# L3 Cavity Mode Simulation

Thanks again @bkhanaliloo

Thanks for the detailed explanation. I think I understand now.

I have been trying to perform Q analysis for the same cavity. Using the Q analysis module, I get a Q of around 388 for the fundamental mode with no displacement of the center holes in the structure. However, the reference reports a theoretical Q of 5300 for the fundamental mode. Please look at Table 1 of the reference.

There are a few things that I have tried. I have used finer meshing and got around Q of about 391. But the calculated Q is still about an order of magnitude lower than the reference. I have tried with filter width in the Q analysis script and time length for calculating the slope of the decaying exponential signal in time domain. But nothing seems to work here.

I am attaching my file here again.
Chalcraft.fsp (373.9 KB)

Can you suggest some other things that I need to look into?

Hi @kanak

Unfortunately I couldn’t see much improvement with finer meshes or location of the Qanalysis group.

One more thing that will be good to double check is the dimensions of the cavity reported in the paper. It seems like if the holes are misplaced by 15% of the lattice constant, Q value will be increased by ~10 times. This means that the cavity is very sensitive to the small changes in the dimensions. Also, it will be a good idea to run the simulations with different values of lattice constant i.e. a=240-270 nm.

I would also recommend to place the Qanalysis in the center of the cavity where Ey field is maximum. You can reduce the number of monitors to 1 to speed up the simulations as well.

Dear @kanak

@kchow and I spent some more time on your case. I think that the Q value calculated from high Q analysis group makes sense. Below is the electric field behavior captured by time domain monitor:

Ignoring the first portion of the data (which probably belongs to the signal emitted by dipole), electric field decays exponentially which corresponds to Q~300.

The only thing that we were concerned a bit is the material behavior at wavelength ~830:

Since refractive index shows a jump at these wavelengths, and your design is very sensitive, I was thinking maybe this causes such a drop at Q values. Maybe you can change the lattice constant an/or hole sizes to see how your Q values change?

Thanks

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Thanks a lot… @bkhanaliloo

Yes, the design appears to be very sensitive indeed. However, if I choose a constant index value rather than the material database parameter Q improves significantly. In your examples also, I see that the bandstructure or cavity analysis, one single value of index has been employed. Using a single value of index, which is 3.6 for GaAs, I got Q of 2836, which is about half the reported value for the same cavity. I am attaching the file here:
Chalcraft.fsp (370.0 KB)

Hi @kanak

I am glad that finally results make sense. It is possible that in the paper they used a constant value for refractive index, but I guess for applications in the wavelength range of <900nm, you need to watch for the imaginary part which makes devices to behave lossy.

I also had one question for you: why there is a big jump in the imaginary part of GaAs at wavelength ~900nm? Is it because of the material bandgap?

Thanks

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Thanks @bkhanaliloo

I am not sure whether bandgap is the reason for sudden jump in imaginary part of GaAs.

I have a question with another reference. In this case, the authors report results of H1 cavity modes in a bilayer heterostructure photonic crystal made of Alq3:DCM2 and SiO2. Here is the reference.

I have been trying to generate their results. But here, due to the nature of the structure, we can not invoke symmetry along Z direction. In that case, despite having TE bandgap, when excited with dipole sources, the structure should show some TM modes. Is it possible to excite only TE modes in this case? Cause otherwise the quality factor will be low. I am attaching my simulation file here
Kitamura.fsp (606.6 KB)

Hi @kanak

The quality factor of the devices should not be affected by symmetry as long as we are capturing the electric field properly.

In your case, you have selected the magnetic dipoles to be along the z direction (thus electric field on the plane of the devices). This means that you are mainly exciting TE modes. However, as you mentioned, because of the asymmetry along the z-direction we will not be able to excite only TE modes. Thus we expect to excite TM modes which we can not avoid it.

One idea that I think might improve your results: since your device is asymmetric, I guess you could re-position the source in the maximum electric field of H1 mode so that they are not in the centre of the devices. Also, can you modify your sources and use a longer pulse such that they excite a pulse at the H1 frequency?

Hi @bkhanaliloo,

Do you mean that mean that one should do their 1st simulation without x and y symmetry BC and Z with symmetric BC and then after we know all about mode symmetries then we can put BC condition accordingly for more finer simulation?

If this is the case then, we are not saving time as 1st simulation will always be time consuming.

I have another question about high Q cavity simulation. I am simulating L3 cavity with some 3 displaced holes nearby and because of this they should have higher Q. In reality (measurement), these cavities are excited by a line defect waveguide (W1) which is 4 holes far from the cavity vertically (side coupled) . So, in order to extract Q factor and mode volume of the cavity, should I use W1 waveguide in simulation or not?

Saurav

Dear @saurav.kumar

A good approach will be to not to use any symmetry in the first simulations. As we discussed in previous posts, use of symmetry might suppress some modes. Once you know the symmetry of modes of interest, you can employ symmetry.

Depends on what you want to measure. If it is the intrinsic quality factor (quality factor of the cavity decrease in the presence of external waveguide which we refer to it as loaded quality factor) and mode volume of the cavity, then you do not need to include the waveguide. However, if you want to see how your cavity will behave in the presence of external waveguide and calculate the coupling coefficient etc, then you need to add it into your design.

Dear @bkhanaliloo,

                Thanks for your quick reply.


If the intrinsic Q-factor is very high ( close to a million), then I am told from Lumerical team that the simulation become very sensitive and it might take a while to extract Q-factor from such cavity.

Also, my real design contains waveguide. So, I think it’s better to simulate the complete system and not just the cavity. How to extract coupling coefficient and what do mean by etc? Are there any other factors which I need to look into.

Saurav

I am trying to simulate the same structure in the reference using scripting method this time. The reference paper is :
Mode structure of the L3 photonic crystal cavity.pdf (361.7 KB)

I have done simulations using the layout mode and the results obtained agreed well with the literature. Now I am using scripting method. But, the results look different when I use the script. I am attaching both my layout and script files.
layout file:
Chalcraft.fsp (490.5 KB)
script file:
Script_2.lsf (5.6 KB)

I can’t figure out what’s the mistake here.

Kanak

You can calculate the coupling coefficient by comparing the output power with the injected power. Here is a good post for you to read (although it is about ring resonator and might not be exactly what you want but should give you some insights). My other recommendation would be to use a multi-frequency source if you are using a broadband waveguide mode source.

Dear @kanak

What results are different? Can you please clarify it more.

Thanks

Sorry for not being clear enough and a bit misleading too.

Actually, the value of the electric field intensity varies in the two simulations. Here I am attaching two files.
Fundamental mode using script:
Fundamental mode using layout:

Please look at the magnitude of the field intensity.
Sorry again for not being precise and clear enough.

Hi @kanak

It looks like you are using no Normalization state in the layout approach. You can change it to CW normalization state as is shown in the screenshot below:

Please note that we use no normalization in the nonlinear cases where light from one wavelength is transformed to another such as harmonic generation.

https://kb.lumerical.com/en/index.html?ref_sim_obj_cw_normalization.html

Dear @bkhanaliloo.

I know this thread is already some months old, but it was the only one that I found here concerning with the Q-factor calculation of L3 photonic crystal cavities in membrane waveguides.

I am a student and new to FDTD simulations in general and to the extraction of Information about the Q-Factor of those cavities with lumerical, so apologies if any of my questions are answered elsewhere or are kind of obivous.

What I am trying to simulate is this structure and material system published by Nakamura at al, and to reproduce and confirm their simulations: DOI:10.1364/OE.24.009541. I will attach my attempt on modeling this scenario in the end of my post.

The radius of their holes is r = 108 nm, with a period length of r = 420 nm in a slab waveguide with thickness of t = 220 nm and a refractive index of n = 3.46. All these parameters should provide operation of this cavity in the 1.55 µm telecommunication band.

They start from an unaltered L3 cavity and observe the Q-Factor of the (ground) mode in respect to shifting specific holes around the cavity, including the well known increase in Q-Factor by shifting the two inner cavity holes.

Now to my problem. They mention a Q-Factor of 5300 already for the unaltered design (whereas I just got values of something of around 2700) and if I shift the two holes by their proposed amount of 0.2*a I get suddenly negative Q-Factors (in this case -139505), which makes obviously no sense.

As I said I have just started to use lumerical and what I have chosen here for the settings is mainly based on the cavity tutorial for the H1 cavity that is shown on your website, with the only difference, that I am using just one source, right in the center of the cavity and Qanalysis in the center of the cavity, too. The mesh sizes are dx = 0.1a, dy = 0.1asqrt(3)/2 and dz = 0.1t. Maybe I have missed something important?

Nakamura_silicon_L3.fsp (3.7 MB)

Best regards,

Lucas

Dear @lucas.rickert

Thank you for providing a detailed question.

Calculation of quality factor is challenging and requires patience. The main challenge, other than properly setting the simulation, is setting source and monitors to make sure that you are capturing a proper electric field signal.

As you mentioned and is explained in the KB application example (https://kb.lumerical.com/en/index.html?diffractive_optics_pc_3d_cavity.html), you will need to use more sources and monitors. The problem of using only one source and one monitor is that if source can not excite the mode of interest or monitors can not record the electric field signal properly, the value for Q will not be reliable. So, I strongly recommend you to start with the application example, and try more sources and monitors.

There are couple of more things to bare in mind:

Please take a look at them and let me know if you had further questions.

Thanks

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3 posts were split to a new topic: Photonic crystal waveguide coupled to an L3 cavity

Hi all,

I know this post is not active for a while, but I need to do the same simulation of the paper “Mode structure of the L3 photonic crystal cavity” with different material system Si/SiO2. I made a simulation file following tips provided above but using my material system. I use symmetry only at z boundaries to be able to see all available TE modes. I am using 3 magnetic dipole sources in the cavity and Qanalysis group inside cavity with 12 monitors.

The problem is my Qanalysis gives me results that I cannot understand (I am not sure if it is even correct or not). As a start, I am searching for 8 resonances.
I am attaching a screen shots of the plots I got and also the fsp file.
The following figure shows 8 decayed resonances.

In the next figure I cannot see these resonances. Only one sharp peak. Does the small side peaks counted as resonances too?

I added profile monitors at the peaks frequencies to observe the mode profiles, but I only get one mode at 188.708 THz (which is the sharp peak in the spectrum plot) and other modes are not confined in the cavity!!

Can you tell me if my file is properly created? what can I do to see other confined modes?

A post was merged into an existing topic: Coupled L3-Photonic crystal nanocavities