Effective index method for modelling sub-wavelength two-dimensional periodic structures

An approximate method is here proposed for modelling two-dimensional sub-wavelength periodic structures. The method is based on the effective index method, where the two-dimensional problem structure is split on two one-dimensional problems, which can be solved by conventional tools. It provides in a natural way the biaxial character of a two-dimensional periodic structure with different period along different directions. The method has been tested by comparing the effective refractive index provided by more exact algorithms with the one provided by the effective index method, showing quite good agreement. Also, the EIM has been used to simulate the reflectance and transmittance behaviour of pyramidal profiles, showing also good agreement with the results supplied by exact calculations using RCWA technique. The main advantages of the method are that it is easy to implement, and the short computational time required to model a given structure.