Abstract
Based on a numerical solution of the nonstationary wave equation, an algorithm for determining the eigenfunctions and eigenvalues of the LPim modes of axially symmetric optical waveguides is suggested. The cutoff frequency of the LP11 mode of different waveguides is determined using the algorithm constructed. The results obtained are compared with the well-known analytical formulas and results of numerical calculations for the equivalent step-index waveguide model. Based on the analytical results obtained, an eigenfunction and eigenvalue search algorithm is suggested for a waveguide with a two-dimensional refractive index profile (in particular, for an axially nonsymmetric waveguide).
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