The fields in the junctions between straight and curved rectangular waveguides are analyzed by using the method of separating variables. This method was succeeded because the authors developed the method of numerical calculation of the cylindrical functions of complex order. As a result, we numerically calculate the reflection and transmission coefficients in the junctions in various situations, and we compare these results with the results by the perturbation method and with the results by Jui-Pang et al.

We frequently need to calculate the Neumann function Nν(x) of complex order ν numerically in order to solve boundary problems on electromagnetic fields. This paper presents a new method for the numerical calculation of Nν(x) of complex order ν. This method can calculate Nν(x) precisely even when the order ν is close to an integer n, and the algorithm by the method is very simple.