Learning Forum

[fdtdisgreat]

Hi,

I am simulating a periodic structure with a unit cell consisting of a single dielectric resonator and a single substrate. The excitation source is a normal incident plane wave. I would like the simulation to reach autoshutoff level = 1e-7, but each time it reaches to around 1e-6, it will suddenly start to diverge (this usually takes around 30,000 to 35,000 fs).

I have tried many different things to resolve this problem. I have decreased dt stability to 0.5, I have changed the meshing several times to adjust the aspect ratio, I have changed the number of PML layers; the simulation continues to diverge. I am using a single value of n and k for all wavelengths, for all materials in the simulation, so material fit shouldn't be the cause of the instability (as far as I know).

My override mesh around my dielectric resonator is 5nm in x,y and z. I am using custom non-uniform global mesh, with maximum mesh cell size of 50nm for x,y and z. Grading is allowed in x,y and z. The PML behind my plane wave source is just over 1 wavelength away from it (in the normal direction i.e. z), and the top of my resonator is at least 2 wavelengths away from the closest PML layer. I'm using 24 layers of normal PML. k is set to 0 for all materials, which is reasonable given their properties at this wavelength. dt stability = 0.5. Periodic boundary condition with symmetric/anti-symmetric BC applied as appropriate.

I'm not sure what else to try. I need my simulation to reach at least 1e-7 (preferably lower) in order to get publication-quality transmission spectra. Please let me know if you need more information about my simulation in order to help diagnose the cause of the divergence.

Thank you in advance.

[Guilin Sun]

Thank you for the detailed description. Here is my suggestions:

1: do not reduce dt factor if you have not identified the cause of divergence. Only when using Metal BCS and it is still diverging then you can reduce it.

2: The distance of PML is good, in most cases except there is long-tail SPP or evanascent wave. You can use a profile monitor to check the field.

3: when simulating periodic structure, most likely it has higher order diffraction. Even though there is no higher order diffraction in the wavelength range you are interested (mostly the source bandwidth), it does not prevent large diffraction angles from shorter wavelength in the source, outside of the interested bandwidth. You can use a transmission/reflection monitor to record shorter wavelength, and check the farfield by using Visualizer with about 10 periods (approcimately. or you can use grating analysis). You may need to use log scale to find the higher orders.

I guess it is most likely due to #3. You can 

1: set the source in time domain, using longer pulse and offset. For example 50/100fs:

2: using Steep Angle PML with more number of layers 

 

[fdtdisgreat]

@Guilin Sun Thank you so much for your detailed reply. I will try your suggestions and let you know how they turn out.

I have 2 quick questions:

1) I have yet to try Metallic BC to see if it still diverges. To clarify, that would be replacing just the PML layers (z+ and z-) with Metallic BC, and leaving the other 4 BCs (x+, x-, y+, y-) as Periodic BC, correct? (as opposed to all 6 BCs being Metallic).

2) I can try extending the length of the pulse to decrease the wavelength range. Just to check, this can also be achieved be de-selecting the 'Optimize for Short Pulse' Option? (as opposed to manually setting the time domain options)

Best wishes

[Guilin Sun]

A1: if it is for periodic structure, yes, only replace PML with Metal. This way we will count the diffraction from the periodic structure.

A2: No, do not  deselct it as it is optimal, even with narrow bandwidth. Instead, set the pulse in time domain as the above screenshot shown.

 

[fdtdisgreat]

 

Thank you for answering my questions. I have tried 2 of your suggestions so far:

1) I have changed the pulselength and offset as shown in your screenshot, to reduce the wavelength range of the source. The autoshutoff level reached 1e-5 quickly, but then oscillated between 1e-5 and 1e-6 for the majority of the simulation (from 15,000fs to 40,000fs) before starting to slowly diverge up to 1e-3 towards the end (at around 40,000 fs),

2) I ran a simulation with Metal BC replacing the 2 PML z-direction BCs. The autoshutoff level oscillated between 0.6 & 1.0 for the entire simulation (50,000fs). Typically the simulation will start to diverge at around 30,000 fs to 35,000 fs. I guess this means that dt stability will have no impact on the divergence? I know there used to be a page on Lumerical’s website that detailed different types of divergences, and that diverging/not diverging when using Metallic BCs could be used to determine the origin of the divergence. However, since Lumerical’s new website move, I can’t find that page. Would you have a link to it?

Based on these 2 results, would you have a better idea of the origin of the divergence? I will try steep angle PML now and let you know how it turns out.

Best wishes

 

[Guilin Sun]

From point 2, you may need to check the material fitting. You may also need to reduce dt factor. Where the periodic BCs are located? on a uniform geomtry or on a changing geometry such as small sphere or triangle?

Please place one or more time monitor, check the spectrum and see if the resonance is inside the source spedified range or outside?

Did you check the diffraction angles? please use grating analysis to check the largest diffraction angles: https://optics.ansys.com/hc/en-us/articles/360034407094-gratingu1

if the angle is large, you may also need to use more PML layers with Steep Angle PML.

[fdtdisgreat]

As mentioned in my initial post, there is no material fit. I am using a single-value n and k for all wavelengths. Can this still cause divergence?

My periodic BC are only intersecting air and the substrate i.e. a uniform geometry.

To clarify, if there is no divergence with Metallic BCs, then what are the potential causes of the divergence? There used to be a useful Lumerical webpage about this but I can't find it since the site moved.

I have checked the largest diffraction angle using your suggestion of gratingu1 and u2 commands. The only beam is at normal incidence. This is expected from the structure I am simulating. Nonetheless, I did try the simulation again with 50 layers of Steep PML (together with setting pulselength and delay), but the simulation once again diverged.

I can try using time monitor, but I'd rather try other options first since the expected simulation time required would be very long and having a time monitor for the entire simulation (50,000fs) will result in a huge amout of data.

Is there a recommendation on how close a planewave can be to a simulation object? The only other thing I can think of is that my plane wave is currently ~1/2 a wavelength from my substrate surface. There is no particular reason I chose this distance, other than not making it too large so as to keep FDTD region small. Could this potentially be leading to problems?

For all of the above simulations, I reset dt stability factor to 0.95, based upon the metallic BC not diverging.

I can next try Stabilized PML, but I am running out of ideas as to what can be causing this divergence. I've spoken with my collaborators who are also simulating this structure, and their FDTD simulations have also been diverging.

Thank you in advance. Best wishes.

[Guilin Sun]

I maybe confused by this description:

 

I guess you mean when you use PMP it diverges around 30,000 fs to 35,000 fs.If so, it is not dt factor issue.

 

Have you checked the time monitor spectrum before it diverges? It may have resonance not in the interested source bandwidth.

You may need to try 64 layer SttepAngle PML.

Divergence is subtle: KB gave two typical types of diverging: dt factor and PML. Other causes could be:

large mesh aspect ratio;

large diffraction angle

strong resonance outside of the interested wavelength range

Metal materials and SPP

The plane wave source can be closer to material interface a few meshs away.

But you can increase the PML distance to the material interface.

Please add a line monitor along the injection and see if there is any evanescent wave or SPP that has long tails to interact with PML.

Here is the original KB information moved to forum https://forum-legacy.ansys.com/discussion/25566/ansys-insight-diverging-simulations

 

 

[CL Liu]

The true reason is that: Maxwell divergence equations (div B=0, div E=$\rho$) are not solved. 

Please see https://physics.stackexchange.com/questions/702278/is-this-transfer-correct

[Guilin Sun]

Sorry, no, this is not the reason. Div B=0, and Div D=0 are automatically met, which is the ginus contribution of Prof. Yee for this algorithm.