Quasi-Periodic Array Modeling Using Reduced Basis From Elemental Array

Quasi-periodic arrays have appeared in many electromagnetic devices, such as reflectarray antennas, metasurfaces, and nanoparticle arrays. In these devices, elements with similar configuration are positioned on a periodic lattice. The entire array is usually a large multiscale structure. Therefore, efficient modeling of quasi-periodic arrays can be very challenging due to the loss of periodicity and the multiscale feature in the array. In this work, based on the similarity among elements, we apply the reduced basis method to integral equation solvers to model wave interaction with quasi-periodic arrays. The matrix equation can be constructed through interpolation instead of matrix assembling as traditional method of moments. A linear transform is used to reduce the sampling in interpolation from two to one dimension. Furthermore, the reduced basis can also be generated from elemental arrays to take the mutual coupling between elements into the basis set. Numerical examples show that both the computation and memory efficiency are improved compared with direct modeling using method of moments.