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We propose the nonlinear Fourier Modal Method (FMM) [J. Opt. Soc. Am. B 31, 2371 (2014)] as a convenient and versatile numerical tool for the design and analysis of grating based next generation all-optical devices. Here, we include several numerical examples where the FMM is used to simulate all-optically tunable functionalities in sub-wavelength periodic structures. At first, we numerically investigate a 1-D periodic nonlinear binary grating with amorphous TiO2. We plot the diffraction efficiency in the transmitted orders against the structure depth for normally incident plane wave. Change in diffraction efficiencies for different incident field amplitudes are evident from the plots. We verify the accuracy of our implementation by comparing our results with the results obtained with the nonlinear Split Field-Finite Difference Time Domain (SF-FDTD) method. Next we repeat the same experiment with vertically standing amorphous Titanium dioxide (TiO2) nanowire arrays grown on top of quartz which are periodic in two mutually perpendicular directions and examine the efficiencies in the direct transmitted light for different incident field amplitudes. Our third example includes analysis of a form birefringent linear grating with Kerr medium. With FMM we demonstrate that the birefringence of such a structure can be tuned by all-optical means. As a final example, we design a narrow band Guided Mode Resonance Filter (GMRF). Numerical experiments based on the nonlinear FMM reveal that the spectral tunability of such a filter can be obtained by all-optical means.This work is partially supported by the Academy of Finland (contract 285880)

Analysis of all-optically tunable functionalities in subwavelength periodic structures by the Fourier modal method.