Analysis of NRD Components via the Order-Reduced Volume-Integral Equation (ORVIE) Method Combined with the Tracking of the Matrix Eigenvalues

This paper presents a novel technique for the calculation of the proper modes of two- and three-dimensional nonradiating dielectric (NRD) components for millimeter-wave applications. The electromagnetic analysis is performed by the order-reduced volume-integral-equation method, which leads to a homogeneous matrix problem. The calculation of the dispersion diagram of NRD components and of the resonance frequencies of NRD resonators require the determination of the frequencies that correspond to nontrivial solutions of the matrix problem. Those frequencies are determined by the eigenvalue tracking (ET) method, which permits to follow the path of the matrix eigenvalues in the complex plane when varying the frequency. Compared to standard approaches (based on the direct search of the determinant zeros or on the singular value decomposition), the ET method requires a much smaller number of frequency points and, therefore, a much smaller number of electromagnetic analyses. The effectiveness of the proposed approach is demonstrated through the determination of the dispersion diagram of an NRD guide and the calculation of the resonance frequencies of an L-shaped resonator. The comparison with experimental data is also reported in the case of a rectangular NRD resonator.