# Free spectral range issue

#1

My simulation file and results are attached to this link:

Basically it is a simulation of the coupling between a 5um Si3N4 ring and waveguide, with 1um cladding layer on top and on bottom of it. The simulation time is not converged for this case, but that shouldn’t matter to the discussion below.

However, the results, as can be shown in the “after” monitor, has a wired free spectral range.

In general, we expect FSR=c/(n_eff*L), where L=2piR
Plugging in the above equation I got n_eff for this system is in the range of (2.40,2.43).
However, all the materials I used in the simulation has refractive index smaller than 2.40. (SiN is 2.34, SiO2 is 1.444, background air is set to 1) And all of them should have no or little wavelength dependence as can be seen in material explorer window.

So, how does it predict n_eff larger than any of the materials? If that is true phenomenon, please give a brief explanation. If not, please tell me how to get rid of this error.

#2

Dear @pufanliu2021

As it is mentioned in this link, FSR is inversely proportional to the group refractive index (n_g) of geometry which for dispersive material will be different than n_eff.

I don’t know the value of n_g in your structure, but you can check this value by setting up an FDE simulation in MODE solver as explained in the above mentioned link or similar to this example.

Thanks

#3

@bkhanaliloo

Thanks for your response. Firstly, the effective group index differs from the effective index by a derivative term as shown in https://www.rp-photonics.com/group_index.html. So since the refractive index of all materials does not change or change little with wavelength, I don’t think that is the problem.

About running FDE simulaiton, I think it is worth noting that the group effective index is ~2.15 in MODE solver. And the 2.5D FDTD simulation predicts similar FSR as the theory. So now the problem is: Why does 3D differ that much from theory and 2.5D simulations?

#4

@bkhanaliloo

NVM. Problem solved. I did not take take the mode profile wavelength dependence into account, which, if I used narrow-band simulation in 2.5D FDTD, is not changed. That is the reason for the difference between 2.5D vs.3D simulation.

#5

Dear @pufanliu2021

This statement is true if all of light/mode was confined inside the material, SiN in your case. However since this is not the case and part of your field will be inside other material, you expect to see effective index changes with wavelength (longer wavelength will be less confined). Thus, n_g will be different than n_eff. This is why you need to study the n_eff of a geometry and not only the material itself.