In this example, we will characterize the optical response of a thermally tuned waveguide. The HEAT solver is used to simulate the temperature profile of the waveguide with different input powers. This result is then imported into the FDE solver to characterize the optical responses – the effective index, phase and loss as a function of the input power.
Overview
Understand the simulation workflow and key results
Phase shifters are used to change the transmission phase angle of an input signal. A temperature-dependent phase shifter can be developed using a metal wire in the vicinity of a waveguide which acts as a heat source to thermally tune the waveguide. Since the refractive index of materials is temperature-dependent, by varying the temperature of the waveguide, the modal characteristics of the waveguide, such as effective index, phase and loss, will change.
The phase shift of a waveguide depends on the change of the effective index and the length L of the waveguide:
$$Δφ = {2π(n_{eff}-n_{eff0})L \over λ}$$
Step 1: HEAT - Obtain the temperature profile
Using the HEAT, we first sweep the input power and obtain the temperature profile at the waveguide cross-section for different input power values.
Step 2: FDE - Calculate the temperature-dependent phase shift
Using the FDE, we obtain the temperature-dependent effective index of the waveguide’s fundamental mode by sweeping the input power and calculate the corresponding phase shift.
Run and Results
Instructions for running the model and discussion of key results
Step 1: Obtain the temperature profile
- Open the simulation file waveguide_heat.ldev and run the save_T_profile.lsf .
The project file contains a silicon waveguide on a silicon substrate. A wire is placed 2um above the waveguide and acts as a heat source to tune the waveguide and achieve the desired phase shift.
A sweep object is used to sweep the input power from 20 to 30mW. A temperature monitor has been placed around the waveguide region, which will automatically store the temperature map into the output file for each input power.
The script, save_T_profile.lsf, extracts the power-dependent temperature profiles and saves them into a matlab file format (T.mat) to be used in the subsequent optical simulations in MODE.
Step 2: Calculate the temperature-dependent phase shift
- Open the simulation file waveguide_fde.lms and run the script file waveguide_sweep.lsf.
The script will automatically import the temperature profiles from the HEAT simulations into the optical simulation. An index perturbation grid attribute is used to convert the spatial temperature changes into the changes in the refractive index of the material.
The script first disables the index perturbation grid attribute, runs the FDE solver at room temperature and stores the calculated effective index. Then it enables the index perturbation grid attribute and runs the FDE solver for different input power values.
From the effective index, we can calculate the phase (for L=200um) as a function of input power. To get a π phase shift, an input power of 28mW is required.
Important Model Settings
Description of important objects and settings used in this model
Heat transport boundary conditions
A temperature boundary condition is used to set the temperature of bottom of the simulation region at fixed 300K.
Furthermore, since the top of the simulation region is bounded by air, “convection” boundary condition is used at the SiO2/air interface.
Power sweep
A uniform power heat source is used on the wire. In the Optimizations and Sweeps window a power sweep is introduced. This sweep will calculate the temperature map from the temperature monitor for each input power of the power heat source.
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NOTES: 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. The changes to the geometry will not be reflected in the simulation if the mesh lock is turned on. To change the geometry, turn off the mesh lock, modify the geometry objects, mesh or run the simulation, then turn the mesh lock back on before running the parameter sweep. |
Thermo-optic coefficient
The index perturbation grid attribute used to convert the temperature map into a change in the refractive index of the material is based on a user-specified thermal-optic coefficient. For this reason, a new index perturbation material, named silicon_thermal, is added to the material database using silicon as base material. In this simulation, dn/dt = 1.8e-4 K-1 is used for silicon.