Exploitation of symmetries in the impedance matrix for moment-method analysis of arbitrary frequency-selective surfaces

Recently, a direct computation technique for the generalized scattering matrix (GSM) of a frequency-selective surface (FSS) between two media was proposed. This technique is based on the spectral-domain moment method and it is well suited to the analysis and design of multilayer FSS´s by the GSM cascade approach to account for the multimode interaction. When the number of unknowns for the induced current is large, the computation of the impedance matrix is intensive. The computation of subdomain impedance matrix for the analysis of a FSS with a suitable grid for using fast Fourier transform (FFT) has been previously reported and the associated reduction of computation time is between 75% and 87.5%. However, the discretization grid of a practical FSS depends on its geometry and usually is not appropriate for the use of FFT. This paper describes the exploitation of implicit symmetry and the improvement of numerical efficiency in the analysis of a FSS with an arbitrary discretization grid. It will be shown that making use of the symmetry results in considerable saving of computation time of the impedance matrix. With the improved efficiency, our direct technique of computing the GSM of a FSS becomes more powerful in analyzing and designing multilayer FSS´s.