In this section, MODE will be utilized to study the modes of a SOI waveguide and analyze its dispersion properties.

## Simulation setup

The file waveguide_dispersion.lms contains a simple silicon on SiO2 ridge waveguide with a ridge width of 500 nm and a ridge height of 180 nm. The simulation area is defined in the XY plane with perfectly matched boundary conditions. The eigensolver is used to solve for the modes of this waveguide. The refractive index values of Si and SiO2 are sampled data that have been entered in the materials library.

## Frequency Sweep Analysis

Any single frequency analysis of the mode, can be done with the sampled data model obtained by simply interpolating the data points for the available wavelengths. For the waveguide defined above we find the following when running the eigensolver analysis.

### Problem

If the refractive index data is used directly to sweep over a range of frequencies for calculations that involve the derivative of the refractive index function with respect to wavelength, such as dispersion, any discontinuities from the experimental data will lead to artificial peaks in the resulting plots, as seen in the figure below:

Material fit using sampled data interpolation

Dispersion of the mode as a function of wavelength with discontinuous material fit model

### Solution

To overcome this problem, the index data can be modeled using Lumerical's Multi-Coefficient Model feature. The screenshot below shows the Material Explorer to modify the fit. This tells the software to fit and use the smooth curve for simulation. Make sure you save the parameters and setting before closing the Material Explorer.

### Results

This fit will generate smooth dispersion curves. Using the eigen solver frequency sweep tab, several mode properties such as loss, effective index, group velocity and dispersion curves can be calculated for a specified range of frequencies.

Material fit using multi-coefficient model

Dispersion and refractive index of the mode as a function of wavelength with multi coefficient material fit model

Note: Accuracy (mesh and the detailed dispersion calculation option) The number of mesh cells in the solver region could be increased to get slightly better accuracy. Also, the DETAILED DISPERSION CALCULATION option is turned on to obtain more accurate results, but the downside is a slower simulation. To run a quicker simulation, simply turn off this check box. For more information, please see the frequency analysis page. |