Acceleration of Parameter Studies in the Fourier Modal Method by Introducing Lateral Shift Matrices

The analysis and optimization of the optical properties of nanostructured gratings requires intensive parameter studies. In stacked grating systems, often one grating layer is shifted with respect to the others. We present a way to accelerate such parameter studies in the Fourier modal method by introducing a lateral shift matrix between the grating layers. Thus, we have to calculate each grating layer only once and can apply lateral shifts between the layers with low computational cost. Our formulation is very general and can be also applied when using advanced coordinate transformation methods such as adaptive spatial resolution and matched coordinates.