# Topology Optimization of a 4-channel wavelength demultiplexer (2D, TE-polarization)

## Overview

In this example, we use the topology optimization feature from the inverse design toolbox lumopt to design a wavelength demultiplexer for 4 channels. We target a 10nm transmission band around the center wavelength of 1270nm, 1290m, 1310nm and 1330nm. Between the channels, there is a 10nm gap for isolation.

In this example, we restrict the design area to 6um x 6um.

## Run and Results

Download the file CWDM_splitter_1310_4ch_2D_TE_topology.zip (2.6 KB) and unzip the files into one common directory.

To speed up the optimization, it is recommended to set the resource configuration of FDTD such that the job manager can run several jobs in parallel. Since each job is a relatively small 2d simulation, it makes sense to configure several Resources which use one thread each. For example, if the computer that will run the optimization has 8 physical cores, it makes sense to add 8 resources with one core each as shown in the screenshot below. In this example, there is no point in having more than 8 resources. So, if the computer has 16 cores, it makes sense to add 8 resources with two cores each.

Running the python script then starts the optimization. This example is a complex and the full optimization runs for about 1000 iterations. Depending on the available compute resources, this can take several hours up to a few days.

## Important Model Settings

### The initial condition

In this example, we initially fill the design area with a fictitious average material parameter, which often results in solutions with good performance. However, depending on the FOM and other settings, it is possible that a different starting condition will yield better results

### Maximum number of iterations, especially during the binarization phase

The 4-channel wavelength demultiplexer is a complex device and the optimization requires significantly more iterations than simpler devices (such as the Y-splitter). In this example, we increased the number of iterations for the initial grayscale phase to 500 and we increased the maximum number of iterations for each binarization step to 50. Further increasing those values will lead to longer optimization times but can also further improve the results.

Here is a list of settings that you can modify to obtain different results:

Structure
The structure itself can be changed by modifying the footprint and also the smoothing filter radius as shown below:

Warning: Along the y-axis, the structure should not be less than 5um tall because the optimization region won’t be connected to the output waveguides anymore.

Initial conditions
Since we use a local, gradient-based optimizer, the result often strongly depends on the initial guess. The given example has four different initial conditions built in to try:

By uncommenting any of the lines, one can try different initial conditions. In addition, it is possible to provide custom initial conditions such as random noise or specific structures.

Convergence parameters of the optimizer
Lumopt has a number of parameters which determine the progress of the optimizer. Changing them often allows to make trade-offs between the best results and computations time. Here are some of the most important ones:

• max_iter: Determines after how many iterations, the greyscale phase ends. The optimizer can terminate before this number due to other criteria (e.g. see below) but it will never perform more iterations. Increasing this number will often require more computational time but can lead to better performance. The default value is 400 in this example.

• tfol: The minimum require change in the figure of merit (FOM) between two subsequent iterations for the greyscale optimization to continue. The default value is 1e-5 in this example

• continuation_max_iter: The maximum number of iterations for each binarization step. If not specified, the default is 20 iterations but for complicated structures, explicitly setting a larger number as shown below can lead to better optimization results (at the cost of more simulation time)

• beta_factor: After each binarization step, the new beta value is computed by
$$\beta_{new} = \beta_{old} * \beta_{factor}.$$ The default value is beta_factor=1.2 but you can set other values as shown below. Increasing beta_factor can make the optimization faster. Decreasing can give better optimization results but at the cost of longer compute times.