Hyperbolic Biosensor simulation using FDTD algorithm


I am trying to simulate the device in this paper nmat4609-s1.pdf (2.9 MB)
.As mentioned in this paper,FDTD(even Lumerical software) has been used for simulation purpose here.I am trying to regenerate the result.Here is my simulation file similar to the figure S16©.My simulation file is biosensor.fsp (354.9 KB)
But i don’t get the correct result when I do the single wavelength simulation under optimization and sweep tab.
I hope you guys will help me,



I tried to modified some simulation settings, but it does not seem to show me a plot that is similar to S16© at all. However, it looks like it may share some features with plot S16(a). I might have missed some information in the paper, can you tell me which section does it contain the structure parameters information. I would like to make sure what are the structure parameters of the GC-HMM and reference sample?


Here is the main paper,biosensor.pdf (801.7 KB).In this paper you will find the full GC-HMM discription.


Here is the main paper biosensor.pdf (801.7 KB)
you can find the full structural description of GC-HMM.


Thank you, I will need to time to take a look a this. Thank you for your patience.



So far I dont seem to be able to reproduce the S16c), not even close. I suspect that there might be something critical we might have missed here. I wanted to make sure you had the structure drawn correctly in FDTD but I dont seem to find any obvious information in the paper that clearly state the grating parameters. Can you tell me where did you find the grating parameters?

I have edited your simulation based on some simulation best practices, and my experience. If we got the correct structure parameters, and material information, I believe we should be able to simulation this device. I cannot think of any reason why FDTD fails to do that, given that the author had also used our software for simulations.

Below is some changes I have made:

  • I noticed that it has a superstrate of DI water, therefore it should have a background index of about 1.33
  • on figure s19c), looks like the substrate should be at least 400nm
  • I think the mesh override you had initially is a bit too fine. I reduced the mesh size a bit, but added another override region on the gold upper teeth region

biosensor.fsp (351.9 KB)


Thanks for your response.The grating parameters are specefied here biosensor.pdf (801.7 KB)
in figure 1 as > 2D subwavelength gold diffraction grating on top of the

HMM with an average period of 500nm and hole size of 160nm (scale bar, 2 um).

even if you look at the ‘Method’ part of the paper (at last page) you will find how this 2D grating was fabricated.
Or if you can generate the electric field profile from S19 it will be great help.


Thanks for the follow up information, I guess it can translate to the pitch and the size of the x span of the smaller gold plate. However, would you have idea where in the paper has explicitly indicate these parameters? a,b,c,d,e,f.


As 20nm gold was deposited so d,f,c=20nm.and obviously a=340nm(500-160).The PMMA was used as an etching material to fabricate the grating.There is no mention of what should be the height of that grating a.


Do you know if Figure S19 are supposed to be the simulated field profile of a 500 nm pitch? Looks like the pitch there is less than 400 nm ?

Second, I can see that the paper has been mentioning 2D grating? On Figure 1a in the article, looks like it may be referring to a two-dimensional array? If this is the case, I think you will need to set up a 3D simulation region with the two-dimentional array. In the current simulation setup, you have a 2D simulation region, and a one-dimensional array.

I have tried lots of different things with the current simulation file but I dont seem to be able to reproduce S16C. I think we are missing something fundamental here, we should definitely clarify the above two points.


Thanks for that observation.Sorry for my late reply.My Internet connection was very bad during the last week due to heavy rain and thunderstorm.
For simulating a normal grating,I then take this paper Experimental demonstration of surface and bulk plasmon polaritons in hypergratings.pdf (1.5 MB)
which is the reference paper of that main paper of biosensor.pdf.Here we see a 1D grating.I am trying then to simulate the device.Especially I want to retrieve figure 4.Figure 4(a) was pretty simple and I get it from simulation.But for getting figure 4(b) I built this simulation filereference_sample.fsp (339.3 KB)
The device information is given in page 2(especially grating).The desired curve doesn’t come.What do I do wrong this time?Can you help?Further problem is that,when I do a single wavelength simulation(under optimization and sweep Tab) and choose 500 points between 200nm and 2500nm there has been “divergence problem” for some sweeping points.Why is that happening?


For some reason, I did not receive any notification on your replies.

I will take a look at your questions as soon as I can.


hi @arnabeee10

Sorry for the very late response. I think my forum account setting is now updated to keep track of replies.

I took me a while to test your file. I have tried lots of different things but did not seem to affect the reflection plot a lot, except one thing - the source polarization. You had the polarization perpendicular to the grating grooves, but the reflection never look similar to the reported results. Once I have changed it to parallel, the plot now look much closer to figure 4b (although not exactly the same yet. We can probably fine tune the plot later, but we should definitely confirm the source polarization. Do you know if figure 4 results are experimental or simulated?

While I am testing your file, I switch the plane wave type to BFAST so it can return broadband results for angled plane wave incident. It is going to be very useful if you want to return some quick results. But the sweeping the single wavelength like you had it will be a more accurate method.

I have also made other minor changes, like mesh, PML, etc. But the most critical change is the source polarization. Let me know if you want to discuss more.

For diverging simulation, you can look into the particular file and try to debug that. For more info, you can refer to here or we can take a look at the particular diverging file.

Edited file
reference_sample_KC.fsp (334.8 KB)


Thank you.
1)If you look page 3 of that paper,It says that it is p polarized wave.So polarization angle is zero degree.In theory it has been proved that no surface plasmon exists for s polarization only for p polarization.
2)It may seem that graph of 4b is close for s polarized light,but I cannot derive other graph like 4c 4d 4e for their respective device structure in the case of s polarization.
3)Actually it was an experimental result.But I am trying to simulate it and make the simulated result as close as possible to the experimental result.My previous file of biosensor is a similar type of application of hyperbolic metamaterial. The main problem here is to excite surface plasmon using grating coupling technique.In this paper the 1D grating technique was used where in the previous paper a 2D technique was used.
Here is my file wiith full hypergrating,
reference_sample_KC.fsp (1.5 MB)
I just insert a Au/TiO2 bilayer between spacer and substrate.


Sorry for the slow response. I have spent quite a bit of time testing your files but I don’t seem to be able to get the reflection plots exactly like what is shown on figure 4.

Although there could be two sets of conflicting definitions of s and p polarization, I think you are right that the reflection plots, for parallel polarization, it doesn’t seem right when bilayers are introduced. However, the plot for the reference sample (no bilayer) did not seem to correlate with the reported results neither. I still can’t understand this part. This simulation itself looks simple, and I cant find anything suspicious. This part is puzzling me.

For the below results, I have used the grating_transmission analysis group to analysis the reflected and transmitted light. The blue curve is total, the green curve should the amount of the energy carried by the zeroth grating order. Not sure how it is measured in experiment, but it should it may be a piece of information to consider. See here for more information (https://kb.lumerical.com/en/index.html?diffractive_optics_gratings_order_transmission.html)

I have tried to simulate the 4 cases, reference, control, 4 bilayers and 6 bilayers. Although they don’t look super similar to what is reported, but there are actually some features that we can learn from it. I could be wrong, but looks like there could be a shift to the plots – the features seem to start after 1000nm. For example, the control plot shows these two little peaks after 1000nm, and a flat spectrum afterwards. The reference plot has these 4 sharp peaks after 1000nm, and a relatively broader peak at longer wavelengths after 2000nm. For the rest of the plot, the peaks are shifting and varying, but not quite in a way that is reported. I am not an expert to comment the SPP and BPP positions, but I think you might be able have a different perspective to it?
reference_sample_refl_oblique.fsp (408.7 KB)

On the other hand, I have also tried to Figure S6 in the supplementary material. This is reported as the transmission plots, normal incident. Again, the simulated and experimental results are not the same, but I can see some similarities. For example, there is a relatively broad peak in the transmission_reference plot. In the control plot, it becomes some sharper peaks. These sharp peaks with reduced amplitude when increasing the number of layers. These features seem to agree with Figure S6.
reference_sample_trans_normal.fsp (408.7 KB)

In summary, I think it is hard to conclude something solid here. There are definitely some major discrepancies between the simulation results and the reported experimental results. Often times, it might not be super easy to reproduce a perfect match from simulations, since there can be quite a few of uncertainties in experiments. From the simulation perspective, the two major factors here that could be significant are the material data and the design parameters. The material data have a huge play in the simulations results because the solver rely on it a lot to solve Maxwell’s equations. Obviously, the design parameters are critical too. The device should have fabrication tolerance associated with it, however, in simulations, 10 nm is 10 nm.

I hope this helps and able to give you some idea of the simulation results. If you discover more or have follow up questions, please let us know again.