Continuum analog of coupled multiple waveguides

This paper presents an analysis of the eigenmodes and wave evolution of a coupled multiple-waveguide system in terms of an equivalent graded-index waveguide: The coupled wave equation is approximated by a partial differential equation. By an appropriate gauge transformation, the wave equation of a graded index waveguide is obtained. Several examples of eigenstates and wave evolution in coupled multiple waveguides are studied to clarify some conceptual subtleties and to show the accuracy, usefulness, and limitations of this method.