Formulation of the normal vector RCWA for symmetric crossed gratings in symmetric mountings

The utilization of symmetries in rigorous coupled wave analysis in order to reduce the matrix sizes and thus the computation time is an appropriate measure for an effective numerical implementation with no loss of accuracy. Another method to improve the convergence is the so-called normal vector method. This method is based on the transformation of the components of the electromagnetic fields in a lateral plane (or slice) from global coordinates into local normal and tangential coordinates relative to the boundaries between two different materials. In this way, the lateral boundary conditions of the electromagnetic field can be imposed more correctly as opposed to the traditional approximation introduced by Li, resulting in a better convergence in many cases. This paper shows how both methods can be combined to attain an optimum solution.