A Fast Modeling Algorithm for Quasi-Periodic Array

With the development of electromagnetic theory and microwave engineering, researchers have proposed many novel quasiperiodic arrays to realize various functions in controlling electromagnetic wave propagation. They have similar elements located on the periodic lattices. Full-wave simulation of the quasi-periodic arrays is necessary and challenging, because the whole array is usually electrically large and multiscale. In this communication, we study a fast algorithm for the full-wave modeling of the quasi-periodic arrays. It constructs a reduced basis set based on the geometric similarities among the array elements. Then, we use linear projection to “recover” periodicity numerically so that the fast Fourier transform can be used to accelerate the computation of the whole array. The computational complexity of this algorithm is O(NlogN), where N is the number of elements in the array. Numerical examples verify its potential in solving large-scale quasi-periodic arrays.