This paper deals with the theory of dielectric waveguides in a graded‐index media. The theory is first developed in terms of electrical and magnetic potentials and a gauge condition which is a generalization of the Lorentz gauge used in classical electromagnetic theory for the isotropic, homogeneous medium. The existence of these potentials under the generalized Lorentz gauge in the context of a generalized Helmholtz theorem are then proven. Even though this generalized gauge uncouples the governing equations, it does not lead to partial differential equations in thenormalform. To alleviate this problem, superpotentials of the Hertzian variety are introduced and it is shown how equations governing the vector superpotential can be reduced to a form which is amenable to standard analysis. Then several uniqueness theorems associated with this superpotential are proven. As an illustration of the use of the superpotential and its relative merits, it is applied to certain waveguide problems in an inhomogeneous medium with variable permittivity.