The Finite Element EigenMode (FEEM) solver in Finite Element IDE is used to characterize straight waveguides. These parameters are then used to create a waveguide element in INTERCONNECT.

## Overview

Understand the simulation workflow and key results

The characterization of the waveguide is done using the FEEM solver.

** Step 1 ** : Calculate the supported modes from a 2D cross section of the waveguide. The solver provides a list of mode properties: spatial mode profile, effective index, loss.

** Step 2 ** : Run 2 simulations at 2 different wavelengths/frequencies to obtain the group index of the fundamental mode.

** Step 3 ** : Import the waveguide effective index and group index to INTERCONNECT to create a new waveguide element that can be used in a circuit simulation.

## Run and results

Instructions for running the model and discussion of key results

### Step 1: Mode calculation

- Open the simulation file.
- Edit the FEEM properties and set the wavelength/frequency in the "Modal Analysis" tab.
- Click the run button
- Explore the results from the FEEM solver or run the "Waveguides_FEEM_modeproperties.lsf" script to extract the effective index and loss of the fundamental mode and plot the mode profiles.

The FEEM solver returns the spatial mode profiles and mode properties (effective index and loss) versus mode number and frequency/wavelength. The simulation is set to calculate the first 20 modes and the modes are ordered according to their effective index (descending order). Mode number 1 will then be the fundamental mode.

### Step 2: Group index calculation

- Open the script file "Waveguides_FEEM_ng_sweep.lsf".
- Set the wavelength.
- Run the script.

The script calculates the group index of the fundamental mode (TE) from the slope of the effective index versus frequency:

$$ n_g(\omega_1) = n_{eff}(\omega_1) - \lambda_1 \frac{n_{eff}(\omega_2) - n_{eff}(\omega_1)}{\lambda_2 - \lambda_1} $$

Where

$$ \lambda_i = \frac{c}{\omega_i} $$

### Step 3: Import to INTERCONNECT

- Open the simulation file
- Enter data from FEEM to the Straight Waveguide element. In the "Property view", specify the effective index and group index
- Click the run button
- Explore the results from the Optical Network Analyzer (ONA)

The ONA returns the normalized group velocity, \(v_g\), that can be used to calculate the group index, \(n_g\) and compare it to the value obtained from the FEEM simulation:

$$ n_g = \frac{c}{Lv_g} $$

Where \(L\) is the waveguide's length.

## 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 the evanescent tail. Ensure the fields have decayed of at least \(10^{-4}\) near the boundaries. This is easy to visualize by plotting the fields on a log scale.

Note: If the fields are negligible at the boundary, the choice of boundary conditions is not important.

## 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
- Substrate material
- Clad material

The wavelength/frequency is set in the "FEEM" property window ("Modal analysis" tab):

### Step 3:

In the INTERCONNECT "Straight Waveguide" element, you can modify the property:

- Waveguide length

## Taking the model further

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

Using the symmetries: It is possible to use the symmetry of the waveguide to simulate only half of it, by using PEC or PMC boundary conditions at the plane of symmetry. The choice of PEC or PMC at the plane of symmetry will affect the mode calculation as only the compatible modes will be found.

Note: this allows to calculate the effective index and group index selectively for the fundamental TE and TM modes.

## Additional resources

Additional documentation, examples and training material