This topic compares the analytical solutions and results simulated with MODE for a ARROW slab waveguide at a wavelength of 632.8nm.

## Simulation setup

The figure above shows the geometry and refractive indices of the multilayer dielectric ARROW slab waveguide at a wavelength of 632.8nm.

## Results

The script arrow_waveguide.lsf finds effective index and propagation loss corresponding to the TE1 mode and plots the results and the corresponding % errors as a function of the number of grid points. The results from the FDE calculation are compared with values taken from E. Anemogiannis et al.

The plots can be generated in Matlab by setting the flag "use_matlab" to be 1 (Matlab Integration must be enabled).

(Left) Effective index (red) and loss (blue) calculations for TE mode of ARROW waveguide at 632.8nm. The symbols (o) denote MODE calculations, and the lines show the comparison results. (Middle/Right) The same figures (effective index/propagation loss) generated using only built-in MODE functions (no Matlab interface).

(Left) Error amplitude of MODE calculation for ARROW waveguide TE mode at a wavelength of 632.8 nm. The x-axis is the number of grid points in the calculation region. (Right) The same figure generated using only built-in MODE functions (no Matlab interface).

### Related publications

E. Anemogiannis et al., "Determination of Guided and Leaky Modes in Lossless and Lossy Planar Multilayer Optical Waveguides: Reflection Pole Method and Wavevector Density Method" IEEE Journal of Quantum Electronics, vol. 17, pp. 929-941, 1999