Modeling nonlinear optical phenomena in nanophotonics

In this paper, we review various numerical methods currently used to model nonlinear optical processes in nanophotonics. Among the different theoretical frameworks that have been used to study nonlinear photonic structures, we particularly focus on the application of both perturbation theory and coupled-mode theory to the analysis of complex nonlinear nanophotonic devices. This description is illustrated on several examples of how these techniques can be used to design photonic-crystal-based nonlinear devices. In addition, in all these examples, we show that. the predictions made by the two mentioned techniques are in a good agreement with the numerical results obtained from a nonlinear finite-difference-time-domain approach to these problems.