.

I have spent some time to test your simulation and it looks like the PML profile is playing an important role here. In order to not lose too much PML performance, I tested the simulation using steep angle profile and 24 layers. It seems that the feature near 44.1 degree is now able to show. The peak looks quite sharp, you will probably want some higher resolution to resolve the peak. For better accuracy and more reliable results, you will likely need some convergence testing.

Note: The evanescence tail looks quite long at resonance, so I extended the simulation x max just to reduce unphysical absorption from the PML.

sp_film_resonance_edited.fsp (258.6 KB)