A fast algorithm for modeling quasi-periodic arrays

Many electromagnetic devices, such as metasurfaces, reflectarray antennas, nano particle arrays, can be modeled as quasi-periodic arrays. Simulation of electromagnetic wave interaction with such arrays are very challenging because they are usually large multi-scale models. In this work, we develop a fast algorithm to model quasi-periodic arrays. In this algorithm, we take advantage of the similarities among elements and apply reduced basis method to construct a small basis set for elements. The periodic location of element allows us to apply fast Fourier transform to further accelerate the computation. Numerical example demonstrates that this method has potential in solving larger scale quasi-periodic arrays.