Numerical Analysis of Planar Periodic Multilayer Structures by Method of Moments

Abstract

Numerical analysis of planar periodic multilayer structures is often carried out with the aid the method of moments (MoM). The advantage of the technique against the other, more general methods (like FEM and FDTD) is in faster computation of reflection and transmission properties of a periodic structure. Besides of computation speed, usage of MoM typically results in lower memory requirements when compared to FEM and FDTD. The method of moments can be either formulated in the spatial or spectral domain. For analysis of periodic structures the spectral formulation is more advantageous – a discrete space spectrum (Scott, 1989). Thus, the original integral equations reduce into algebraic ones (that is double summations are being used instead of surface integrals). The disadvantage of the spectral formulation is that double summations arising in MoM formulation are slowly convergent and a high number of Floquet modes is needed for analysis of periodic structures having fine patch details inside the periodic cell or densely stacked structures. Simple spectral domain MoM codes for analysis periodic structures consider uniform mesh of cells and utilize FFT to accelerate the double summations (Cwick & Mittra, 1987; Wan & Encinar, 1995). These simple MoM codes also typically use small domain basis functions (like rooftops (Cwick & Mittra, 1987), or triangular (RWG) basis functions (Kipp & Chan, 1994)). If more general geometry is to be analyzed, then a non-uniform mesh of rectangular or quad shaped cells (Kolundzija, 1998) must be used. From the computational point of view it also highly desirable to consider use of higher order large domain basis functions for representation of surface currents. Then, the conductive currents in patches may be accurately described with a small number of unknown expansion coefficients. Solution of reflection/transmission properties of a multilayer periodic structure can be performed either directly (Wu, 1995) or by the use of a cascade approach (Mittra et. al, 1988) or (Wan & Encinar, 1995). The cascade approach is suitable for periodic structures which with a large or a medium electrical thickness of individual dielectric layers. When the electrical thickness of a particular dielectric layer becomes too small then a large number of Floquet modes must be used during the cascade process (Wan & Encinar, 1995). In such a case, which is a typical for periodic structures with microscopically thin layers (e.g. carbon fibre composite materials) the direct approach is being used. 2