# FDTD simulation on a SiN nanobeam resonator

I’m trying to reproduce the mode profile from this paper for a SiN nanobeam resonator.

I made the exactly same structure. My goal is to calcualte Q (230,000) at 637 nm and obtain mode profle (Ex) from FDTD simulation.
When I used a broadband dipole source (0.55-0.7 um), I obtained spectrum from a time monitor (see attached picture below). There’s supposed to be a peak at 637 nm. But I saw a stop band around 637 nm. Will anyone share some idea to approach this goal? I attach the file.nanobeam_si3N4.fsp (569.3 KB)

Hey @fpan22,

I ran your simulation with different indices, and obtained a number of different transmission spectra. The resonances of the nano-beam structure will be highly dependent on both material and geometric properties.

In this simulation you are assuming that the beam has a constant index of 2 for all frequencies. To get more realistic results you should consider the dispersive properties of SiN.

This quick analysis suggests that the actual index is lower than 1.95, but it should be noted that for a 340 nm film of pure $\text{Si}_3\text{N}_3$ the index quoted there is closer 2.04 for the wavelength of interest. Which brings up an interesting point about silicon nitride. It is rarely stoichiometric when deposited, and so the material properties may vary and it is often refereed to as SiNx for that reason. That being said you should explore the parameter space of geometric and material properties to find the resonances you seek.

One more thing to be aware of, that you may have considered already, is that your placement of point time monitors will change the spectrum you measure(See Below). Be sure to place the monitor where the field confinement is strong which you can identify with field monitors.

Cheers,
Taylor

Thanks, Taylor! @trobertson Yes, there is no clear stoichiometric info about SiN in that paper. I tweaked the refractive index a bit and found the same behavior as you showed. My another question is spectral range of source used to excite cavity modes. I used a dipole source with quite broad band and saw oscillation stopped at around a few hundred fs. I haven’t obtained the same mode profile like the one shown in the paper. I’m thinking about whether I should use a narrow band source around the resonance. Apparently the oscillation can be forced to be stopped by simulation time, but the oscillation amplitude will be quite stable when it’s close to the end of the simulation time. So my question is when the tapered holes around the center introduce the high-Q resonance, will energy be stored in the cavity for quite long time, leading to steady-state oscillation within the simulation time? Any thoughts?

Hey @fpan22,

Yes since you are only interested in the Q of the cavity mode you can implement a narrow band dipole source after the resonance is identified. It will likely take quite a long time for the energy to decay if it is a high quality factor cavity, so the simulation time will likely have to be increased. There are a couple of ways of calculating this. Please refer to the following resources.