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The vector electromagnetic problem for eigenwaves of optical fibers, originally formulated on the whole plane, is equivalently reduced to a linear parametric eigenvalue problem posed in a circle, convenient for numerical solution. The study of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. Asymptotic properties of the dispersion curves and their smoothness are investigated for the new formulation of the problem. A numerical method based on finite element approximations combined with an exact non-reflecting boundary condition is developed. Error estimates for approximating eigenvalues and eigenfunctions are derived.

Accurate Full-Vectorial Finite Element Method Combined with Exact Non-Reflecting Boundary Condition for Computing Guided Waves in Optical Fibers