Back from Photonics West, a top topic was tapers and how FDTD simulations are too slow and require expensive cloud computing to keep up. We discuss EME’s successes for taper simulation.
An overwhelming number of those we spoke with at this year’s Photonics West are struggling through long FDTD simulations of waveguide and fiber tapers. While FDTD will (eventually) solve a taper rigorously, the EME method that Photon Design have pioneered for decades delivers faster simulations, more information, and the opportunity for rapid optimisation.
One demonstration the Photon Design team put together was too impressive not to share, a full 3D rigorous taper simulation paired with an optimisation algorithm that manages to evaluate a new design every second; no cloud computing required.
So why is EME suited to simulating tapers?
EME is length invariant in its simulations. A 10 um taper simulates in the same amount of time as a 20um taper which simulates in the same time as a 100um taper. In fact, once our EME software FIMMPROP has simulated a taper once, it can reuse modes that it has calculated to provide results for that taper at any length.
Tip: We can use this fact for very fast parameter sweeps of taper length that reveal the adiabatic limit of a taper. We use this to great effect in the optimisation discussed later.
On the other hand, FDTD scales with the number of tiny grid steps required to evaluate the taper. Double a taper’s length and we double the number of grid points and the number of time steps required for light to propagate through the taper; quadratic scaling and no fast iterative design opportunity.
FDTD simulation results show how the field evolves over time through the taper; the end result is the output field (as a spectral response). Unless non-linearity is involved, the dynamics offer no immediate benefit though a spectral response could prove beneficial if multi-wavelength characteristics are of importance.
EME evaluates the modes at multiple positions along the length of a taper to calculate the device’s scattering matrix. This allows FIMMPROP to provide the evolution of all the mode’s properties varying with length easily.
Graphing the mode powers and eigenvalues as a function of taper length shows the skilled engineer areas where tapering must be more gradual and where tapering can be more rapid. Extracting such a result from FDTD would be cumbersome at best.
Left: Mode power of first 5 modes along taper length.
Right: Eigenvalues of first 5 modes along taper length.
Both for an initial 6um design.
At the Photonics West show we were set with a challenge of optimizing a taper operating as an elevator coupler, moving light from one core to another using two tapers. FIMMPROP performed an automatic optimisation on this device using Kallistos managing to evaluate the result of a new 3D simulation once per second…
How can this run so fast?
As mentioned above, changing the length of a taper section in FIMMPROP does not require re-simulation to see results; FIMMPROP recycles the calculated modes between simulations.
Instead of tapering from start point ‘A’ to end point ‘Z’, this taper is created with 10 smaller composite taper sections; tapering from ‘A’ to intermediate step ‘B’, from ‘B’ to ‘C’, and eventually to end point ‘Z’. Each section has its own length which allow for a wide variety of monotonically decreasing tapers designs. Even more composite sections could be included for even more finessed designs.
Each length can be varied by Photon Design’s automatic optimiser Kallistos. The optimizer picks values for each length, evaluates the scattering matrix (with no recalculations of mode lists required), then iterates. The result, a 99% efficient coupler in ~ 1 minute of optimisation.
Taper geometry before (left) and after (right) optimisation.
Instead of tapering from start point ‘A’ to end point ‘Z’, this taper is created with 10 smaller composite taper sections; tapering from ‘A’ to intermediate step ‘B’, from ‘B’ to ‘C’, and eventually to end point ‘Z’. Each section has its own length which allow for a wide variety of monotonically decreasing tapers designs. Even more composite sections could be included for even more finessed designs.
Each length can be varied by Photon Design’s automatic optimiser Kallistos. The optimizer picks values for each length, evaluates the scattering matrix (with no recalculations of mode lists required), then iterates. The result, a 99% efficient coupler in ~ 1 minute of optimisation.
Mode power and eigenvalues as a function of length after optimisation. See taper geometry has been stretched in the key area of the mode’s anti-crossing.
Why not make the taper as long as possible?
In this project, surface roughness from the etching process caused the bottom silicon core to become lossy. While extending a taper usually allows it to improve its performance, the competing effect of loss meant an optimum length could be found within the range of minimum and maximum.
There are a great many examples of simulations that appear to require a data center of compute power that can run on a laptop. If you’d like to talk more with the experts at Photon Design on your waveguide simulations then reach out for a conversation:
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