Calculating the Gap in a Ring Resonator

Please I want an easy approach to calculate the gap between the input waveguide and the ring in a ring resonator.

Thank you in advance.

What is your design target? For example, is it high Q?
Or is it that you think no power is basically coupled to the ring?

Feel free to upload your simulation file and I will be happy to follow up.

Simulation.fsp (226.9 KB)

My design’s target is, indeed, a high Q factor (i.e. a large transmission depth for modulation purpose).
I’ve uploaded a figure of the transmission peaks, and they appear very shallow, which may be due to not enough coupling between the waveguide and the ring cavity (shown in the attached file “Simulation.fsp”).

Thank you Aya for your help.

Best regards,


I don’t have a clear way to calculate the gap for critical coupling condition other than several trials, especially when the gap itself is small (exponential decaying field approximation does not apply). But the problem of your simulation is perhaps the lack of loss than lack of coupling. I see all the materials you are using are self-defined dielectric with no imaginary index part. So Lumerical cannot count for most of the loss of that system (I would suppose remaining losses are waves coming out of your simulation region and bending loss, if you specify that), and you got nearly 1 transmission.

Maybe try to argue the sources of loss in your experiment, and add that to the simulation.

Hello @m.badr_44,
The problem with your design is that the waveguide is 1um wide which makes the excited mode highly confined inside the waveguide and doesn’t get coupled to the adjacent ring. Even a gap of Zero won’t solve this problem. I looked into 2D simulations. However, by examining the 2D mode profile in 3D FDTD, it seems you will have exactly the same problem.

Watch this movie:

If you used a waveguide of 450 nm width, here is how the results improve (could be further improved) :