Efficient and accurate waveguide mode computation using BI-RME and Lanczos methods

In this paper, a special purpose algorithm for solving large eigenvalue problems based on the Lanczos method is successfully applied to an engineering problem: the electromagnetic analysis and design of passive waveguide devices. For dealing with such complex problems, the boundary integral-resonant mode expansion (BI-RME) technique has been recently proposed. This technique solves integral equations (IEs) through the well-known method of moments (MoM), thus leading to structured eigenvalue problems. These problems frequently become very large when solving complex arbitrary geometries with high accuracy. In such cases, the eigenvalue problem cannot be efficiently solved with standard methods by means of personal computers, essentially due to CPU time and memory allocation requirements. In this paper, we propose an alternative technique, based on the Lanczos method, for the fast and accurate solution of large BI-RME generalized eigenvalue problems. The novel theoretical aspects of this approach, as well as the impact on the original BI-RME formulation, are described. Comparative benchmarks are also successfully presented for the full-wave analysis and design of real passive microwave devices.