Fast diffraction computation schema for multilayer crossed gratings containing layers with 1D periodicity

The diffraction computation of crossed gratings is very slow compared with that of line-space gratings of the same size when using a modal method such as rigorous coupled wave analysis (RCWA) or the Chandezon coordinate transformation method. It is well known that the main bottleneck in terms of computation speed is the solution of an eigenproblem for each RCWA slice or interface in the case of the C-method. Even if the crossed grating contains layers that are periodic only in one direction, usually the full 2D problem has to be solved for this layer in order to connect it to the full system solution. In this paper, a computation schema is presented that takes advantage of the 1D periodicity of layers inside a 2D multilayer grating. This results in a considerable acceleration of the formulation and solution of the eigenproblem for these layers. With this new computation schema the total time required for 1D layers in a 2D layer stack can be greatly reduced.