Analysis of FSS with multiple, arbitrarily shaped elements within a periodic cell

Metal screens perforated periodically with apertures or periodic arrays of metallic patches represent a frequency selective surface (FSS). FSSs are used as filters in the microwave and in the mm and sub-mm wave range. The frequency behavior of the FSSs depends on the shape of the elements (apertures/patches), on their size and spacing, and on the thickness of the metal screen. A further degree of freedom in the design of FSSs can be added by considering groups of N apertures arranged in a periodic array. FSSs with multiple apertures within a periodic cell present some advantages. In fact, by considering two apertures per unit cell, the FSS can operate in two (closely spaced) frequency bands, and two orthogonal polarizations can be separately adjusted. We previously applied the modal approach in conjunction with the boundary integral-resonant mode expansion (BI-RME) method to the analysis of FSSs with one arbitrarily shaped aperture per unit cell. This hybrid method was applied both to the case of thin and thick perforated metal screens, and resulted into a very efficient computer code. This paper extends this hybrid method to the analysis of FSSs with multiple apertures per unit cell. The shape and the number of apertures can be given arbitrarily.