Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal

We investigate efficient fourth-harmonic generation in a single two-dimensional (2D) quadratically nonlinear photonic crystal. We propose a novel parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmonic wave that is collinear to the fundamental. We show that this process is more efficient than conventional fourth-harmonic-generation schemes by a factor that reaches 4 at low intensities and discuss how to design and optimize the nonlinear 2D photonic crystals that are implemented in LiNbO₃ and LiTaO₃.