A fast algorithm for quasi-periodic array modeling using reduced basis method

Planar quasi-periodic arrays are widely used in many electromagnetic devices such as metasurfaces, reflectarray antennas, nano particle arrays, and etc. They constitute similar elements located on periodic grids. Simulation of wave interaction with such arrays are very challenging as they are large multi-scale problems. In this work, we introduce a fast algorithm for quasi-periodic array modeling. This algorithm numerically recovers periodicity using linear current projection and reduced basis method. The reduced basis method can also take advantage of the similarities among elements and reduce the number of unknowns to solve. These two schemes together allow us to recall the power of fast Fourier transform as we solve periodic arrays. The computational complexity of this algorithm is O(N log N) where N is the number of elements in the array. Numerical example shows the potential to solve large scale quasi-periodic arrays.