# Mode expansion monitor - a query

#1

I have a confusion about using Mode Expansion Monitor in FDTD. I am trying to simulate the interleaved PN junction based optical modulator from the knowledgebase of lumerical.com (https://kb.lumerical.com/en/pic_modulators_interleaved_junction_microring.html). I used the “np density” grid attribute object to import the carrier density and used the Soref and Bennett. However, the example in the knowledgebase use (n,k) import option and uses an script to calculate the phase change due to the PN shifter.

I am having some problem understanding the Mode Expansion Monitor. The situation of my simulation is depicted in the following diagram for simplicity. I am launching the fundamental TE mode using the mode source as depicted. After some distance (say 50 nm) is located a frequency domain field and power monitor to act as the “input field” for the expansion monitor. 5 to 10 nm after this frequency monitor is located the PN junction phase shifter. Again, after 5-10nm distance after the PN junction shifter is located the Mode expansion monitor. Both the monitors have same span (in x and z directions). I have setup the expansion monitor to calculate the power coupled in the fundamental TE mode after the mode has propagated through the phase shifter.

My understanding was that the neff and mode profiles contained in the mode expansion monitor would reflect the phase change accumulated by the injected mode after it has traveled through the phase shifter and hence the neff would be different than that of the neff in the mode source, However, in the simulation both have same value. Could you please explain a little as to where am I going wrong and how can I setup my simulation to record the phase change and loss due to the phase shifter? Can I get complex value of the neff from any monitor which represents the accumulated phase and loss of the injected mode.

I hope I explained my problem clearly but please let me know if there is any ambiguity in my post.
Eagerly waiting for a prompt response.

Thank you.

#2

Hi. The mode expansion monitors are simply giving you the optical mode profile at the corresponding cross-section of the waveguide and the effective index of the mode. These results are not coming from the actual transmitted light in the simulation. If you take a closer look at the KB example (https://kb.lumerical.com/en/index.html?pic_modulators_interleaved_junction_microring.html), you will see that it uses a DFT monitor to calculate the loss and phase shift in the waveguide. This is done by placing the DFT monitor one period away from the mode source. Once the simulation is run,

1. The “T” data on the DFT monitor tells us the transmission through that cross-section of the waveguide. By knowing the value of T, you can calculate the loss,

loss_dB_cm = -10*log10(T)/(L*100); where L is the distance between source and DFT monitor.

1. The phase shift can be calculated by calculating the average phase of the electric field data (E) from the DFT monitor. In the example, the fundamental TE mode was used for propagation so the average phase of the Efield at the center was used to get the phase shift. This averaging was done in the script file “ilmod_txresponse.lsf”.

#3

Hi again. I have talked with a colleague of mine (@kchow) and he showed me that you can use the mode expansion monitor to get the transmitted power at different modes as well. Please take a look at this example: Using mode expansion monitors. You should be able to use the result (complex transmission coefficient) to get the phase of each mode as well.

#4

Yes, and I would like to add that one of the best benefits of Mode Expansion monitors is the extraction of S-parameters since they provide you with both the phase and magnitude of transmission in a specific mode. S-parameters can then be used in INTERCONNECT circuits to create higher level architectures.

You can check this post too if you are interested in this application:

#5

Hi saq10_eee040
I think that you should add a second Field&Power Monitor. The second monitor will measure the output field. The Mode Expansion Monitor can work with two Field&Power Monitors. I think that it is impossible to measure the power coupled in the fundamental TE mode after the mode has propagated through the phase shifter with only one Field&Power Monitor.

#6

Dear @aalam, @aya_zaki and @konslekk

Thanks a lot for your contributions in solving my problem.

Best regards