Abstract
For modal expansion in the nonhomogeneous optical waveguides, it is necessary to develop a high-precision mode solver. In this work, the differential transfer matrix method is applied, and an exact dispersion equation is built generally by the matrix similarity transformation and may be solved iteratively by Newton’s method. In justification of the proposed method, truncation error analysis for the old method is provided. Furthermore, the asymptotic solutions in the form of simpler formulas for the approximated equation are derived. These approximate analytic results are valuable and may well act as initial guesses for numerical methods. More accurate results can be obtained through our method in numerical simulations.
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