Abstract. We present a numerical method to simulate the third order Kerr effect in wavelength scale dielectric structures. The intensity dependent refractive index is modeled by a spatial grid. By performing iterative linear eigenmode calculations, this index grid converges to the rigorous continuous-wave non-linear solution. Because the underlying eigenmode tool is bidirectional, feedback effects such as bistability can be calculated. We describe the influence of grid size, quantitative agreement with the literature and a photonic crystal switch.