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A unified approach using curvilinear hybrid edge/nodal elements with triangular shape is, for the first time, described for the study of guided-wave problems. Not only the lowest order (fundamental) but the higher order elements are systematically constructed. The advantage of curvilinear elements lies in the fact that they can model curved boundaries with more accuracy and lesser number of degrees of freedom than rectilinear elements. The vector basis functions derived here are also applicable to rectilinear cases. To show the validity and usefulness of the present approach, computed results are illustrated for rib waveguides with straight boundaries and circular waveguides with large refractive-index differences.