In this example, we use MODE to study a multilayer planar waveguide that takes advantage of the Anti-Resonant Reflecting Optical Waveguide (ARROW) described in F. Prieto et. al. The goal is to plot the propagation loss from 0.5 to 1 microns.
Set up ARROW A Structure
The structure in this example is based on the optimized ARROW A Structure for sensing applications from the Prieto reference.
We construct the core of the waveguide with a rectangle. To make the coating 1 layer, we take the same rectangle, change the material and make it a bit larger. Then we set the mesh order property. This acts like a Boolean operation so that when the core and the coating rectangle overlap, the FDE solver uses only the material properties from the core.
The coating 2 layer is created similarly. We use an even larger rectangle, and place it on top of the core and first coating layer. Then we set the mesh order so that where the three materials overlap, the eigenmode solver uses only the material data from the core. When the two coating layers overlap, the eigenmode solver uses only the material data from the first coating layer.
The medium to which this structure is exposed, in this case water, is modeled by setting the background index of the FDE solver to 1.3325.
Find TM Mode at 632.8nm
First, we will find the fundamental TM mode for this structure at the wavelength of a He-Ne laser source which is 632.8nm.
Because we are looking for the fundamental TM mode, we know that we can use symmetric boundary conditions. This filters out the modes which do not have the correct symmetry, for example the fundamental TE mode. You can get a complete list of the modes the structure supports by setting all the boundary conditions to PML. You can find more information about symmetric/anti-symmetric boundary conditions on the Symmetric and anti-symmetric BCs page.
Note that the simulation x span is 3 times the width of the core. Also the y span is large enough to include both the silicon substrate and a bit of the solution above the top coating layer. This is done to ensure that the location of the PML does not affect the mode profile, and hence the loss and effective index. Some convergence testing should be done to find the optimal size of the simulation span.
Three mesh override regions were added in this example to resolve the thin coating layer deposited on top of the core. The image shows a close up of the xy view when the view mesh button, , has been selected. You can see that there are four mesh cells in the coating layers.
The reason that the boundary conditions have been set to PML is because this waveguide is expected to have attenuation loss. The loss returned by the FDE solver is equal to the loss to dispersive materials plus the loss through the PML.
The loss returned for this mode is 2.07 dB/cm. Figure 12a of the reference contains a plot of loss versus structure size for a slightly different structure. Nevertheless, the loss from the FDE solver is close to what would be expected from the plot in the paper.
Loss as a function of Wavelength
- In the Frequency analysis tab, select the mode that you want to track on the mode list
- Set the calculation parameters as shown in the screenshot below
- Press the Frequency Sweep button. You will see a progress bar appear.
- To plot the results of the frequency sweep, set the plot drop-down on the Frequency plot tab to "loss", or visualize the result from the object tree (see below).
The following plot shows the loss for this mode as a function of wavelength. You can see that the loss increases quickly as the wavelength increases.
F. Prieto, L. M. Lechuga, A. Calle, A. Llobera, and C. Dominguez. "Optimized silicon antiresonant reflecting optical waveguides for sensing applications," IEEE J. Lightwave Tech., 19, 75-83 (2001)