2D quasi-periodic array modeling using reduced basis method

Abstract

Planar quasi-periodic arrays are widely used in many electromagnetic devices, such as reflectarray antennas, metasurfaces, nano particle arrays, and etc‥ They can be modeled as elements with geometrical control parameters located at periodic locations. Modeling quasi-periodic arrays are more challenging compared with periodic arrays. The entire array is required during the modeling process due to the difference of each element. Moreover, a quasi-periodic array may include a large number of elements, and each element contains fine details. Therefore the unknown number can be very large when modeling an entire quasi-periodic array, and full wave simulation of the entire array is only suitable in the validation stage but not in the design stage due to its computational complexity. In this paper we apply the reduced basis method (RBM) to integral equation solvers for 2D quasi-periodic array modeling. A new basis set based on the varying control parameters is constructed through an offline process. As the electromagnetic properties of each element changes continuously with the control parameter in certain ranges, the dimension of the final matrix equation can be reduced. Therefore, this method is very suitable in modeling quasi-periodic arrays as the changes of the elements can be parameterized with only a few variables. For a new set of control parameters, the matrix equation of the reduced basis is constructed through an empirical interpolation method (EIM). In order to further accelerate the interpolation of multiple parameters, we propose a new parameter sampling scheme that reduces the searching time for interpolation points. Numerical examples show that both the computational and memory efficiency are improved compared with direct modeling using method of moments.