Huge enhancement of backward second-harmonic generation with slow light in photonic crystals

We study theoretically forward and backward second-harmonic generation in a two-dimensional photonic crystal structure made of lithium niobate. The aim of this article is twofold: First, we propose a reliable modal algorithm for describing the light propagation taking into account the vectorial character of the interacting fields as well as the tensorial character of the nonlinearity and verify it by means of the nonlinear finite-difference time-domain method. Second, we propose a photonic crystal where we obtain a giant efficiency increase for backward second-harmonic generation with slow light.