Waveguide (FDE)

In this example, the Finite Difference Eigenmode (FDE) solver in MODE is used to characterize a straight waveguide. The calculated mode parameters are then used to create a waveguide element in INTERCONNECT. How to extract these parameters for compact model generation using the CML Compiler is also demonstrated.

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Overview

Understand the simulation workflow and key results

The characterization of the waveguide is done using the FDE solver in MODE.

Step 1: Calculate Supported Modes

Calculate the supported modes from a 2D cross section of the waveguide. The solver provides a comprehensive list of mode properties including spatial mode profile, effective index, loss, etc.

Step 2: Frequency Sweep

Select the mode(s) of interest. Run a frequency sweep to obtain their properties as a function of the frequency/wavelength. Export these properties into a file.

Step 3: Import Waveguide Data in INTERCONNECT

Import the waveguide data into INTERCONNECT to create a new waveguide element that can be used in a circuit simulation.

Compact Model Generation with CML Compiler

To generate the compact model of the waveguide with CML Compiler, simply skip Step 3 and provide the data extracted in Steps 1 and 2 to CML Compiler. The Parameter extraction for CML Compiler section uses a script to automatically go through these steps and extract the data for CML Compiler in the required format. Advanced users already familiar with this example can proceed to this section directly. If you are new to this example, we strongly recommend going through the preceding sections and learning about the individual steps before moving to the Parameter Extraction for CML Compiler section.

Run and Results

Instructions for running the model and discussion of key results

Step 1: Mode Calculation

The FDE solver returns a list of supported modes, along with mode properties such as effective index and spatial mode profile.

Step 2: Frequency Sweep

The frequency sweep calculates the modes’ properties (including effective index, loss, propagation constant, group velocity, dispersion) over the selected frequency/wavelength range. These properties are exported to the file that will be imported to INTERCONNECT.

Step 3: Import in INTERCONNECT

The ONA returns the normalized group velocity, \(v_g\), that can be compared to the value obtained from the FDE simulation.

Important Model Settings

Description of important objects and settings used in this model

Step 1 & 2

Simulation Region Dimensions

The solver region must be large enough to completely contain the mode, including evanescent tails. Ensure the field have decayed to at least 1e-4 near the boundaries. This is easy to visualize by plotting the fields on a log scale.

Boundary Conditions

• Straight waveguides: Use metal boundaries. If the fields are negligible at the boundary (as recommended in the previous comment), then the choice of boundary is not important. Metal boundaries are fastest and minimize the simulation memory.
• Bent waveguides: Use PML boundaries. Bent waveguides may have radiative losses, which means PML boundaries are required. Note that PML boundaries can introduce non-physical modes near the boundaries. These modes can be ignored.

Material (incl. Fit for Frequency Sweep)

It is important to model the material data using Lumerical’s Multi-Coefficient Model feature, especially when running a frequency sweep. This can be set by checking the fit materials with multi-coefficient model box in the Material tab of the FDE region properties.

Step 2

Detailed Dispersion Calculation

Checking this box in the Frequency analysis tab allows you to calculate the mode properties at some additional frequencies to obtain more accurate results over the frequency/wavelength range of interest.

Store Mode Profiles While Tracking

When the store mode profiles while tracking box in the Frequency analysis tab is checked, the mode profiles at each frequency will be stored and exported to INTERCONNECT. This is useful if you want to visualize the mode profiles in INTERCONNECT using the Mode Profile Analyzer element.

Updating the Model with Your Parameters

Instructions for updating the model based on your device parameters

Step 1 & 2

The waveguide simulation file is parametrized to allow easy modification of the common properties:

• Waveguide width
• Waveguide height
• Waveguide material and index
• Substrate material and index
• Clad material and index
• Boundary conditions (metal or PML whether the waveguide is straight or bent)

The wavelength/frequency is set in the Eigensolver Analysis window in the Modal analysis tab, available once you have clicked the Run button. Similarly, the wavelength/frequency range is available in the Frequency analysis tab.

Step 3

In the INTERCONNECT MODE Waveguide (WGD_1) element, you can modify the length property to change the waveguide length.

Parameter Extraction for CML Compiler

Instructions for parameter extraction for CML Compiler for compact model generation

This section describes how to automatically run the component level simulations of the waveguide and extract the parameters for CML Compiler. Once the parameters are extracted in the required format, they can be used in CML Compiler to generate the compact model. Here we extract model data for two waveguides in the template foundry library, Waveguide Straight (Fixed) and Waveguide Straight (Statistical) .

Note that the running of the CML Compiler is beyond the scope of this example. For more information about CML Compiler visit the CML Compiler overview and CML compiler product manual .

Steps to get the data and build the nominal Waveguide Straight (Fixed) compact model using CML Compiler are:

Steps to get the data and build Waveguide Straight (Statistical) compact model using CML Compiler are:

Mode information

In the script Waveguide_FDE_dataCMLCompiler.lsf , you must specify the number of the modes of interest in the list calculated by the eigensolver. It is recommended to calculate the modes beforehand to identify the appropriate mode numbers as explained in Step 1 of Run and Results; in addition, it is necessary to specify the desired name and ID for these modes. See the documentation in the script for more information. Note that the example in the script selects the fundamental TE and TM modes.

Temperature sensitivity

You can include temperature sensitivity of the effective index in the model by providing the appropriate value of \( dn_{eff}/dT \). This can be obtained from experiment or from simulation using the temperature to index conversion explained here .

Additional loss

The additional_loss parameter in the script allows you to add a loss value on top of the loss calculated by the eigensolver. This is particularly useful when the loss is underestimated by the simulation (for example, losses due to roughness are not accounted for in the simulation).

Statistical parameter information

In Waveguide_FDE_dataCMLCompiler_statistical.lsf , we introduce support for statistical modeling and simulation to the CML Compiler data file by defining the stat_parameters cell array. Component level simulations are run to capture the model sensitivity as a function of these parameters. Additional statistical parameters can be added.

Taking the Model Further

Information and tips for users that want to further customize the model

Using Symmetries

Symmetric and anti-symmetric boundary conditions can be used to reduce the simulation area. The choice of symmetry will affect the mode calculations as only the modes with the same symmetries will be found.

Overriding Loss

The solver will only determine propagation loss due to the materials (absorption) or radiative loss (for example in a bent waveguide). To take into account other sources of loss, you can override the loss when exporting the data to INTERCONNECT from MODE.

In the Mode Label and Orthogonal ID Editor window, set Override Loss to true and enter the loss for each mode in dB/cm.

Additional Resources

Additional documentation, examples and training material

See Also

• Dispersion analysis
• Bent waveguide solver
• Symmetry and anti-symmetry
• Waveguide (FEEM)

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