An Accurate and Numerically Stable Formulation for Computing the Electromagnetic Fields in Uniform Bend Rectangular Waveguides

This article describes a numerically stable formulation for the analysis of electromagnetic fields in rectangular cross section waveguides with a curved longitudinal axis. A novel set of scaled Hankel functions for real-valued arguments and complex-valued orders is introduced for rescaling the characteristic equations associated with the transverse electric (TE) and magnetic (TM) fields of the exact boundary value problem. The exponentially scaled cylindrical functions presented here prevent numerical underflow and overflow errors associated with large real and large imaginary orders without sacrificing accuracy. The proposed methodology is validated against variable-precision arithmetic (VPA) results. Numerical results are also presented for waveguides with large radii of curvature, where the present methodology is compared with perturbation ones in several examples. Dielectric-filled waveguides with small radii of curvature are investigated, and our solutions are compared with finite-integration technique (FIT) results.