Resonant frequency shift between different solvers and simulation set up


#1

Hi there,

I am simulating a photonic crystal nanobeam and determining the Q factor via the built in Q analysis group. I have noticed when I run my simulation in 2.5varFDTD the resonant wavelength found by the analysis group is always ~40-50nm larger than that found when ran in the 3D FDTD solver. I have also noticed that in my simulation for determining transmission (using a mode source at the input of the nanobeam as opposed to a dipole at the antinode) the resonant frequency wavelength according to the Q analysis group is ~5-10 nm larger than in my Q determination set up.

I am curious what the cause and significance is of this discrepency, and if it is to be expected. I would think the reso wl should be independent of the source, but I am not seeing this.

Also, given that this discrepancy is to be expected, what is the best way to confirm I am extracting the same resonant mode between simulations? Would the mode profile found via the field and profile monitor be the most useful?

Thank you in advance,

Leea :slight_smile:


#2

Hi @lstott

The 3D FDTD simulation is the most reliable approach. varFDTD can be used for initial/quick simulations, however FDTD will be required for final calculations as it solves Maxwell’s equations with no assumption about the fields polarizations or geometry. You can also perform convergence testing to make sure that simulation setup is correct and results converge:
https://kb.lumerical.com/en/index.html?layout_analysis_test_convergence_fdtd.html

Was the geometry identical in both cases? For example adding a bus waveguide to couple the light from a mode source adds a loss channel to the system. Also did you check the fits to make sure that envelope decay is exponential as is explained in the link below:
https://kb.lumerical.com/en/index.html?diffractive_optics_cavity_q_calculation.html

I guess what I am trying to say is that even for a single simulation results may vary depending on the data that you used for post processing. You may try to change the simulation time and visualize the data for fitting to make sure you are selecting a proper data to fit.

You can use a profile monitor or use time monitor and visualize the spectrum. The Q-calculations scrip file identifies the peaks and separates the resonances with fft (fast Fourier transform) and ifft (inverse fast Fourier transform) for quality factor calculations (the fit to field time signal).

I hope this was helpful.


#3

Hi @bkhanaliloo,

Sorry for the late reply, but I wanted to collect more data before responding.

The geometry is the exact same in both cases. With the mode source the light is being coupled to the nanobeam directly from the feeding waveguide.

Between the 3D and 2.5varFDTD simulation (both using dipoles), every setting is identical, except, of course, the material fit. Also in the 3D simulation I have increased the z span by 0.8 micron in order to give more distance between the PML and the structure. I have performed convergence testing for the 2.5D simulation, however because of long simulation times, I have not done much convergence testing for the 3D simulation.

In my convergence testing in 2.5D I found that a sim time of 12000 fs is adequate to obtain the same fit as for much longer sim times ( >100 000 fs).

Here is an image with some comparisons between the two simulations:


I have all my field and power monitors with start apodization at 8000 fs with a 1000 fs time width. I found that the fundamental mode appears at the first resonance, of which is very different between the two simulations.

Also note that these figures are simulated at low mesh
image

My yMin boundary is set to Anti-Symmetric, and I believe this has little effect on the sim results given tests on my 2.5varFDTD simulation. (also I happen to be looking for TE modes anyhow)

Do you have any idea why this difference occurs? I will work on running longer 3D simulations, but in the mean time I would love your thoughts on this deviation.


#4

Hi @lstott

Thank you for sharing your results with me.

varFDTD results are good initial guesses, but for final results you need to run 3D FDTD simulations. Since varFDTD uses some assumptions about the field polarizations, the results may not be precise.

The high-Q calculations might be challenging in 3D FDTD as simulations may require long time to finish. You do not need to wait for the simulations to trigger auto shutoff, but you need to check the E-field as a function of time and make sure that you can see an exponential decay of the field. For example, in the E field vs time plots, there seems to be more than one resonance frequency and I cannot see the exponential decay. Q-analysis calculation uses fft and invfft to separate the resonances, and you can check the plots to make sure that there is a reasonable exponential field decay. You can try to select different portion of E(t) for Q-calculations fitting.

As always, you need to perform convergence testing to make sure that results converge.