Fast Linear Taper Design - FIMMPROP

This example shows how Kallistos can be used with FIMMPROP to optimize a waveguide taper’s geometry to reduce its length while remaining adiabatic and simple to fabricate.

The EigenMode Expansion (EME) method provides rigorous simulations of waveguide tapers; the runtimes of these simulations are independent of length (depending only on the number of unique cross sections). 

By storing mode lists simulated in previous calculations, Photon Design’s EME FIMMPROP can quickly produce simulation results of a taper as its length is changed.

This allows the FIMMPROP user to use the scanning tool and find the adiabatic length of the taper quickly.

In this example we take this principle further, subdividing a taper into multiple sections. Instead of 1 global length controlling the taper the example has ‘N’ lengths; this allows Kallistos to vary all N of these lengths and as such create a piecewise monotonically decreasing taper.

As the lengths are changed in each section there are no new mode calculations or scattering matrices to perform, making the optimisation routine blisteringly fast - 1000s of results per minute using the global optimiser.

Any taper created in FIMMPROP can be easily subdivided this way using the python script provided by Photon Design found within the installation files (or upon request).

The objective function in this script is given by:

Objective = Transmission ⋅ e^{-α ⋅ ΣL}

• Transmission in this case is the coupling from the input fundamental mode to the output fundamental mode.
• α is a user defined parameter analogous to the waveguide’s loss per unit length. Increasing this value motivates the optimisation routine to find results at a shorter total length, potentially with compromise to the transmission.
• ΣL is the sum over the ‘N’ sublengths, the total length of the taper.

Once a global optimiser finds an optimum area of parameter space, the local optimiser is used to refine this result. The process in total is complete in less than 10 minutes.

The output of this routine found a 99.8% transmission taper could be found with a total length less than 12 um. With the initial linear taper, a 12 um length produced only 90%. A 99.8% transmission isn’t achieved until ~30 um meaning this 10 minute routine has decreased the footprint by roughly a third.

For adiabatic operation, waveguides should taper gradually where there are mode anti-crossings and can taper more rapidly where there are not. Looking at the 30um linear taper we see there is a substantial length before the first and after the final anti-crossing. In the optimised taper we reduce this length with a much more rapid tapering. Kallistos’ result matches our physical understanding of what makes a good taper design.