We present an efficient numerical technique to simulate the third order Kerr effect in wavelength scale dielectric structures by expanding upon the eigenmode expansion method. A two-dimensional spatial grid models the intensity dependent refractive index. By performing an iteration of linear eigenmode calculations, this index grid converges to the rigorous continuous-wave nonlinear 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. The differences with other methods, such as finite-difference time-domain and beam propagation method, are discussed. References: 5
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