In this topic, we demonstrate how to design a polarization converter based on reference [1]. We will start with MODE' finite-difference eigenmode (FDE) solver to quickly narrow down the design choices prior to running full simulations of the entire device using the eigenmode expansion (EME) solver.

## Initial design using FDE

The design of the polarization converter is based on reference [1]. For this design, it is useful to start the FDE solver to quickly narrow down the design choices (varying the waveguide width in this case) prior to running full simulations of the entire device using the EME solver. For the polarization converter, the FDE solver can be used to identify the regions where mode-crossings occur. This design will convert the TE1 mode into the TM0 mode, where the mode-crossing occurs at around 0.9um.

Open [[taper_width_sweep.lms]] and run [[taper_width_sweep.lsf]]. The script will run a number of FDE simulations, varying the waveguide width from 3um to 0.5um. At each step, the effective index (neff) for the first 5 modes will be stored. The neff values of the waveguide are subtracted by that of the slab mode (without the ridge). When the simulations are finished, the script will create the following figure, which can be used to identify the regions where mode-crossings occur and which waveguide widths are required to achieve polarization conversion. For the subsequent simulation using the EME solver, we will use an input and output waveguide width of 1.5um and 0.8um respectively.

## Length scanning using EME

We will simulate light propagation in this device using the EME solver. The simulation setup is similar to the spot size converter getting started example. It is recommended that you go through the getting started example in detail before running [[pol_converter.lms]].

The [[pol_converter.lms]] contains the input and output ridge waveguides, connected by a taper with 1.5um and 0.8um as the waveguide input and output respectively. We track 3 modes and note that the modes are listed based on their neff, i.e., (TE0, TE1, TM0) at 1.5um waveguide width and (TE0, TM0, TE1) at 0.8um waveguide width. The order can be visualized by drawing a vertical line on the above figure at the particular waveguide width. We will scan the length of this taper and track how efficiently the TE1 mode can be converted into the fundamental TM mode. Run the simulation to calculate the modes at each cell. Once the simulation is complete, use the "Propagation sweep" widget in the EME analysis window to scan the taper length (group span 2) from 5um to 500um and then click on the "eme sweep" button.

Clicking on the "visualize eme sweep" will display the results of all the S parameter elements (6x6) in the visualizer. The S matrix index mapping table can be used to see which S element maps to which port. Since there are 2 ports (with 3 modes each), S42, S52, S62 will give us the conversion efficiency from TE1 to TE0, TE1 to TM0, and TE1 to TE1 respectively. One can click on the "Remove" button to reserve the Attribute of interest. Then select "Abs^2" in the "Scalar operation" drop-down list. In the plot below, one can see that there is no energy transferred from TE1 to TE0. At the taper length of around 250um, the TE1 mode is almost completely transferred to the TM0 mode.

The EME method is ideal for taper designs because one can scan the taper lengths very quickly without having to recalculate any modes. Not only does the simulation time required for FDTD-based methods increase with the taper length squared, but the accuracy also decreases due to numerical grid dispersion.

### Related publications

- D. Dai et al, “Mode conversion in tapered submicron silicon ridge optical waveguides”, Optics Express. Vol. 20, No. 12, 2012.