Waveguide collection of emission source

[p.liu-2]

I’m using FDTD Solution to simulate the waveguide collection of emission sources. I used a dipole source lying on the waveguide.

I want to obtain the fraction between the power collected by the waveguide and the power emitted by the dipole. I’m thinking of doing a overlap analysis between them, but I don’t figure out a certain way to do this.

1. Does anyone have experiences about this?

And I found a paper which is quite relevant to what I’m looking for. The authors also used Lumerical to simulate it and they got some technical support from Lumerical. There is one figure talking about the collected power part from a radiation pattern.
2. Does anyone have a clue how they defined the regions of surface collection and end collection?
3. Does someone know how to plot the radiation pattern like that?

This is what I have. It takes about 30 mins to finish the simulation. The file is too big to upload, therefore I put a link for the file down below. Really appreciate for any helping and advice.

Dropbox - Link not found

[gbaethge]

Hi @p.liu-2,

I’m not too familiar with this set up, but I had a look at the simulation file and I would have a few comments:

• In your simulation, the structure is smaller than the FDTD region (in the direction of propagation of the waveguide). It means you have 2 interfaces at the end of the waveguide that will generate some reflections.
• The dipole will emit in a non-homogeneous material, the power radiated will be different than in a homogeneous material, as explained here. You will have to be careful when calculating the coupling into the waveguide, as in the default settings, the results are normalized by the standard sourcepower function (corresponding to the analytic power radiated in a homogeneous material).
• Far field projections assume the fields are propagating in an homogeneous material. in scat_ff, it is not the case of the side monitors. It means the far field projection will not be correct.

Regarding your questions 2 and 3, the best would be to contact the authors and see if they can share the simulation settings. Also, can you post the reference of the paper?

[p.liu-2]

Hello @gbaethge,

Thank you for your comments. I used PML boundary conditions for each side of the simulation region. I think the FDTD simulation reguion should be larger than the structure. Finally, I placed a field profile monitor on the waveguide core to compute the power going through the core. Thank you for the suggestions of dipolepower and sourcepower function. I noticed the difference and I used dipolepower function which represents the actual power of the dipole that is injected into the simulation region. I’m not struggling with the far field projection. It seems the situation in the paper is more complex than what I have.
Sorry for that I didn’t include the reference.
For reference of the paper: Surface and waveguide collection of Raman emission in waveguide-enhanced Raman spectroscopy

[gbaethge]

The size of the simulation region should be defined depending on what you intend to model. As I mentioned, having the structure smaller means you have 2 interfaces waveguide/air that will add some reflection. The monitor will include the reflected fields in your results.
If your intend is to model a setup where the light emitted by the dipole couples with modes in the waveguide and you would like to estimate how much is actually coupling into the selected mode, I would avoid to include any unwanted reflection.

To calculate the coupling, you can use the mode expansion monitor. When using other source that a dipole, Tfoward/Tbackward would give you the amount of coupling into the selected mode, normalized by the source power. Using a dipole in non homogeneous material, you may have to calculate the coupling using the a and b coefficients (the complex transmission coefficients of the forward/backward propagating waves, of the selected model field).

[p.liu-2]

Thank you so much @gbaethge! I understand your first comment. Thanks for the thoughtful explanation. I made the waveguide structure longer than the simulation region in the propagation direction. I was wondering how to calculate the power coupled into the fundamental TE mode of the waveguide. And your suggestion “using mode expansion monitor” exactly gives what I want.

Now, I get some further questions.

• The value of the result “T_total” varies with the size of monitor’s area. If I most care about that the power transmits through the waveguide core, I should place the monitors over the cross-section of the core. Is that right? Because if the monitors includes some parts of substrate, the results will include the power which penetrates to the substrate.

• I placed several power monitors with different distances far from the dipole source. The results highly depend on the distance between the source and the measure point, shown in figure below.
  
  In practical, the length of the waveguide would be much longer than the length used in the simulation, like a few centimeters. I have no idea how to find the relation between the coupling power and the waveguide length.
  I was thinking of using periodic boundary condition for x (the propagation direction). Then the simulation will include multi dipole sources, that is reasonable, considering that the dipole signals randomly exist in the waveguide surroundings. However, for the power monitor, I won’t have any inputs and outputs. Since each periodic of simulated segment has a source and several monitors. Do you have some ideas to solve this?

• The material data of dielectrics cannot be fit, due to the zero imaginary part. Will it influence the waveguide loss calculation?

Really appreciate for your help.

[gbaethge]

Hi @p.liu-2,

I’m glad if I can be of any help! Regarding your questions:

• T_total is the total transmission of the monitor, it is the same as the value calculated by the transmission function:
  
  For than reason, it varies depending on the size of the monitor as, if the monitor is too small, it will record only a part of the fields.
  In your case, you want to know how much power is coupled into the TE mode. This would be given by T_forward (if you are looking at fields propagating towards the positive direction of the axis). T_forward is calculated by:
  
  As we discussed previously, with a dipole in a non homogeneous material, sourcepower will not give the correct power, so T_forward will not be correct. You should calculate it replacing sourcepower by dipolepower (the other coefficient, a and N are given by the mode expansion monitor).
• It is expected, as depending on where you place the monitor (and depending on its size),. the recorded fields will be different. Again, what is of interest, is the coupling between what is recorded by the monitor and the mode you selected. Only the part that couples with the mode will propagate in the waveguide, the rest will most likely be lost on the way.
  If you use periodic boundary conditions, as you mentioned, you will model multiple sources along the waveguide. Light will propagate bidirectionally and you will get interferences between the neighbouring periods. I would suggest to keep the PML and model a finite section of waveguide.
• This is often a tricky point. The materials have a constant imaginary part of the permittivity, equal or very close to 0, while the real part varies. It’s impossible to get a good fit for both and you may have to decide what is more important for your simulation. You can modify the material fit to give more or less importance to the imaginary part. For instance, if I decide to decrease the weight of the imaginary part of the silicon nitride permittivity:
  
  
  
  The fit of the real part is much better, but I introduce a non null imaginary part that will add some absorption in the material.

[p.liu-2]

Thank you for the quick replying and all the points @gbaethge! Using the T_forward results makes a lot of sense. I noticed that the results are calculated by using sourcepower which is the power radiated in the homogeneous material as denominator. I will replace it by dipolepower. I will try to fit the material data with FDTD model.
I’m keeping on looking for some methods to calculate the waveguide loss against its length.