Advanced Modeling of Circular Waveguide-Based Devices With Smooth Profiles Using Transformation Optics and Hierarchical Model Reduction

Abstract

A powerful and accurate analysis method for the full-wave analysis of circular waveguide-based devices is introduced. The method uses transformation optics, hierarchical model reduction, and the finite element method. First, transformation optics is applied to map the original device in a cylinder filled with an anisotropic and inhomogeneous medium. Second, exploiting a hierarchical model reduction approach, the electric field is expanded in terms of the modes of the circular waveguide in the transverse plane, while the longitudinal dependence of the fields is tackled by a 1D finite element method. The BCs are fulfilled rigorously. The 3D integrals arising from the discretization of the vector electric field equation are separable, thus allowing for solving radial and longitudinal integrals once and for all, while the angular integrals are the only ones to be computed for each specific device geometry. The limitations of the method are: (a) the input and output waveguides must be circular waveguides, even with different radii; (b) the device lateral surface must be expressed as a strictly-positive single-valued function in cylindrical coordinates; (c) the device profile must be smooth. The method is verified against full-wave simulations from commercial software and measurements available in the literature, showing good agreement and efficiency.