In this paper an algorithm for numerical investigation of the transmission line having a generalized polygonal cross-section and open interface is proposed. Solution of the eigenmode problem is based on the method called the domain product technique, which employs a Mathieu function expansion and provides an efficient technique to the analysis of the structures with multiangular boundaries. An agreement at the obtained numerical results with existing data confirms the applicability of the theoretical analysis given in the paper.

The scattering problem of a plane wave by an axially slotted conducting elliptic cylinder in homogeneous medium is investigated. We present an accurate analysis using the modified point matching method, which can reduce the order of the simultaneous equations to be solved at least by a half under the condition of the same accuracy as compared with an usual point matching method. The accuracy of our results is checked by evaluating the relative errors. Numerical results are given for scattered field patterns by a conducting elliptic cylinder with a slot aperture of angle width 120 when the angle of incidence θinO.

The improved point-matching method with Mathieu function expansion for the accurate analysis of the W-type elliptical fiber with layers of any ellipticity is proposed. Results of our method are reliable, because we expand the electromagnetic fields by a sum of the complete set of wave functions in each layer of the fiber. Numerical results are presented for the highly-birefringent fibers with a hollow layer outside an elliptical core. It is found that such fibers can realize the large value of the modal birefringence as well as they can be suitable for the single-mode and single-polarization transmission. From the convergence tests, it is confirmed that the relative error of the modal birefringence is less than 0.01%. The comparison of our results with those by previously reported method is presented. The proposed method can be extended for analysis of the elliptical-core fibers with hollow pits and electromagnetic scattering by targets of the complex elliptical geometry.