One of the simplest ways to design a highly efficient polarization splitting grating coupler compatible with CMOS processes is to use a nonuniform grating with a backside metal mirror. While not all fabrication processes allow designers to machine micron sized holes in the substrate and deposit a metal, CMOS processes for MEMS generally support this option. Some groups have exploited CMOS MEMS fabrication processes to design polarization splitting couplers  as well as highly efficient single polarization grating couplers . This post describes how to use Lumerical’s inverse design parametric adjoint optimization tool to design a polarization splitting grating coupler with a backside metallic mirror that achieves simulated coupling efficiency results comparable to those presented in reference .
Grating Coupler Design
The target fabrication process dimensions and materials are shown in the diagram below. As described in reference , a TM waveguide mode is excited on port 2 when the electric field of the fiber mode is parallel to the ribs and a TE waveguide mode is excited on port 1 when the electric field of the fiber mode is perpendicular to the ribs.
The goal of the optimization is to tune each individual rib and groove length (ai and bi in the above diagram) to maximize the coupling efficiency of the TE and TM waveguide modes excited on ports 1 and 2, respectively. As discussed in reference , the exact position of the fiber (p in the above diagram) strongly alters the peak coupling efficiency of each mode. In this case, the target is to reach the same coupling efficiency for both modes at the center wavelength (1550nm).
Since the design targets two output waveguides carrying two different modes, the employed figure of merit is the sum of the coupling efficiencies of the two outpus. Lumerical’s inverse design parametric adjoint optimization tool allows users to define multiple figures of merit corresponding to different waveguide modes. As it is usual for grating coupler designs, picking a good starting structure is key to reaching a high coupling efficiency. In this example, the starting grating has 23 groove and rib pairs spanning 14.7 µm. The grooves vary smoothly in length from 220nm at the edges to 320nm at the center. This provides an initial coupling efficiency of approximately -3 dB at the center wavelength for both TE and TM modes. The final coupling efficiency results are close to those presented in Fig. 6 of reference . The peak coupling efficiency for both output modes is approximately -1.1 dB at the center wavelength (1550 nm):
Note that the optimized grating has a minimum feature size of 100 nm and a smooth etching pattern:
The key steps required to define the optimization and generate the above results are described next.
Step 1: define base simulations
The first step to create an optimization is to create a base simulation specifying all the simulation settings whilst leaving a place for the optimization tool to insert the parameterized geometry. In this example, two separate simulations are used to generate each of the of the two figures of merit. The first figure of merit is defined as the transmission into the TE waveguide mode at port 1, and it is generated using the base simulation file grating_base_TE.fsp (2.4 MB). The second figure of merit is defined as the transmission into the TM waveguide mode at port 2, and it is generated using the base simulation file grating_base_TM.fsp (2.4 MB).
Step 2: define optimizable shape
The second step is to create a Python function defining the shape under optimization as shown in grating_optimization.py. The function must take the optimization parameters and produce polygon vertices. In this example, the length of each rib and grove corresponds to one optimization parameter (46 in total).
Step 3: launching the optimization
Once the base simulations, the parametrization function and the figures of merit have been defined, these must be put together in a Python script as shown in grating_optimization.py. The script can be run from the script editor in the finite difference IDE, and it produces a simulation file grating_final.fsp with the optimized grating coupler geometry.
Step 4: sweep source position
To balance the coupling efficiency of both outputs, the source position must be fine tuned to achieve exactly the same coupling efficiency for both output modes at the center wavelength. This step is optional and can be done by sweeping the source position for two orthogonal source polarizations:
By picking the source position at which both curves intersect, the peak power will be balanced exactly at the center wavelength for both outputs.
Step 5: extract coupling efficiency
Finally, the coupling efficiency must be extracted from the final simulation file by running two simulations with orthogonal source polarizations. The script grating_final.lsf does this and generates the shown coupling efficiency plot.
 W. S. Zaoui, A. Kunze, W. Vogel and M. Berroth, “CMOS-Compatible Polarization Splitting Grating Couplers With a Backside Metal Mirror,” in IEEE Photonics Technology Letters, vol. 25, no. 14, pp. 1395-1397, 2013.
 W.S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke, F. Letzkus and J. Burghartz, “Bridging the gap between optical fibers and silicon photonic integrated circuits,” Optics Express, vol. 22, pp. 1277-1286, 2014.