Keywords:
Mode Extraction, Photonic Waveguide, Guided Mode, Semiconductor
This example demonstrates the process for extracting the effective index and fields of a guided mode by directly solving an eigenvalue equation. The use of permittivity averaging enables second order accuracy in our solution. The waveguide axis runs parallel to the x-axis, and is surrounded by a background cladding with a greater permittivity. We will run the simulation for 1 step and then use the dielectricWaveguideModeCalc_invEps_0.h5 file to solve for the guided modes using the computeDielectricModes.py analyzer. This analyzer will find the entire basis set of modes for this waveguide and output each into a separate .vsh5 file. These mode files can be used to launch the exact modes into your simulation. This process is shown in the multiModeFiberModeLaunchT example.
Eigenmodes in such a simulation have the form:
The effective index of refraction of a waveguide mode is given by \(\bar{n} = k / k_0\) where \(k_0 = \omega / c\). If the waveguide has index of refraction \(n_w\) and the cladding \(n_c < n_w\), then a guided mode will have a modal index in the range, \(n_c < \bar{n} < n_w\).
This simulation can be performed with a VSimEM license.
To open this example open an instance of VSimComposer and follow the steps below:
This example contains a number of variables defined to make the simulation easily modifiable.
The Materials section contains just silicon and silica. The Geometries includes the CSG waveguide and its defining parameters. In Field Dynamics, there are FieldBoundaryConditions and CurrentDistributions to be aware of. In photonics simulations, Matched Absorbing Layers (MALs) are the most stable boundary conditions for preventing reflections. The gaussian approximation is defined under SpaceTimeFunctions and is set to drive the y-component of the currentSource.
As delivered, the system is set up to generate the data needed to run the computeDielectricModes.py analyzer. To ensure that your simulation has second order accuracy, expand the Basic Settings branch and verify that the dielectric solver field is set to permittivity averaging. This algorithm is a powerful VSim feature. This setting is shown in Fig. 244.
After performing the above actions, continue as follows:
After performing the above actions, continue as follows:
Now update the analyzer fields accordingly. Some of these parameters are described above under Parameters
We set the number of modes (nModes) to a value greater than the number of modes we expect. The analyzer will only find guided modes. Also check Overwrite Existing Files. Run the analyzer by clicking Analyze button in the upper right corner. The analyzer output should resemble Fig. 246. We see that the analyzer found 3 modes. They are listed in decreasing order of effective index.
After performing the above actions proceed to the Visualize window by pressing the Visualize button in the left column of buttons. You may need to Reload Data (bottom left). Visualize an eigenmode by following these steps:
The resulting visualization pane should resemble Fig. 247.
One can select other components of the H, E, or D field to see how they vary for the eigenmodes. These eigenmodes are now saved in .vsh5 files in the folder where the simulation was run.
Change the geometry on the Setup window and rerun the simulation and analyzer to see the effects on the modes.
Once you have your desired mode, launch it down the waveguide using the procedure laid out in the multiModeFiberModeLaunchT example.
One can run a full convergence study of eigenmode effective indices by varying the RESOLUTION constant in the Setup window and re-running the simulation and mode extraction script. A plot of the effective index as a function of transverse cell area is shown in Fig. 248. The linear relationship shows the second order accuracy of our dielectric algorithms.