A semi-analytic method for solving rib-type waveguide problems

C. S. Hsiao, Y. J. Chiang, Likarn Wang*, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A new semi-analytic method for solving optical rib-type waveguide problems is presented. In the method, the cross-section of a rib-type waveguide is divided into several regions. In each region, the refractive index profile and field distribution are expanded into Fourier cosine series, and then are substituted in the wave equation. A second-order differential matrix equation is then derived for each region, with a closed-form solution obtainable. With the boundary conditions used, an eigenmode equation for the rib waveguide can be derived and solved numerically to give the modal indices. Here, the presented method is used to deal with two rib waveguides in different geometric dimensions and/or compositions, respectively. Computational results show that the presented method is quite efficient, in terms of CPU time, in finding the modal indices accurately. The relative error in computing the modal index with the method is about 10-5-10-6.

Original languageEnglish
Pages (from-to)1315-1329
Number of pages15
JournalJournal of Modern Optics
Issue number8
StatePublished - 1 May 2008


  • Eigenmode equation
  • Fourier cosine series expansion
  • Rib-type waveguides
  • Semi-analytic method

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