Comparing EME and FDTD: Rings

EME and FDTD are the industry’s go-to waveguide simulation methods; both as rigorous solutions to Maxwell’s equations. When both methods are applicable and configured correctly there is no reason their result should differ. 

So how to pick which method to use?
This page shows pros and cons of each method for creating ring resonators as used in WDM, extended cavity lasers, and modulators.

Typically an EME simulation is not able to simulate an entire ring resonator. As waveguide paths diverge it becomes unfeasible to build a basis set of modes that describe propagation in perpendicular directions (not to mention the exceedingly large cross sections that would be needed).

Only Photon Design’s EME tool MT-FIMMPROP is able to simulate a full ring resonator in EME by natively combining manageable EME simulations in a singular environment. 

FDTD simulations scale with the bounding volume of a simulation. For a ring resonator this can be fairly large and consist of uninteresting empty spaces. The simulation’s duration also increases the run-time; with high Q-factor rings  light is confined to the ring for many loops leading to longer run-times at resonance.

Simulations in MT-FIMMPROP EME scale with the number of unique cross sections that need to be simulated.

• Constant curvature bends and straight sections require just one mode list so are comparatively instant to simulate.
• Coupling region simulations can be re-used when repeated [Read More],
• This allows for symmetrical coupling regions to be simulated twice as quickly.
• Only the computational regions are simulated so bulk regions (like the center of rings) are not simulated.

The behaviour of a ring resonator as a function of its wavelength is a critical result at some point in designing any ring resonator. 

• Time domain methods like FDTD provide the spectral response in each result.
• An EME simulation captures the steady state solution, but delivers this result much more quickly. 

Considering rings are often designed to operate at individual resonant frequencies, there is a benefit of having a tool that can return fast results at the target wavelength of interest. However, for EME to return a spectral response with ‘N’ wavelengths without approximation it will take ‘N’ times as long, potentially making FDTD a competitive comparison in run-time depending on hardware. 

Tip: Approximations can be included in EME for much faster sweeps of wavelength dependence. A small change in the wavelength can be fairly approximated without full mode recalculation of a mode by instead changing only the rapidly varying exponential that relates to a mode’s propagation.

Time domain simulations capture a simulation’s dynamics such as non-linearities or even modulation. EME delivers steady state results so the dynamics involved with non-linearities cannot be captured.