# Field enhancement of MoS2 layers on the substrate

I am trying to simulate the field enhancement of MoS2 layers on the SiO2 substrate. Here is my results.

However, my results did not show a large increment of electric field inside the MoS2 layers like the case that presented in this paper (link: http://pubs.rsc.org/en/content/articlehtml/2015/nr/c5nr03133h)

Meanwhile, in my results, the field inside the Si is somehow much smaller than that of the paper results.
I have checked the material fit, it looks fine. I don’t know if I am doing something wrong.

Thanks for any help.

I also attach my FDTD file:
field enhancement.fsp (2.7 MB)

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I have tried to perform it by using the nonorm simulation and using a Chi2 MoS2 model.Here is the results.
In this paper, strong field enhancement is expected to be observed in the MoS2 layers at 800nm and 400nm because of the SHG.

At 800nm (fundamental wavelength):

At 400nm (2nd harmonic wavelength):

the results are still not satisfactory. At 400nm, the MoS2 layers did show some increment of electric field comparing to its vicinity. But it is still far from the result in the paper.

Meanwhile, I am curious why in the paper, the field in the air at 400nm can even larger than that at 800nm. I expect that the field in the air at 400nm is only due to the SHG, the field of the SH wave should be much smaller than the field of the source wave at 800nm. Am I wrong?

Apart from these, i have another question.
If i am using the nonorm simulation, how can I obtain the field enhancement (E/E0)? In the nonorm simulation, the field is in the unit of volt per meter per hertz. So, should I convert the source amplitude to E0/(c/lambda) where lambda = 800nm and then divide all the data by E0/(c/lambda)?

I also attach my FDTD file:
field enhancement nonorm.fsp (280.7 KB)

Thanks again!

Dear @chaulwong5-c

I guess there is one concern about your simulations. Based on the paper, the injected light is focused onto the MsO2 layer by 60 objective with NA=0.85. I am not quite sure how this will change the results but this is something that requires attention if we want to replicate the results. Maybe you can adjust your simulation files and then see if the results make sense or not.

I guess the authors are calculating the total field, which is different than line monitor that you are using. My guess is that most of the 800 nm is transmitted but maybe most of the 400 nm is being reflected? I agree that generally total SH light intensity will be weaker than injected light, but we need to consider the geometry where reflection varies with frequencies.

We have some notes regarding frequency domain normalization, but I think an easier way to calculate the conversion efficiency would be to use frequency domain field and power monitors. To calculate the injected light intensity, I suggest running simulations in air and calculate T(w). Then you can calculate the total intensity by integrating over all the frequencies. You can repeat the same process for another monitor on the place of interest (representing your detector) for \lambda=400nm. Dividing these two values should give you the conversion efficiency.

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Thank you so much for you reply!

Based on the paper, the injected light is focused onto the MsO2 layer by 60 objective with NA=0.85. I am not quite sure how this will change the results but this is something that requires attention if we want to replicate the results.

I have tried to use the gaussian source instead of plane wave. I simply put the NA = 0.85 and increased the width of the simulation because of the beam size. The result turned out to be not much different. Since this is the first time I use the gaussian source, I don’t know if I made something wrong.

I guess the authors are calculating the total field, which is different than line monitor that you are using.

Instead of using the line monitor to record the spatial variation of field, how can I measure the total field? Do you mean I should use a 2D monitor?

I think an easier way to calculate the conversion efficiency would be to use frequency domain field and power monitors.

I know I can easily get the conversion efficiency by the way. But in this project, I am focusing on getting the field enhancement factor. I get the (E/E0) value by running two simulations: the first is the simulation with structures(getting E(800nm), E(400nm)); the other one is the simulation without any structure(getting E0(800nm)). But if I do this, E(400nm)/E0(800nm) will be unreasonably small. Am I correct?

Thanks again!

Also, in the paper, the authors mentioned that

“For calculation of the electric field enhancement factors, a continuous wave was employed to approximate the pulse train used in the experiments.”

I have tried to adopt it by following the method on this page, but still there is not much change.

I have even simplified the problem by illuminating only a single slab of MoS2, with thickness equal or less than 17nm, none of the results excited a field inside the MoS2 slab with E(800nm)/E0(800nm) larger than 1.

I have double checked the MoS2 material indexes and it was fine. The paper said nothing more than the materials’ indexes, so I think simple material model is adequate.

So did I make some big mistakes? If I did, please tell me.

I really appreciate for any help.

Can someone help me? I have no idea how to reproduce these results.

I think using the norm approach is the right way, right?
since if the paper was using the nonorm approach, the enhancement factor E(400nm)/E0(800nm) was no possible to be larger to 1, it will be possible only when it was using the norm approach, where the enhancement factor is E(800nm)/E0(800nm).

Thanks for any help.

Dear @chaulwong5-c

Sorry for the wait.

As you mentioned earlier, paper is missing providing enough information about some of the features in Fig 3(b). For example, why for \lambda=800 nm, the filed has a sharp termination at -0.2um or the blue line (\lambda=400 nm) behaves as a standing wave in free space? This behaviour would make more sense if there was a reflecting mirror (or lossy metal) at z=-0.2um. I guess our simulation is different than what is in the paper and without enough information, replicating results will be difficult.

Yes, A 2D monitor is the solution. By integrating over the electric field, we can calculate the intensity in the cross section of the structure.

This should work. Are you planning to calculate E-800 over the entire geometry? If its just the injected field, you probably don’t need same calculation with no structure as a frequency domain-field and power will give you the same results. Does paper report any value for the results as I don’t know how much enhancement we should expect!

The reason for using no norm is because of the nature of nonlinear simulations. Since the injected light is 800nm, CW normalization state for injected light would return zero for E(400). This will cause the problem when you want to normalize the SH generated field.

In summary, we need further information about the simulation setup. I am not seeing problem in your simulation file, and our results make sense. You can play with this KB example and see how the E filed evolves over space by adding monitors and mastering the proper use of monitors.