## Photonics

#### Simulation Time and Frequency Domain Monitors, FDTD

• zfritts
Subscriber

When simulating with FDTD (I am using Lumerical), I know there is a relation between the simulation time and the accuracy and frequency resolution available from the frequency domain monitors [mentioned in this video on the

" target="_blank" rel="noopener">Auto-Shutoff Level in Lumerical]. The video, however, does not go into detail on the relationship. If I would like to obtain 1 MHz frequency resolution from my monitors, then is there a simple rule which specifies how long the simulation must run? (My intuition from Fourier Transforms says that there must be!).

Thank you in advance for any help!

• Guilin Sun
Ansys Employee

Is this to resolve a very strong resonance or just to get transmission/reflection at many frequency points? Autoshutoff min is to ensure the accuracy of Fourier transform. Frequency resolution can have two different meanings:
1: you want accurate spectral result, such as transmission, reflection. In such case, you do not need many frequency points, no MHz frequency resolution is required for photonic simulation, since any other frequency result can be interpolated from coarse sampling. Since it takes more time with more frequency points for a given bandwidth, in general 50 points are sufficient, except that result is wavy.
2: You want to get the resonance spectrum with very high Q.  eg, Q is on the order of 10^6 or above. In such case depending on the result you want, the simulation time can be long or short:

• zfritts
Subscriber

Thank you for the quick reply! It is much appreciated. I am simulating the scattered power from a small, extremely high Q resonant scatterer, which is resonant near 1 GHz. Because it is so high Q, it will take a long time for the fields in the resonator to decay, which means the autoshutoff time is already fairly long. However, I am wondering if I will need to run the simulation for perhaps a longer time in order to obtain the spectrum of the scattered power with high frequency resolution near the scatterer resonance.

• Guilin Sun
Ansys Employee

The forum does not work well as it does not allow me to write long reply. In short, if you just want to get Q and resonate wavelength, no need to simulate long time; if you want to get transmission/reflection with high Q, long simulation is needed. The spectral resolution is inversely proportional to the simulation time in this case.

• Guilin Sun
Ansys Employee

When you want to get the spectrum, the frequency domain result must be accurate to resolve 1MHz FWHM. This is because, The delta_f is inversely proportional to the signal length in time.

I actually prepared a long reply at the beginning. Unfortunately the forum does not work well as expected.

Later on, please be more specific like in your 2nd post so we can better answer you.

• zfritts
Subscriber

I will try to be more specific, as requested. However, I am not sure that we understand each other just yet. Certainly the frequency domain result must be accurate, but per my original post, the longer time used to simulate the resonator, the more time points will be used in computing the DFT, which means that the frequency points are closer to each other (much like zero-padding a signal allows smaller spacing between DFT frequency samples). The type of resolution I mean (and I apologize for the confusion) is the spacing of the frequency samples in the DFT, which must be small enough in order to resolve the FWHM, as you say. My question is whether there is a simple relation between the total simulation time and the minimum possible spacing of adjacent frequency points from the DFT - so that I know how long to run the simulation for in order to achieve the spacing that is necessary for observing the resonant peak. Hopefully this makes clear what I am asking!

• Guilin Sun
Ansys Employee

"the longer time used to simulate the resonator, the more time points will be used in computing the DFT, which means that the frequency points are closer to each other"

More time points do no mean more frequency points! this is because, users specify the spacing of the frequency samples in the DFT. eg, you predefine the total number of frequency points in the frequency-domain monitor. It does not related the length of the simulation time.

However, more frequency points (sampling) do not mean the narrow resonance can be resolved. The resonance resolution, eg, the full-width-half-max of the resonance is related to the actual length of the simulation time. If the original signal is not long enough, padding error will not increase the actual resolution.

"whether there is a simple relation between the total simulation time and the minimum possible spacing of adjacent frequency points from the DFT"  I believe I have replied you:

1: The spectral resolution is inversely proportional to the simulation time in this case.

2: The delta_f is inversely proportional to the signal length in time.

Which is a more theoretical question other than simulation question.