How to find Re(neff) and transmission spectra?

I am trying to simulate Figure 2(d) and 3(a) from this paper:
Boundary condition is pml. I do not know how find it?please tell me problems?.
My simulation file plasmonic filter based on graphene.fsp (248.5 KB)
Wavelength is too much larger than structure width.But I can not find spp between dielectric and graphene layer.
Thanks for helps.


It looks like this device involves a 2D circle and you are trying to use the volumetric approach to deal with it. In fact, we could make use of a ring and 2D rectangle to mimic the 2D circle. You just need to set the mesh order properly. I am attaching an example here. With some effort to construct a structure group, you should also be able to make a 2D object similar to figure 9(a), if you wish to do so. You can use the Index monitor to look at the conductivity of the resultant object. 2D circle.fsp (234.4 KB)

For figure 2(d)-2(g). The FDE solver should allow you to generate those plots. The Re(neff) vs width plots should be doable with the help from the Parameter Sweep tool. This example has some step by step instructions for you to start with.

For figure 3(a), you will need FDTD Solutions to simulate the full structure. It should allow allow you to reproduce 3© as well. In this case, you will need an Integrated Mode Source to inject a mode for simulation, one mode at a time. I think the Mode Expansion Monitor will be useful too.

For you last statement, I am happy to continue the conversation once you have the simulation set up properly.

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first, I can not creat 2D circle from 2D rectangle because part of ring structure located in 2 Rectangular waveguides.
second,I added fundamental mode source at left edge of waveguide.Simulation file is here.fsp (349.3 KB)
I added a field monitor at surface dielectric and graphene and simulated.
Ez component at 20 THz:
and transmittance from 20 to 40 THz:
I saw my simulation is not converged.
I do not know what to do to find the correct answer!!
Thanks a lot.

  • I thought you should be able to make a 2D circle by properly setting the mesh order of the pieces. ( 2D circle.fsp (244.3 KB)

  • Mesh x and y – too coarse to resolve the circle; Mesh in z direction – very fine and makes the aspect ratio very large and may potentially lead to divergence. I think the 2D material approach may reduce the need for having super fine mesh in the z direction.

  • Since mesh in y and z are too course, the mode calculated by the Integrated Mode Source is rather rough. I suggest you look at the mode calculated by the source and see if you think the resolution is enough.

  • Since the waveguide is like 8-300 um, I would recommend a larger simulation spans. The current simulation spans are rather too small. Usually we would recommend simulation spans that are roughly in a similar scale compared to the wavelengths.

  • As far as the mode expansion monitor goes, you will need it if the transmission plot you are reproducing is referring to a particular mode (eg, abs(S21)^2). If not, the regular transmission returned by the frequency is likely enough.

I think you might find this example interesting if you have not seen it. It will likely give you a good starting point to practice some simulation skills. ( In this example, we used metal BC on the sides to speed up the simulation. But I think you would want to use PML in all sides if there might be some scattering.

I think with the 2D material, it might be easier to reproduce the published results. I am happy to look at it again when you have it set up and gone through the above example.

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Thanks for reply
I did what you new simulation file is here.fsp (501.9 KB)
But I have a problem.My Sio2 substrate does not allow graphene layers to be seen When I set 2 mesh order for Sio2.I change mesh order 2 to 5 but I Did not receive the correct answer.
Thank you very much.

I could solve my last problem by your advice.
New simulation file is here.fsp (1.6 MB)
But I can not find tranmission characteristic.My transmission is below:
Please help again.
Thank you so much.

I did some modification on your file:

  • mesh - It looks a little too coarse in z. It is true that you dont need fine mesh to resolve material when 2D graphene is used. But you still need some reasonable mesh resolution to resolve the mode. So I used finer z mesh in “mesh circle” override

  • spans: - source, monitor, simulation region. I increase the spans of the source, monitors and simulation just to make sure the mode is well included in the region. Also, since the wavelength is a lot large than the size of the structures, you may want to further increase the spans of the simulation region to test convergence. When I run this simulation now, I am able to obtain some peaks near the positions of the the peaks on Fig3a). However, the transmission value are not quite the same yet so I believe there should be some room for results convergence. I suspect mesh size and simulation spans could noticeable affect your results.

uplo_KC.fsp (2.7 MB)


I increase spans of monitors,source and simulation.
transmission result is better than before.

It is clear that absorbtion is very high.
but still is not trasmission reported in article.I can not to reproduce it.:confused:
Thank you for help.
Simulation file:test.fsp (2.5 MB)

There are several things I would suggest you to try:

  • In fig 1c) it has the back-gate configuration. I might miss that in the paper but do you think the authors might have used this configuration for the simulation for figure 3a) ? If gold was used in the simulation, the mode calculated should be affected.

  • Page 1, line 107, it mentions the dz they used is much smaller than the dz you used. I think this may make a difference in terms of the resolution of the mode calculated.

  • For figure 3a), do you think the author obtained the spectrum in one simulation? In FDTD Solutions, the mode calculated by the Integrated Mode Source is only for the center frequency. Since the spectrum is across a very wide range of frequencies, the eigenmodes may look differently in space. In your simulation, you are using the center frequency mode file only and assumes that the mode is unchanged across the entire spectrum. I think it is worth running some single-frequency simulations in the higher frequency range to test the transmission.


I did what you said.But result has not changed.I think paper result is not true or I do not know what is author pupose.
I started to reproduce result of this article(figure 3_b):
My simulation file:1.fsp (1.6 MB)
for start I set large mesh.I increase span of simulation.I do not see converge in simulation result.I think pml boundary do not work correctly.I think I have huge problem.
Please Solve my problems .
Thank you for helps.

Hi, I will be busy in the next week or two. Somebody else may look into your questions later. Thank you for your patience.

I have a question about SPP.
Someone else can help me.
Thanks for any helps.

Hi Dezyani,

I will help you with your questions. At the moment I am looking at the nanoring paper and your simulation. Is the question about surface plasmon related to this simulation?

I have not any question about surface plasmon theory.
I saw in many paper that surface plasmon propagate between graphene layer and dielectric by a TM mode source or one dipole at edge of graphene nanoribbon.At first try I used mode source and calculate transmission by one monitor.
My simulation result was not similar to paper result.I guessed reported result in first paper is not valid.
I started to reproduce result of second article.Please look at simulation files and solve my problems.
Thanks for helps.

Hi Dezyani,

Sorry for the long wait. It took me some time to find appropriate settings for your simulation. There are some challenges due to the strong confinement of light, which requires a very fine mesh near graphene. Please take a look at the attached file: graphene_ring_resonator_modified.fsp (1.9 MB). In Fig. 4b of the paper the authors show three peaks for transmission; I focused on the middle peak, near 21THz. There is still some work to be done but I think this is a good starting point.

Some important comments:

  1. Boundary conditions: I used metal boundaries for all directions except the propagation direction (x). This is a good starting point since the mode is expected to be confined. Later on you can compare with the results using PML boundaries everywhere. For the PML in the x direction I used standard settings with 16 layers; it is probably a good idea to do some convergence testing increasing the number of layers.
  2. Size of the simulation window: I reduced the size in the x direction to make the simulation faster. The z span is quite critical since you need to make sure the boundaries are far enough from the ribbons so that the mode is not disturbed. From the mode profile it seems the z span used is good enough.
  3. Mesh for graphene ribbons: It is quite critical to use a fine mesh for the input/output ribbons, the ring and the gaps in between. I modified the mesh override regions you had and added some more. It is also important to do some convergence testing by refining the mesh in these regions; the peaks are probably very sensitive to the mesh there.
  4. Source bandwidth: The range covered in Fig. 4b is quite broad, from 3THz to 30 THz. It is important to be aware that there can be mode mismatch errors when using the mode source as broadband; this is explained in detail here. A way to minimize this error is to reduce the source bandwidth. That is the reason why I decide to start with one of the peaks.

Hope this helps!


Thank you very much for reply
I used fine mesh in my simulation,I can get middle transmittance frequency.
but I get 0.2 magnitude.Paper result is very high.I am so confused.
Please help me.
Thank you so much

My problem in last simulation exactly is magnitude of transmittance.In first simulation I had same problem.
I think use one monitor to find transmission is not true.
Thank you for helps,

Hi Dezyani,

An improvement for the transmission calculation is to use a mode expansion monitor (as explained here) and two monitors, one at the output and one at the input (in front of the source). The transmission of the particular mode of interest is the forward transmission in the mode at the output divided by the forward transmission in the mode at the input. This would give a more accurate value for the transmission. However, I would not expect it to double the transmission as required to get agreement with the paper.

Some additional comments:

  • It is possible that the transmission is affected significantly by the position of the monitors. In the paper I could not find the distance “ls” between the ports and the end of the graphene strips, so maybe you could try a few positions of the monitors.
  • The other thing to check is how the other peaks look like by changing the center frequency of the source and check if at least we are getting the relative magnitude of the peaks correctly; for example you can check if you get the first resonant peak, near 12 THz, higher than the second peak, near 19 THz.
  • Finally, it would be good to check if you can get the dispersion relation in Fig 1a, to make sure the mode we are injecting is consistent with what was used in the paper.

Hope this helps.

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Hi Federico
Thank you so much.
I used mode expansion monitor.but transmittance never changed.
Do you think my simulation is correct ?
Thank you so much.

Hi Dezyani,

I did get a small difference when using the mode expansion monitor as shown below:

This is the simulation file I used: graphene_ring_resonator_modified_2.fsp (2.1 MB) mode_expansion.lsf (358 Bytes). I would suggest going through the checks I mentioned in my previous reply. It is possible that we are not using exactly the same material properties for graphene, or that the position of the monitors is not the same used in the paper.