Guided-wave characteristics of optical graded-index planar waveguides with metal cladding: a simple analysis method

The guided mode characteristics of metal-clad graded-index waveguides are generally determined by complex eigenvalue equations or perturbative methods. However, these methods either require several iterations in the complex plane or are only suited to the class of waveguides whose guided field can be described analytically. We describe a method of calculating complex propagation constants for metal-clad graded-index waveguides under very general but weakly guiding conditions. The method, based on Galerkin´s formalism using trigonometric basis functions, allows arbitrary inhomogeneous and complex refractive index profiles. Applications to three generally used waveguide models show our approach to be in good agreement with other analytical or numerical methods