Frequency selective slot array analysis by hybrid finite element-boundary integral and spectral domain integral equation techniques

Frequency selective surfaces (FSSs) for optical frequencies typically involve thick uniform substrates together with periodic resonating elements of various shapes. Efficient and versatile analysis of such structures is achieved via the infinite periodic array model using the hybrid finite element (FE) - boundary integral (Bl) technique extended to include planar multilayered Green's functions. Thus, part of the volumetric dielectric region is modeled via FEs whereas possibly thick uniform multilayered regions are characterized using multilayered Green's functions. The multilayered Green's functions are analytically computed in the spectral domain and the resulting Bl matrix-vector products are evaluated via the fast spectral domain algorithm (FSDA) without explicit generation of the Bl-matrix. Furthermore, the number of Floquet modes in the Bl expansion is kept very few by appropriately placing the Bl surfaces within the computational unit cell. Several FSS arrays are analyzed with this method to demonstrate the accuracy and capability of the approach. One example includes complicated multilayered substrates above and below an inhomogeneous filter element and the other is an optical ring-slot array on a multilayered substrate several hundred wavelengths in thickness. Comparisons with measurements are included and the optical ringslot array is also analyzed by a specialized spectral domain integral equation solution via the method of moments (MoM).