Analysis of multilayer array structures with different cell size and axes orientations

We present a general analysis of multilayer structures. The analysis accommodates different cell sizes of the layers, including angular rotations. We first find the global unit cell dimensions, which is equal to the lowest common multiple of the cell dimensions of the layers. We then find the generalized scattering matrix (GSM) of the individual layers with respect to the global unit cell. Construction of the global GSM for each layer is necessary in order to apply the GSM cascading rule for analyzing a multilayer structure. It is found that a set of local GSM (GSM with local unit cell and local coordinate system of an individual layer) can be used to construct the global GSM for that layer. The mode numbers (Floquet mode indices), however, will be different for the two different cells. Therefore, if one could find a mapping relation between the mode number associated with a local cell and a global cell, then one can construct the global GSM for the layer using the local GSM elements. We have established such mapping relations for different cases. To find a local GSM of an individual layer, we use Floquet modal analysis and Galerkin´s method of moments. Once we find the global GSM for all the individual layers, we can find the overall GSM of the structure. Three examples illustrate the analysis method and verify the accuracy