Plasmonic enhancement of SHG


I am simulating the SHG enhancement of a SiO2 coated nanorod on a single layer WS2. The WS2 is supposed to emit the second harmonic light at 610 nm (excited at 1220nm), which has a Chi2 value = 1.15e-9.

In the 2D simulation, the coated nanorod with length = 210nm was found to has a resonance near 1220nm in the linear simulation(judge by the max. electric field enhancement).

It later on obtain a desired SHG enhancement in the nonlinear simulations.
(NR+WS2 File:
(WS2 File:
Scrpit of integrating the poynting vectors:2d.lsf (315 Bytes)

In the 3D simulation, the coated nanorod with length = 89nm was found to has a resonance near 1220 nm in the linear simulation.

However, the nonlinear simulations shows there is no enhancement at all comparing to the SHG from the pristine WS2. The results are quite nonsense. It should have certain enhancement when the field enhacement at the fundamental wavelength is large.
(NR+WS2 File:
(WS2 File:
Scrpit of integrating the poynting vectors:3d.lsf (348 Bytes)

Can anyone please help me to check whether any of these file goes wrong? (especially the advanced setting under FDTD, I’am not sure whether I set it correctly.)
Thanks for any kind of help!


Dear @chaulwong5-c

Sorry for the late reply.

Thanks for providing the simulation files. Can we focus on 3D case with NR material in which you can’t see the expected results (if I understood your post correctly?). Maybe you can provide screenshot of the results that don’t make sense?

Sorry that I am not much of help at this moment, but I am keen to solve your problem.



Dear Behzad,
thanks for your reply. The SH power from a WS2 (without nanorod) is shown below

the SH power is with the magnitude of 7.81e-34 W/Hz^2.

However, when I excite the same system except to add a coated nanorod on the WS2,

the near field profile shows some dipole response to the incident light at 1220 nm and the SH power is now with the magnitude of 6.69e-34 W/Hz^2, which is lower than the case without any plasmonic structure.

According to the linear simulation, the nanorod supposes to have a resonance near the fundamental wavelength (i.e. 1220 nm).
Linear absorption:

So I do not understand why the power is smaller after adding the nanorod. This is counter-intuitive to me.

I am wondering whether my settting is wrong.

Thanks again for your help.


Dear @chaulwong5-c

What I understood, you expect that since nanorod traps the field at 1220, you expect to see enhacement in SHG. This is because in the case without nanorod, light passes through nonlinear medium once. But in the nanorod case, trapped light will interact with the nonlinear medium a few times. Is this correct? Do you have any references?

To begin with, can we step back and try to do a simple linear simulation i.e. nanorod on a glass substrate to study the resonance, with the goal of having a plot like the last plot in the previous post.

My other question would be how you are calculating the SHG? Does it rely on the time monitor set on the middle of FDTD region?



Dear Behzad,
Thanks for your reply.

Yes. Since in the linear simulation, strong absorption and field enhancements were found in the wavelength near 1220 nm. So I expect to see enhancement in SHG for these reasons.
Unfortunately, I don’t have any exact references. But this paper (link: demonstrates by FDTD simuulation more than 10 times enhancement of SHG at the resonance when gold nanorings are placed onto the nonlinear substrate (LiNbO3). I think the situation is simular (except their gold rings are periodic in structure), if I am wrong, please let me know.

I already did that. Introducing the 2D material and coating only red shift the resonance and induce extra peaks between 400 - 700 nm.

I calculate the SHG power by integrating the poynting vectors, which are recoreded by the frequency-domain monitor. I already uploaded the script at the beginning of this post.

Thanks again.


Dear @chaulwong5-c

simulation wise, you are working on a difficult case: 1) There is a very thin layer (0.8nm) 2) nonlinear material 3) cavity with plasmonic modes. Each of these cases require extra attention to details.

To start with simulation, I recommend you to use a plane wave with periodic BCs and have only galss substrate with linear WS2 material. Make sure that you results converge and match with theory. A good link is to take a look at this case 2d material reflection but please note that we are still going to use 3D material because we don’t have 2D nonlinear material. The linked paper in that post has some studies on WS2 material. After studying and running these simulations, you should be able to answer: how many layers you need to resolve thin layers, FDTD mesh accuracy, and type of PML layers.

For the next steps, I noticed that you were using PML with plane wave source. This might cause edge effects that is explained here:

I assume that you are not working with periodic structure and the goal is to study the effect of a single nanorod. If this is the case, you will need to use TFSF source with two simulations: one with nanorod and one without nanorod (in both you have glass substrate with nonlinear WS2 material) so that you can compare the results of these two simulations to calculate enhancement. Please note that monitors need to be located inside the TFSF region to make sure that you are collecting the total light (if its outside the TFSF region, it will capture only the scattered light). One more thing is to set the simulation bandwidth from FDTD advanced options tab to include the SHG frequency as well:

You can read more about this here:

Since the simulation require long time, I will not be able to do much of troubleshooting and will rely on the results that you provide me.

I hope I could be of a help.


Dear Behzad,
Thanks for your reply,

Indeed, I did get the didelectric function from that linked paper. I already did the test in linear simulations, and I found that 0.1 nm mesh in z-direction works fine.

Thanks so much for your advice. I will try to simulate the case with a plane wave and periodic BCs and the case with a TFSF source. I will keep you updated on the results.


Dear Behzad,
I try to simulate the non-coated gold nanorod with periodicity of 500 nm. Now I can set the BC of y and z with symmetries, it allows the simulation to run much faster and only did minor change to the linear far-field and near-field profile.

I also did minor change to the excitation wavelength and length of the nanorod. The excitation is now 1176 nm, the gold nanorod with length 79 nm is supposed to have a resonance near 1176 nm.

However, the nonlinear simulation somehow diverged when I tried to run it. The chi2 value of the WS2 is 1.23e-10 and the amplitude of the source is 5e-8. I tried to change the “dt stability factor” from 0.99 to 0.95 and change the PML to “stabilized”, but it did not work.

Can you please help me to figure out what is wrong with my file? Thank you so much for your help.

Nonlinear: WS2_NR_L79_WL1176_1nm_E5e-8_period500nm_not coated.fsp (429.0 KB)


Dear @chaulwong5-c

Thanks for the update and all the work you put on this.

Again, since your simulation takes a long time to run I will not be able to do troubleshooting myself. First, I can see that you have a very high mesh aspect ratio. This might cause unwanted PML behavior and unstable simulations. Please refer to these links to learn more:

If you still had problem, you can try few things:

  1. set all of the BCs to metal. If simulation converges it is the problem with PML. Then you need to try using different PMLs. You can increase the layer for standard PML and then use stablized or steep angle.
  2. If simulation was diverging, use the original settings for PML and try to change the dt from 0.99 to 0.95, 0.90 and 0.5.

Please keep me updated with the results.

The reflection is greater than 1 in the simulation of the Metal mesh based electromagnetic interference device

Dear Behzad,
Thanks for your reply. I notice the problem may arise from the high mesh aspect ratio. I have already tried to

  1. reduce the mesh size dx=dy=dz=1 nm to dx=dy=dz=0.5 nm in order to reduce the aspect ratio.
  2. use steep angle PML and stablized PML.
  3. change the dt stability factor from 0.99 to 0.5.

But all these measures did not work, it still diverge. Do you still have any suggestion on this issue? Thanks again for your help.

(In case you want to run my file, you can decrease the y span and z span of the simulation region from 500 nm to 200 nm. The simulation can be done within 2 hours with my laptop and it will know whether it will diverge within an hour.)


Dear @chaulwong5-c

I can see the override mesh has dx=dy=dz = 1nm, but how about the rest of the simulation region? For example the aspect ration on the area shown in the screenshot below is 30:1 (this is actually caused because of the override mesh that you used to mesh the cylinder):

Also, can you please explain what did you discover when you changed all the BCs to metal? Was the problem PML or dt stability factor? I am keen to find an answer for your problem, but I work in many cases everyday and troubleshooting simulations that need one-two hours run will require more help from the customer.



Dear Behzad,
Thanks for your reply. I tried to change all the BCs (both x,y,z min and max bc) to metal, the diverging message was showing at 10%. However, when I look at the E vs t in the time monitor, the field seems to start decreasing before it reach the max shutoff.

I also tried to decrease the dt factor even further to 0.3, but the simulation was still diverging. The problem seems neither PML nor dt factor. But I do not find any problem with the nonlinear material because it works well without the plasmonic structure.

So do you think the problem is the large aspect ratio now? Do have any suggestion on how to fix the high mesh aspect ratio in the region that you have pointed out?
Thanks so much for your help.

(edit: I did further tests on the simulation. I found that when I remove override mesh that is used to mesh the cylinder, the simulation still diverged. This implies that the problem may be the source amplitude, so I tried to lower the amplitude to 1e8. After doing this, the simulation did not diverge, but this time the field did not hit the min shutoff.)


Dear Behzad,
I think I fix most of the problems.

  1. The problem that the field did not hit the min shutoff results from the “stablized” PML. After I change it back to “steep angle”, the problem is fixed.

  2. As I mentioned in the previous post, after I lower the amplitude of the source to a relatively low value(1e7), the simulation can run properly, and I can get a desired enhancements.

But I am curious why I need to set to such a low amplitude before it can be ran without diverging. It is due to the energy “gain” in the plasmonic resonator that exceeds the max shutoff value? Or due to other factors?

It there any method that I can possibly rise the amplitude without diverging? Because when I remove the plasmonic structure, the SHG signal is extremely weak.

Thanks again for your help.


Dear @chaulwong5-c

I think this means that PML is not the source of divergence. However, I don’t know why divergence problem is fixed when you used steep angle.

I also do not have a clear answer why your simulation diverges with the source power. A movie monitor will be quite useful in these cases, but I know that it will insanely increase simulation time. Maybe you can do an overnight run?

I started to simplify your simulation file. Since you are only interested to study the plasmonic enhancement, and you decided to go with periodic BCs, I decreased the FDTD span on x-y. Please note that for periodic structures the FDTD span is not arbitrary and depends on the system of the study, but since you want to get some plasmonic enhancement, I guess it will make sense to decrease the span.

I had to use a fine mesh accuracy of 8 to make sure that mesh aspect ratio is reasonable over the FDTD region (this is being said that results of time monitor didn’t change much if I used a coarser mesh).

WS2_NR_L79_WL1176_1nm_E5e-8_period500nm_not coated.fsp (417.4 KB)

Here are the results comparing these two cases:

This is showing ~3 times enhancement in the presence of nanorod.

It will be a good idea for you to run some convergence testing using finer meshes. Also, please check and make sure that the nanorod still has resonances at wavelength of interest.

I hope this was helpful.


Hi @zhangbingxyx

Your posts are missing the simulation file. Please feel free to create a new topic with a detailed inquiry of your issue.