This topic compares the analytical solutions and results simulated with MODE for an asymmetric dielectric slab waveguide at wavelength1.55µm.

## Simulation setup

The figure above shows the dimensions and refractive indices of the three-layer asymmetric dielectric slab waveguide. This can be constructed using three contiguous rectangular structures representing the air (etch), core (silica) and substrate (dielectric defined with an index of 1.33) layers.

## Results

The script slab_wg.lsf finds the effective indices of the TE1 and TM1 modes for wavelength 1.55µm and plots the results and the corresponding % errors as a function of the number of grid points. The analytical solution for the effective index of the slab waveguide can be calculated with the Matlab script slab_wg.m, and it is used to verify the MODE results.

Set the flag "use_matlab" to be 1 in order to execute the analytical calculation and plot the results using Matlab (Matlab Integration must be enabled). Otherwise, download the provided text files with the calculated results for the analytical solution, which will be read and used to generate the plots with Lumerical's plotting functions.

(Left) Effective index values for TE (red) and TM (blue) modes as calculated via MODE (o) and via analytic relations (lines). The x-axis shows the convergence of MODE to the correct answer as the number of grid points is increased. (Right) The same figure generated using only built-in MODE functions (no Matlab interface).

(Left) Magnitude of error of MODE calculation. The x-axis shows the number of grid points in the one-dimensional calculation region. (Right) The same figure generated using only built-in MODE functions (no Matlab interface).