Analysis of multilayer infinite periodic array structures with different periodicities and axes orientations

This paper presents a general procedure to analyze a multilayer array structure, where each layer may have different periodicities, different lattice structures, and/or the array axes between the layers may be nonparallel. The procedure involves the determination of a global cell with a global coordinate system, then computations of local generalized scattering matrices (GSMs) of individual layers followed by modal mapping from local to global GSMs. The global GSMs for individual layers are then combined to characterize the entire structure. The mapping relations are derived for two layers with different lattice structures, different periodicities, and array-axes orientations. Three examples of practical importance are considered to demonstrate the methodology. The first example is a two-layered patch array with different periodicities. The second example is an array of subarrays with several patch elements within a subarray. It is shown that a subarray can be characterized rigorously by characterizing only one element of a subarray instead of analyzing all the elements of the subarray simultaneously. Consequently, the analytical and computational complexities reduce considerably. The last example is a patch array loaded with a multilayer meander-line polarizer. The patch array and the meander-line array have two different periodicities and the axes are nonparallel. Detailed radiation characteristics of the structure are presented and compared with that of a strip-grid polarizer. The computational advantages of this method are discussed.