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Analysing Large Ring Resonators: the Limits of a Full Solve and a Partitioned Approach

A large-radius ring resonator is prohibitively expensive to solve in full with FDTD. This article sets out where varFDTD helps and where it stops helping, then walks through a partitioned approach: S-parameters for the coupler from FDTD, the bend from FDE, and the whole thing reassembled as a circuit in INTERCONNECT.

Simulating a large-radius ring in its entirety with something like FDTD can mean an enormous amount of computation. There are, however, several ways around this.

Reducing the computational load with varFDTD (a 2.5D solver), and what to watch for

Lumerical FDTDinstead of Lumerical MODE varFDTD solver (see reference ) is one way to simulate a ring this large.

This 2.5D solver can compute a three-dimensional planar structure at roughly the computational cost of a two-dimensional calculation. A ring resonator simulation example using varFDTD is also available.

Before starting a simulation from this example, check your available memory and confirm that the PC has enough left for the simulation region you need.

Note too that analysing a ring this large requires a longer simulation time. The default of 1000 fs will be too short.
For a ring resonator larger still, however, varFDTD is no longer the best choice.

Partitioned analysis in Lumerical: FDTD, FDE and INTERCONNECT together

For a larger ring resonator, FDTD and varFDTD are not enough. In that case we recommend splitting the ring resonator device into several elements, simulating each one, and taking the resulting data
into Lumerical INTERCONNECT to treat it as a system simulation.

Ring resonator by Lumerical FDTD

Step 1: extracting the scattering matrix (S-parameters) of the coupling region with FDTD

First, simulate the ring section as in the screenshot below. This simulation obtains the scattering matrix of the coupling region.

Because only the coupling region, which is far smaller than the whole ring, is simulated, FDTD handles it comfortably. If the coupling region is large for FDTD, it may be worth optimising the initial parameters roughly in varFDTD and using FDTD for the final check.

Step 2: refractive index and loss of the bent waveguide from the FDE solver

Simulate the bent waveguide with the FDE solver. This simulation returns waveguide properties such as effective index, group index and loss.

Step 3: fast circuit-level system simulation in INTERCONNECT

Once you have the scattering matrix of the coupling region and the waveguide properties of each element, you can import them into Lumerical INTERCONNECT and run a system simulation.

This simulation is not only accurate; it is also far faster than analysing the whole ring resonator with something like Lumerical FDTD.

If the ring is a modulator, there is a related example.

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