This paper considers the solutions to optical fibers and integrated optical dielectric waveguides. The unbounded medium surrounding the waveguide is modeled by infinite elements with edge bases. The inhomogeneous part of the waveguide is discretized into a recently-developed edge finite elements. To match the infinite elements with adjacent finite elements, compatible interpolation functions are proposed for the infinite elements. In consequence, the boundary conditions between finite and infinite elements are exactly satisfied. Also, the formulation in this paper is presented such that any decay function in the radial direction may be employed. However, explicit representations for the infinite element matrices are given for the case of an inverse power decay function. Other functions will be investigated in the future work. The solutions to the final system of equations provide the dispersion characteristics of the optical waveguide. A computer program and an automatic mesh generator were written and shown to be valid by comparing the solutions with other published data.

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