Rapid analysis of metamaterial structures using the discrete Maxwell;s equation method

We propose a discrete Maxwell equation (DME) method for the rapid analysis of multi-layered metamaterial structures. Different from the conventional numerical methods, which make discretizations within the problem space and use interpolating or iterative technique to obtain the corresponding electromagnetic fields, the DME method is strict in the discretization procedure without any numerical error. The average permittivity and permeability have been used in the DME method, where the spatial dispersion has been considered in details. This method could use very sparse grids in the simulation, which is much more efficient than the conventional numerical methods where 1/10 wavelength for each grid is required. We show that the DME method is particularly valid to the analysis of one-dimensional multi-layered metamaterial structures, where each layer is composed of resonant or nonresonant unit cells. The DME method can greatly reduce the CPU time cost in the multi-layered metamaterial structures, which will find great applications in the microwave and optical metamaterial designs.