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A modified finite-difference (FD) formula for an arbitrary dielectric interface is applied to an imaginary-distance propagation method based on Yee's mesh. To confirm the validity of the modified method, we first analyze the eigenmode of a step-index circular fiber. A reduction in a discretization error is demonstrated in the evaluation of the field profile. Calculations of the normalized propagation constant show that the convergence rate of the modified FD formula is faster than that of traditional techniques and is comparable to that of a body-of-revolution technique. As a further application, we analyze the eigenmodes of sloped-side rib guides. These data agree well with previously published data.