# Application Gallery

 AWGs and Star couplers

Arrayed waveguide gratings (AWGs) are essential for dense wavelength division multiplexing/de-multiplexing in optical networks. The sensitivity of these devices to phase errors means that a rigorous design process and simulation tool is required. However, the size and complexity of AWGs make them very challenging for most simulation tools. In this example, we will provide a basic template for a typical AWGs simulation, where the size of the full device can be on the order of 10s of millimeters (or larger).

If you are not familiar with Propagator simulations, you may want to go through the Ring Resonator Getting Started Example before proceeding.

Due to the size of AWGs, it is often not possible to model this device using 3D finite-difference time-domain (FDTD). Some common alternatives for simulating wave propagation at large distances include the Beam Propagation Method (BPM), the Eigenmode Expansion Method and 2D FDTD. However, the approximations required for these methods make them ill-suited for treating AWGs devices. For these devices, the variational FDTD technique used by the Propagator can take into account the important dispersion effects, while only requiring the simulation time and memory of a 2D FDTD simulation.

## Simulation setup

Very often, AWGs designs are on the order of 10s of millimeters, which make them too large to be simulated as a whole even in a 2.5D calculation method. The recommended approach is to break the device into 3 different sections:  First we have the input star coupler, which takes the light from an input waveguide and allows it to propagate through the free space propagation (FSP) region. At the end of the FSP region, the light is spread among the output arrayed waveguides following a Gaussian-shaped distribution. The light then propagates along each arrayed waveguide over a large distance. The length of each waveguide is designed such that they have a constant length increment ΔL, resulting in a constant phase change Δφ across each successive channel. Once the light reaches the output star coupler, it will enter another  FSP region, where it refocuses at one of the output waveguides. Depending on the wavelength, the light will be focused on to the different output channels.

## Input star coupler

The input_star.lms file contains the input star coupler. The star coupler has been parameterized using a structure group, allowing us to change design parameters such as the number of input/output channels, the angle and the radius for the star coupler. Here, we can use a MODE source to launch the fundamental mode along any of the input waveguides. The simulation region is about 600x200 microns, which can be simulated reasonably quickly using a 2.5D Propagator method. Once the simulation finishes running, we can plot the electric field profile using the Visualizer, as shown below: We can see how the input waveguide mode spreads out in the FSP region, and distributes among the different output array waveguides. In the Visualizer, it is very easy to plot a slice of this image along the x direction. However, this image alone does not give us enough information about how much power is actually transmitted into the output waveguides.Mode expansion monitors are ideal for this calculation. In the same file, the mode expansion monitors and transmission monitors have been set up at each output waveguide (rotated at the same angle). This will allow us to determine how much power is transmitted into the fundamental mode of each output waveguide. For more information on how to use mode expansion monitors for this analysis, please see Using Mode Expansion Monitors in the User Guide.

The script expansion_results.lsf will plot the transmission into the fundamental mode of each output waveguide, as well as the total transmission into each waveguide. Since the total transmission is calculated by simply integrating the Poynting vector along the monitor plane, we can see that it is very easy to over-estimate how much light is actually transmitted into the arrayed waveguides.  This is why it is very important to carry out mode expansion calculations, instead of simply looking at the total transmission.

## Arrayed waveguides

The propagation in the arrayed waveguide can be treated analytically. The AWGs are designed such that the length difference between successive channels is (where is an integer).

The phase difference between each channel is , which corresponds to a time delay of between each channel. This means that in order to get the correct phase difference in a time domain simulation, we will need to set this time delay for each input mode of the output star coupler. This time delay can be specified in the "offset" value under the "Edit source -> Frequency/Wavelength" tab (with the "set time domain" option is selected). ## Output star coupler

The output star coupler in output_star.lms contains the output star coupler. The script set_source_star.lsf will automatically add a mode source for each input channel, rotated at the same angle as the input waveguide, with the time delay . For this simulation, we will use a broadband source so we can see how interference in the output star coupler changes as a function of wavelength. Once the simulation finishes running, we can plot the electric field profile at different wavelengths. Note that due to the size of the profile monitor, it may be difficult to plot the results for all frequencies in the Visualizer. If you find that this is the case, you can use the script plot_profile.lsf to plot the profile 1 frequency at a time. Alternatively, you can also reduce the resolution of this monitor by setting the "Geometry -> down sample X/Y/Z" properties inside the Edit window of the profile monitor.

We can see that, at wavelengths near the center wavelength, the light is mostly coupled into the center output waveguide . As we change the wavelength of the sources from shorter to longer wavelengths, we can see the position where the light focuses move along the right edge of the output star coupler, coupling into different channels depending on the wavelength. This de-multiplexing functionality is the result of the phase difference from the time delay that we specified.

Even though this is a very simple example. One can easily extend this basic template to more complex designs. If you need help on how to approach your AWGs design, please visit the Support Center.

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