A planar photonic crystal waveguide based on the semiconductor-on-insulator (SOI) materials system is analyzed theoretically. Two-dimensional (2-D) calculations and comparison with dispersion relations for the media above and below the finite-height waveguide are used to obtain design guidelines. Three-dimensional (3-D) calculations are given for the dispersion relations and field profiles. The field profiles obtained using 2-D and 3-D calculations are qualitatively similar. However, we find that compared with 2-D calculations, the frequencies of the guided modes are shifted and the number of guided modes changes. The theoretically predicted frequency intervals, where the waveguide supports leakage-free guidance of light, are compared with an experimental measurement for propagation losses. Two out of three frequency intervals coincide with low-measured propagation losses. The poor guidance of light for the third frequency interval is explained theoretically by investigating the vertical localization of the guided modes.
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Søndergaard, T., & Arentoft, J. (2002). theoretical analysis of finite-height semiconductor-on-insulator based planar photonic crystal waveguides. Journal of Lightwave Technology, 20(8), 1619-1626. https://doi.org/10.1109/JLT.2002.800380