A hybrid finite element/rigorous coupled wave analysis for electromagnetic scattering from periodic structures

In this paper, a new hybrid FE/RCWA formulation is presented for the modeling of electromagnetic wave interactions with dielectric structures which are doubly periodic. Employment of Fourier series expansion and Floquet´s theory in one of the periodic dimensions helps to reduce the dimensions of the mesh grids. Therefore, 2D grids are used rather than 3D meshes of the structures of interest. This reduction in turn makes significant savings in computational resources and time as well as the time spent during modeling. For the new FE/RCWA method, the matrix factorization is calculated as NB³ and the matrix storage is calculated as N^2/3B², where B is the number of Fourier expansion terms included for the electric field representation and N is the number of unknowns in the full 3D FEM solution. Even though the value of B depends on the dielectric profile, as a reasonable value it can be related to N as (N^1/3)/5. Therefore the computational cost for matrix factorization and storage are calculated as N²/125 and (N^4/3)/25, respectively. This method is more efficient than a fully 3D FEM approach which has computational costs and storage proportional to N² and N¹⁵, respectively. The results show good agreement with the results of the previous solution techniques.