In this example, we will characterize the optical response of a thermally tuned waveguide. Lumerical’s heat transport solver is used to simulate the temperature profile for the waveguide with different input powers. This result is then imported into MODE’ Finite-Difference Eigenmode (FDE) solver to characterize the optical response, including changes to the effective index, phase and loss as a function of the input power.
Simulation set up
The project file thermal_tuning_waveguide_2D.ldev contains a silicon waveguide on a silicon substrate. A wire is placed 2um above the waveguide and acts as the heat source used to thermally tuned the waveguide and achieve the desired phase shift. The bottom of the simulation region is fixed at 300K, and the top of the simulation region is bounded by air. A uniform heat source object is used as the heater wire. A sweep is set up in order to sweep the input power from 20 to 30mW. A temperature monitor has be placed around the waveguide region, which will automatically store the temperature map into output file for each input power. This output file will be used in the subsequent optical simulation in MODE.
NOTE: Since a parameter sweep is performed to obtain spatial temperature data around the waveguide, the simulation mesh is locked to ensure the data is collected from the same mesh locations for all sweep points. Otherwise, since the mesh grid is re-calculated between each sweep, the temperature will be recorded on a different mesh at each sweep point and the parameter sweep object will not be able to collect the temperature data.
To study the waveguide eigenmodes in the presence of a non-uniform temperature field, we need to import the temperature map from the previous heat transport simulation into the optical simulation. An index perturbation grid attribute is used to convert the temperature map into a change in the refractive index of the material based on a user-specified thermal-optic coefficient. In this simulation, dn/dt = 1.8e-4 is used for silicon.
Open the thermal_tuning_waveguide_2D.lms and run the script thermal_tuning_waveguide_2D_mode_sweep.lsf to load the temperature map and calculate the modes for each input power.
Run the heat transport simulation by running the 'sweep' object. Once the simulation is complete, right-click on the sweep object and visualize the T_full data to see the temperature map for any input power. The temperature map for P_in = 25mW is shown below. Here, we can see that the region around the waveguide has been heated by about 20K.
To save the temperature data for optical simulation, run the following lines of the script after the heat transport simulation is complete:
This will save the data in a MATLAB file which can be loaded in MODE for optical simulation.
For optical simulation, the script file thermal_tuning_waveguide_2D_mode_sweep.lsf will load the temperature data and calculate the optical eigenmodes. From the effective index, we can calculate the phase change (for L=200um) as a function of input power. As seen in the image below, we expect to get a pi phase shift at 28mW for this waveguide.