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The vector magnetic field finite difference method presented is a numerical technique based on a variational approach and is suitable for the analysis of optical waveguides. Several characteristics of this method are examined. Eigenvalue convergence for a square dielectric waveguide is investigated, along with the effect of the weighting of the so-called penalty function, which is used to move spurious solutions to higher frequencies. Data for an elliptical core optical fiber and a multiple core fiber is given. The vector magnetic field finite-difference approach demonstrates advantages, such as a banded ordinary eigenvalue solution and ease of implementation and solution, as compared to the finite element solution of such a variational formulation.