How to include propagation loss and coupling coefficient in ring resonator
Ring resonators can be challenging devices to simulate in FDTD given the long lived circulating light, and the size of these devices. A full FDTD or varFDTD simulation of ring resonators is the most conceptually intuitive way of doing this. It would likely be best to do the initial design exploration in varFDTD and the final verification step in FDTD. Initial design of the coupling length could be done in FDE - Evanescent couplers.
A more efficient and accurate way of modelling these devices would be to use MODE and FDTD to extract the important parameters and build compact models in INTERCONNECT for full circuit simulation.
- Calculating the loss by performing bent waveguide simulations. Note that the output from bent waveguide calculations would be the loss for a quarter ring, and if you want to calculate the ring loss, you will need to multiply this value by 4. An additional thing to consider would be the interface loss, this wouldn't be present in a perfect ring, but may be in a racetrack resonator or adiabatic curve.
- For the cross and self coupling coefficients, you can simulate only the coupling section similar to the approach in Y-branch except with a 4-port device using the S-parameter extraction utility. This would be the most general approach, but you could use the more approximate technique in Evanescent couplers as well.
- Finally use these physical parameters to construct a ring resonator from primitives in INTERCONNECT. The advantage here is that you can immediately add more complexity to produce coupled ring filters, modulators, phase delays etc.
Another approach will be to look at transmission and reflection which are related to coupling coefficients in this paper:
Extracting coupling and loss coefficients from a ring resonator. WR McKinnon, DX Xu, C Storey, E Post, A Densmore, A Delâge, P Waldron, JH Schmid and S Janz, Optics express, Oct 2009 12
A method is developed for extracting the coupling and loss coefficients of ring resonators from the peak widths, depths, and spacings of the resonances of a single resonator. Although the formulas used do not distinguish which coefficient is coupling and which is loss, it is shown how these coefficients can be disentangled based on how they vary with wavelength or device parameters.
The Ring modulator covers most points discussed here and should serve as great reference even when looking at passive rings.