The fabrication restrictions that must be imposed on the geometry of optical waveguides to make them behave as single-mode devices are well known for relatively large waveguides, with shallow etch depth. However, the restrictions for small waveguides (\sim 1 ~µm or less in cross section) are not well understood. Furthermore,it is usually a requirement that these waveguides are polarization independent,which further complicates the issues. This paper reports on the simulations of the conditions for both single-mode behavior and polarization independence,for small and deeply etched silicon-on-insulator (SOI) waveguides. The aim is to satisfy both conditions simultaneously. The results show that at larger waveguide widths, waveguide etch depth has little effect on the mode birefringence because the transverse-electric (TE) mode (horizontal-polarized mode) is well confined under the rib region. However, at smaller rib widths, the etch depth has a large influence on birefringence. An approximate equation relating the rib-waveguide width and etch depth to obtain polarization-independent operation is derived. It is possible to achieve single-mode operation at both polarizations while maintaining polarization independence for each of the waveguide heights used in this paper but may be difficult for other dimensions. For example,a 1-µm SOI rib waveguide with an etch depth of 0.64 µm and rib width of 0.52 µm is predicted to exhibit such characteristics.
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