Laser simulations employing the 4 level 2 electron material model are nonlinear simulations. Therefore, there are particular points that are important to keep in mind. A couple of the major differences between linear and nonlinear materials include the needs to think in the time domain and more advanced processing of the signals. For the specifics of the implementation of the model, please refer to Four-Level Two-Electron Material model page. In addition to this page, please refer to the nonlinear simulation tips page for tips on monitor settings, more information on normalization, material, convergence and stability, mesh setup, and source settings.
Quantities of interest (recording storage fields)
Once you have created the material, you can record the storage fields used by the plugin. For the four-level two-electron model provided for the laser simulation examples, storage fields 4 to 7 correspond to the level populations N0 to N3. To record the storage fields, we use a point time monitor in the material. In the edit window of the time monitor, the material to record needs to be chosen. After the simulation runs, in the Result View window, the data are found under the subheading raw data.
Custom source and time signal
For many nonlinear applications, including ones using the 4 level 2 electron model, the precise pulse shape and the source amplitude are very important. The script file cw_source.lsf has been used in some of the following examples to create a custom CW source that slowly turns on, as shown in the following screenshot.
For more information on custom sources, see the following pages:
- Creating a custom source time signal
- Creating a custom source spectrum
- setsourcesignal - script command
- Nonlinear simulation tips
Usually, based on the source bandwidth and material properties, the automatic non-uniform meshing algorithm attempts to generate the simulation mesh. However, as this will not take into account possible higher frequency components that may be generated via nonlinear processes, it is imperative that we consider the entire wavelength range that is necessary for the simulation, and make those corrections needed in the manner shown in the image below (the “override simulation bandwidth for mesh generation” option, in the advanced options tab of the simulation region edit window). For relevant information, please refer to the nonlinear simulation tips page.
From the material database, add a new material of your choice. For the case of a laser simulations, the four-level two-electron model is chosen.Add the new material, then setup the relevant parameters accordingly. It is also possible to create a custom material model using the plugin material framework. For more information on this feature, please refer to the User-defined material models page.
It is important that we consider all the frequencies that may be created. Accordingly, it is needed to set the material fits and set the FDTD mesh settings appropriately for all the wavelengths present in the system. By default, the simulation bandwidth is the total bandwidth of all sources in the simulation and is used for mesh generation and material fits. Modify this according to your simulation settings.
Lumerical uses the multi-coefficient material model generated by fitting to the actual, experimentally collected material data, based on the source wavelength range. To accurately model the material properties outside the source wavelength, it is important to fit all relevant materials over the full simulation bandwidth. The base material for the laser material should also be fit over the relevant bandwidth. It is of worth to note that the Material Explorer, which is used for viewing and modifying material fits, cannot be used to view the material properties of any plugin materials.
To prevent normalizing the fields to the spectrum of the source, which is a problem for nonlinear simulations, the normalization state option of the Setting needs to be set to “No normalization”. Please refer to the figure below. It is also possible to do so using the script command nonorm. For more information, please refer to the nonlinear simulation tips page.
It is important to remember that nonlinear simulations must run much longer than typical simulations. Typical FDTD photonics simulations are less than 1ps for linear systems. But for the laser simulations, we must run 10s to 100s of ps by increasing the simulation time.
- Shih-Hui Chang and Allen Taflove, "Finite-difference time-domain model of lasing action in a four-level two-electron atomic system", Optics Express, Vol. 12 Issue 16, pp.3827-3833 (2004)
- Taflove, Computational Electromagnetics: The Finite-Difference Time-Domain Method. Boston: Artech House, (2005).