Properties of four-layer planar optical waveguides near cutoff

Mode properties of four-layer planar optical waveguides near cutoff are considered. The four-layer structures considered are applicable to waveguiding layers formed on cladding layers above either silicon or gallium arsenide substrates. Perturbation approaches are shown to be accurate except near mode cutoff where a numerical solution of the four-layer equations is required. Numerical calculations of waveguide attenuation due to substrate coupling for thermally nitrided silicon dioxide and for gallium aluminum arsenide waveguides are presented for a variety of layer thicknesses, layer material compositions, and wavelengths. Comparison to some experimental data is included.