Simulation is diverging

Hi all,

I am trying to simulate a structure consisting of cylinders on the top of substrate with a layer of liquid crystal above the cylinders and the liquid crystal layer is dispersive. When I tried to run the simulation, the result was diverging. I changed all of the simulation boundary conditions to Metal, then re-run the simulation and the result was weird but not diverging so I think that the problem is because of PML and dispersive materials according to this link:

I tried everything mentioned in the above link and my simulation is still diverging:
Firstly, I changed the PML to stabilized and increased the number of PML layers.
Secondly, change to custom and increased alpha.
Thirdly, extended the liquid crystal layer into the PML layer.
Fourthly, I had a look on the material fit
Can you kindly help me to fix this problem? I have attached the fsp and lsf files, so you can have a look.
silicon_disks_para_div_chek.fsp (297.6 KB)
silicon_disks_para_div_chek.lsf (2.9 KB)

Hello @ammas2,

This is a strange sort of divergence. It may be something to do with the LC anisotropy in the PML? Have you tried disabling the symmetry conditions? This seemed to work for me, and maybe more realistic but a bit less efficient. I am not sure exactly, what the orientation of the LC is but are you confident that it is not breaking either symmetry condition? I was also able to get the simulation to converge by not extending the LC structure into the PML, but this may not be realistic since it essentially adds an inteface.

I hope this helps.

Best Regards,

Hi Taylor,

Thank you for your reply.

I tried to disable the symmetry as you suggested and used periodic boundary conditions but it didn’t solve the problem. Also, I tried not to extend the LC into the PML and that also didn’t solve the problem.
I am using dispersive liquid crystal material which means that the refractive indices (ne & no) of liquid crystal are changing across the wavelength. However, when I changed to non-dispersive liquid crystal, there wasn’t any problem with the simulation. I don’t know the reason? Do you have an idea why it happens please?
The orientation of LC is planar meaning that ne is parallel to the incident electric field.

Thanks

Hello @ammas2,

This simulation converged for me. Could you please confirm this solves the problem.

silicon_disks_para_div_nosym.fsp (302.4 KB)

Having a dispersive, anisotropic material extending into the PML presents a challenge. The alternative approach may be to perform a frequency sweep of non-dispersive LC indices, updating the (ne, no)_at each wavelength point.

Best,

Hi Taylor,

Thank you for your reply.

I run your simulation but the result wasn’t right and I don’t the reason.

I have checked your file and I have some questions please.

Firstly, I tried to use symmetric boundary conditions but again the simulation is diverging. How does the symmetry affect the divergence?

Secondly, I didn’t get what you mean by performing a frequency sweep of non-dispersive LC indices because if the frequency changes that means a change in the wavelength as well. So what will be the difference and how to do the frequency sweep at fixed wavelength please? It should be noted that I need to do a parametric sweep so I need to run the simulation many times.

Hello @ammas2,

Well I am not sure about the results of the simulation, but it did seem to fix the divergence issue? Could you provide more information on which results disagree. I am not entirely sure what is going on with the symmetry, and LC rotation but it a produces divergence it seems.The other issue is that the anisotropic materials extended into the PML are producing reflections which may be the results you are refering to? These notes provide a good discussion on PML https://math.mit.edu/~stevenj/18.369/pml.pdf

Essentially the workaround I proposed would be to add the wavelength as a parameter to sweep. So you would sweep across the bandwidth updating dispersionless n_o(lam_c), n_e(lam_c) for the center wavelength and collecting the results which should be correct at that wavelength. The (n,k)materials you have defined are meant to used in this context actually.

This would add to the number of simulations you need to do, so if you wanted to do broadband simulations then it is better to use sampled data, or object defined dielectrics if you can ignore dispersion which would be a reasonable approximation to start with.

The challenge will be the anisotropic materials, and refelections from the PML. It may be helpful to use a coarser mesh dz near the z max boundary which will make the PML thicker for a given number of layers. Please give this a try and let me know if it helps. I will get back to you if I can determine any further methods that may help.

Best Regards,

Hi Taylor,

I am using now non-dispersive liquid crystal material. The problem is that the result has many ripples. Regarding the PML’s position, I inserted the PML inside the liquid crystal cell. I didn’t expect that kind of ripples in the result. I increased the simulation time to 40000 fs but I still get the ripple. I have attached my simulation and a photo for the result. How to avoid this kind of nipples please?

lc.fsp (8.6 MB)
result

Thanks

Regarding the PML position, is it right to extend the liquid crystal layer into the PML as I did in my simulation. I tried both situations: the first is the PML outside the LC layer and the second with the PML layer is inside the LC layer and there was a very small difference. I believe that it is more realistic to have the PML layer inside the LC layer. Is it right?

Hello @ammas2,

Which features of the spectrum are you referring to? Do you mean the larger dips and spikes in the 400-500 nm, range, or the smaller variations in the 550-900 nm range?

It may improve your results if you increase the number of layers in the PML to reduce reflections. For a periodic simulation like this, you should also use the “steep angle” PML profile.

At this stage, if you think the settings are close to correct and the divergence issue is solved, you can use convergence testing to determine if settings like the mesh size, simulation time, number of PML layers, etc. are correct. This will help to improve your results as well.

Yes, if the divergence issue is solved then you should extend the LC through the PML. Otherwise there will be reflections at the interface between the LC and the empty space above it.

I hope this helps. Let me know if you have any questions.

Hi Kyle,

Thanks for your reply.

I did the convergence test and changed the PML profile into ‘‘Steep angle’’ and that solved the problem.

I just have questions: it is written here:


that ‘‘It is designed to provide enhanced absorption in situations where light travels in directions that are nearly parallel to PML boundaries’’ for my case light doesn’t travel parallel to the PML but perpendicular, does it affect the results?
Also, I usually change only the PML profile and number of layers without changing all other parameters such alpha, gamma and so on. I guess there’s no problem with that and the profile and no. of layers are sufficient to give accurate results. Is it right please?

Thanks

Hello @ammas2,

In a periodic simulation, light can be scattered into higher diffraction orders resulting in propagation at higher angles, even if the light is injected normal to the PML boundary. This is why the steep angle PML profile is often used for periodic simulations.

These pages have more information about the PML profiles if you are interested:

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Hi Kyle,

Thanks for your reply. That solved my problem.

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