Plasmonic and photonic crystal applications of a vector solver for 2D Kerr nonlinear waveguides

We use our vector Maxwell's nonlinear eigenmode solver to study the stationary solutions in 2D cross-section waveguides with Kerr nonlinear cores. This solver is based on the fixed power algorithm within the finite element method. First, studying nonlinear plasmonic slot waveguides, we demonstrate that, even in the low power regime, 1D studies may not provide accurate and meaningfull results compared to 2D ones. Second, we study at high powers the link between the nonlinear parameter $\gamma_{nl}$ and the change of the nonlinear propagation constant $\Delta \beta$. Third, for a specific type of photonic crystal fiber, we show that a non-trivial interplay between the band-gap edge and the nonlinearity takes place.