FDFD Method Based on Refined Shift-and-Invert Arnoldi Technique for Periodic Leaky-Wave Antennas

The finite difference frequency domain (FDFD) method can be used to analyze the properties of arbitrary complex close/open periodic guided-wave structures. For the open problem, it probably results in a large scale nonsymmetrical generalized eigenvalue problem. In the analysis of the leaky-wave antennas, because the leakage constant (attenuation constant) increases a lot in the working frequency range, the extraction process of the eigenvalues (complex propagation constants) is difficult to converge when the shift-and-invert Arnoldi technique is used to resolve this large scale nonsymmetrical generalized eigenvalue problem. In this paper, a refined shift-and-invert Arnoldi algorithm is adopted to speed the convergence rate by using refined Ritz vectors to approximate the desired eigenvectors. Since the refined method always converges, a simple FDFD method with six field components can be used. The difference equations of this method are much simpler than those of the previous method because the longitudinal field components don´t have to be eliminated in order to approximately transform the generalized eigenvalue problem to a standard eigenvalue problem. Consequently, the accuracy of the method can be improved and the boundary conditions can be implemented easily.