The Weakness of FDTD

With the increase in computer capability comes a wider adoption of FDTD based software tools for photonics simulation. Multiprocessor capability, dedicated cluster systems, native 64 bit FDTD are all options to either increase calculation speed or accessible memory.

FDTD provides a rigorous solution of Maxwell's equations and is probably the most flexible method available and therefore can be very useful. However, today's increased computer power disguises the fact that the FDTD algorithm is quite an inelegant, brute force approach to solving Maxwell's equations and gives you little more information than the quantity of flux passing through user-defined areas. Sometimes the designer needs more than this to be able to understand the physics of the situation.

The weakness of FDTD is demonstrated in the following situation.

This is a 10um diameter SOI ridge-waveguide based ring resonator being designed to operate around 1.55um. A full 3D FDTD simulation with a long enough run-time and small enough grid resolution for sufficient accuracy takes approx. 4-5 hours in this case (using Photon Design's OmniSim on a 2GHz single core PC).

The figure below shows the long awaited result - the flux passing through the sensor in the add-drop waveguide located in the bottom left (source is injected in the top left). Notice that the values on the Y-axis do not go above 2%. This ring resonator has no resonance.

Now, there is a possibility that the FDTD grid size or spectra data resolution was not sufficient to "see" the resonance, so we could run another simulation again and wait (this time for longer than 4-5 hours) for another set of results. In this case we will see a similar graph and we must conclude that this is an accurate simulation and indeed there is no resonance. ***But the problem is that we don't know why*** and with FDTD there is very little opportunity to run diagnostics to find the answer.

The solution is to use a mode calculation software such as Photon Design's FIMMWAVE and if we do so we can have the answer in just 5 minutes.

FIMMWAVE's FMM Mode Solver is able to accurately solve the mode and calculate bend loss for the mode as it travels around the ring. FIMMWAVE is the only software on the market that can do this in cylindrical coordinates (other software use an approximate method called "Conformal Mapping" that is only accurate for slab waveguides).

Immediately upon doing this we can quickly see that the mode is not even close to being well guided and when propagating around the ring has a bend loss of over 700 (1/cm)! In other words, before even one pass around the ring the mode power has decreased to zero. Obviously there will be no resonance in this case!

When dealing with waveguides, ring resonators, tapers etc, mode analysis is critical. The FDTD method does not "understand" the concept of modes, thus is most suitable for validation at the end of the design phase.

For the designer, mode analysis tools such as Photon Design's FIMMWAVE provides more critical information that sheds hours upon hours off design time. Further discussion on using mode analysis software for ring resonator design can be found on the Photon Design site here.

example image