Fast modeling of volume gratings by Fourier modal method

Simulating diffraction of light by volume gratings leads to several problems. The large periodicities in lateral direction and the large number of repetitions of the lattice in perpendicular direction. For thick hologram gratings that are at the Bragg condition, Herwig Kogelnik developed a theory that uses two diffraction orders. We showed that his theory is equivalent to a calculation with the Fourier Modal Method (FMM) restricted to two diffraction orders. In contrast to Kogelnik's theory the approximated FMM allows for a gradually increase of the accuracy by taking more diffraction orders into account if they are needed for accuracy. This allows for a simulation of gratings with large lateral period. For the large number of repetitions of the lattice in perpendicular direction, we calculate the scattering matrix of one repetition. From this matrix, we calculate the total scattering matrix for the actual number of repetitions in the grating.