# Unable to reproduce literature results (Reflection and Transmission in a single mode laser)

Dear Lumerical support team/users,

I am trying and evaluating the suitability of lumerical for my simulation purposes. In a first step, I am trying to reproduce literature results (paper attached). For instance, I am trying to reproduce the transmission and reflection from a slotted waveguide from Lu et al, IEEE photonics technology letters, 22, 11 (2010). I am attaching the paper and have highlighted the relevant simulation parameters. To summarize,

Structure : Ridge waveguide with etched slots

thickness of ridge: 2 micron, depth of ridge: 1.85 micron, slot width:1.1 micron, slot spacing: 7.87 micron, slot depth:1.35 micron

Aim: To calculate the reflection and transmission from the device at 1.55 micron for the fundamental TE mode and reproduce the quoted value of 0.43 and 0.4 respectively.

Method: I am using both EME and varfdtd to reproduce the results.

Problem:

1. I am not able to get the desired results. the s-parameters obtained from the EME do not agree the transmission and reflection value quoted in the paper.

2. The transmission/reflection value from fdtd power monitor also do not agree with the paper.

I am new to this tool. Apologies if I have done something wrong. I am attaching both of the files (eme and fdtd).

singlemodeieee.pdf (420.9 KB) singlemodeieeepaper2fdtd.lms (421.6 KB) singlemodeieeepaper1eme.lms (640.6 KB)

Hello,

Welcome to the community. Thank you for attaching this paper, and providing detailed background. I am not exactly sure why you cannot reproduce these results without some more testing, but l will provide some suggestions and ask that you get back to me.

Both methods should be suitable to accomplish your goals; however, EME will likely be the most efficient method for the results you are interested in and very appropriate for the device you have modeled. The EME solver would also be very similar to the Scattering Matrix Method that this group used. To better sweep the parameters of interest I would recommend only having one or two slotted sections. Since the mode coupling is the same at each ridge you can increase the periodicity of these cells, or change their span, with minimal computational cost through EME propogate. Although you will have to recalculate coupling each time the slot depth is changed.

In this paper they say they are looking at a single mode, but do not say whether it is TE or TM? Both exist in this ridge waveguide. Are there clues regarding the gain material that would suggest one over the other? The TE mode will be highly confined, and so they will not be particularly effected by the DBR structure, so may be why you are seeing higher transmission. Some initial measurements of the TM reflection and transmission coefficient suggest these may be closer to the values quoted in the paper.

One thing to note is that they have given the effective indices and done the simulation in 2D. Using the 3D simulation with the 2D effective indices will likely give different results. Please change EME solver type to XZ:X propogate.

For more information on the EME solver please refer to these . AppGallery pages and check out the EME course for a thorough overview.

Regards,

1 Like

Hi @trobertson ,

Thanks very much for you suggestions. It was really of great help. As suggested by you, it seems they have calculated values for the fundamental TM mode since the values I am obtaining for the TE mode is not even close. Since I don’t have any information regarding the gain media and which mode is dominant, I presume TM is used in their calculations here. However, I have still two questions which I could not able to figure out.

1. Why can’t I reproduce the result in a 3D EME solver simulation, in other words what should I do to reproduce the results for a 3D solver? Even if I don’t use effective index, the refractive index of the layers is around the effective index values. Even if I don’t get exact results as in a XZ solver, at least I should get values around the quoted values. I don’t think I am doing something fundamentally wrong while performing a 3D calculation.

2. Secondly, even if I excite a TM mode from a mode source in the varfdtd, I am not getting the required values, not even close. Should I not get at least values closer to the values I get for a EME calculation ( 2D XZ, X propagation). Vardfdtd uses effective index method, so should not it give the same result?

Thanks very much once again and sorry for the delay in replying.

Hello Saroj,

I suppose you should try and replicate these results in 2D first and then determine the difference with 3D results afterwards. I would double check that you have structure modeled exactly. Luckily EME has a number of convergence testing features. Refer to this page on convergence testing

Try to narrow down whether the abnormally high transmission is an issue with the calculate modes step or the propagate method. Solving for more modes would be interesting see this video from the EDU course.

It may be that the radiated modes are not being found and thus the guided modes are not able to couple to them? This artificially suppresses a loss mechanism. It would be nice if you had more information on the modes being considered, but take a look at what modes are being found and if they are reasonable. Use an index monitor over the structure. In varFDTD is this seeing the index variation due to the ridges.

I believe that the none subcell method, with energy conservation are the best options in EME, but it may be helpful to experiment with these options.

Adjusting the geometric and material parameters until you start to see higher reflection might give you a hint? It seems that these modes are not being strongly perturbed by the ridge region, if they were less strongly confined in the ridge then I am certain you would see higher reflection

Good luck and let me know how it goes.

Regards,

1 Like

Hi @trobertson,

Thanks very much for your help. I am really grateful to you for your help.

Sorry for the delay in reply. I wanted to make sure I am doing everything right before contacting you again. I will summarize below what tests I have done and please let me know if I have made any conceptual or technical mistakes.

First, the problem statement is the same. It’s the ridge waveguide with etched slots. For the calculations below, I have used 10 slots with height of 1.4 um where the ridge height is 1.9 um. I will start with the EME calculation. In the EME, the mesh along longitudinal direction (x) is taken assigned according to the number of cells. Now, since I will use XZ solver, the only mesh that matters is z. Therefore, I varied the number of transverse meshes to get the required structure in the refractive index monitor. It seems for my calculation, 500 points in the z direction does the trick. As you can see from the attached image, I got the required structure.

I went with the none subcell method with conserve energy. I selected the fundamental TM mode in the ports. Then, I ran a mode convergence sweep in the propagation stage. I got a result something like this,

So, it seems the values converge after 36 modes. Therefore, as you can see the transmission and reflection values I got from the codes are around 0.28 and 0.17 respectively. Finally, since I am interested for a range of wavelength, I did a perturbative wavelength scan and the result I got something like the below,

In the second step, I thought to try the same problem through Var-FDTD. I first checked the structure through index monitor which seems fine.

Then, the first step is the collapse of the third dimension and generation of an effective index. In the effective index tab of the solver, I selected the first fundamental TM slab mode through the select mode option using which the effective index will be calculated. In the mode source, I selected the first TM mode.Finally, I plotted the transmission spectrum from 1.5 to 1.6 um. As you can see, the T and R now stands at 0.57 and 0.36 respectively as compared to 0.28 and 0.17 in the case of EME. Again, the spectra also looks different in both cases

I think, the result from varfdtd looks resonable. Plese correct me if I am wrong. Now my question is which result should I trust and why? Please let me know if I have done any mistakes?

Hello @115220097,

Great work here, thank you for your thorough report. I would be inclined to believe the EME model over the varFDTD model as it makes fewer approximations, and it is closer to the simulation method used in the paper. It is unclear how you have defined your cell groups which would have a greater effect than the mesh cells in Z. Just for curiosity sake what is the TE value? Could it be that the values they give are the unpolarized average of TE and TM contributions?

Sorry for the delayed response have you made any progress on this recently?

Best Regards,