Designing ring resonator channel-drop filters with FDTD Solutions and MODE Solutions

In this example,we model a ring resonator with input (through) and output (drop) waveguides around 1552 nm - the center of the telecommunications c-band, to the drop waveguide.  We compare results obtained with FDTD Solutions modeling a ring resonator in 3D to those obtained with MODE Solutions modeling the same device in 2.5D.  The 2.5D method is very similar to the 3D method, except the vertical dimension is collapsed by converting the lateral permittivity distribution into effective dispersive materials that simultaneously account for material and waveguide dispersion of the vertical dimension and that, in this situation, it runs about 100X than the full 3D calculation.

Step 1: Construct the waveguide ring resonator in the layout editor

The layout editor shows all of the simulation objects, and their relative positioning. Different classes of objects (physical primitives, radiation sources, monitors) are color coded for easy identification. Objects can be dragged, dropped, and resized with simple mouse movements, and complicated structures can be easily constructed from the library of dozens of simulation objects within the object library.  Once the structure is completed in MODE Solutions, it can be cut & paste into FDTD Solutions.

• orange regions show the extents of the computation area, bounded by absorbing (PML) boundary conditions
• yellow lines show transmission monitors; yellow X's show time measurement monitors
• window at the left shows hierarchical model definition of waveguide elements, injected waveguide mode, measurement monitors and simulation region

Step 2: Launch the waveguide mode into the ring resonator in FDTD Solutions and MODE Solutions and compare spatial field profiles

The embedded mode solver allows the user to inject either 2D or 3D guided modes into the simulation volume.  Waveguide modes including metal waveguide modes, surface plasmon modes, anti-resonant modes, and the more conventional dielectric waveguide modes can be injected.  Using the integrated eigenmode waveguide solver:

• select the number of modes to be solver for
• view the mode profile for different field components
• pick the mode of interest - whether TE or TM polarized - and select it for injection with the click of a button

After selecting the fundamental TM mode for injection, the simulations can be run.  The spatial field profiles calculated using the 3D FDTD Solutions engine is compared to those calculated using the 2.5 MODE Solutions engine in the figures below.  Very similar intensity distributions are obtained using the two methods.

Step 3. Compare measured ring resonator transmission and drop spectra as calculated using FDTD and MODE Solutions

Using frequency-domain transmission monitors in conjunction with Lumerical's multi-coefficient material models, high resolution and high accuracy broadband transmission data can be obtained for the through and drop waveguides in a single simulation.  The signal transmitted into the through and drop waveguides are shown in the two plots below.  The upper plot shows the transmission in the through waveguide, and compares the 3D FDTD Solutions results to the 2.5D MODE Solutions results.  The lower plot shows the transmission in the drop waveguide for both the 3D FDTD Solutions model and the 2.5 MODE Solutions model.  In both cases, decent agreement is obtained from MODE Solutions at a small fraction (approximately 1%) of the time it takes to complete the 3D simulation.

Step 4. Watch the simulation dynamics calculated by the 2.5D MODE Solutions algorithm and compared to the 3D FDTD Solutions calculation

The built-in movie monitors monitors allow you to create movies of the time-domain dynamics of the simulation.  Here, we watch as the pulse is injected into the input waveguide and couples into the ring resonator structure as calculated by the 3D engine of FDTD Solutions (top movie) and the 2.5D engine of MODE Solutions (bottom movie).  Close comparison of the two movies shows very similar behaviour of the ring when the pulse is launched into the input waveguide, and couples to the drop waveguide port.  It is important to note that the 2.5D MODE Solutions simulation, which provides comparable accuracy to the 3D FDTD Solutions calculation, was completed 100X faster.