Optical third-harmonic generation in one-dimensional photonic crystals and microcavities

The formalism of nonlinear transfer matrices is used to develop a phenomenological model of a cubic nonlinear-optical response of one-dimensional photonic crystals and microcavities. It is shown that third-harmonic generation can be resonantly enhanced by frequency-angular tuning of the fundamental wave to the photonic band-gap edges and the microcavity mode. The positions and amplitudes of third-harmonic resonances at the edges of a photonic band gap strongly depend on the value and sign of the dispersion of refractive indexes of the layers that constitute the photonic crystal. Model calculations elucidate the role played by phase matching and spatial localization of the fundamental and third-harmonic fields inside a photonic crystal as the main mechanisms of enhancement of third-harmonic generation. The experimental spectrum of third-harmonic intensity of a porous silicon microcavity agrees with the calculated results.