Numerical Modeling of Metamaterial and Metasurface with Media Homogenization

Metamaterial and its 2D variation, i.e., metasurface exhibit unprecedent electromagnetic functions which are not practical for the materials from the nature. This advantage is mainly attributed to the more precise arrangement of the sub-wavelength scatters in an array fashion. However, the metamaterial and the metasurface are typical multiscale structures, with possible fine geometries inside each of the cells and the large size of total array. This multiscale characteristic poses challenges for the design of the corresponding numerical algorithms. In the computational electromagnetic community, periodic boundary condition is usually adopted as a powerful tool for the fast simulation of the metamaterial and metasurface, because only one unit cell is required to be simulated. This assumption is widely accepted even though the edge effect of the array is neglected. However, when the array is composed non-uniform arranged cells of different types, such as the coding metamaterial (metasurface) and the phased array, the periodic boundary condition is no longer valid. Consequently, the entire array is usually s in a violent way, e. g., all of the cells are meshed to form a system of matrices with large quantity of unknowns. Even if equipped with advanced acceleration techniques, it still consumes long simulation time and memory which hinders the rapid performance evaluation and iterative optimization.