Resonant second-harmonic generation in a GaAs photonic crystal waveguide

Second-harmonic generation (SHG) measurements in reflection on a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.25}{\mathrm{Ga}}_{0.75}\mathrm{As}$ photonic crystal waveguide show a resonant enhancement when the pump beam is frequency and momentum matched with the photonic modes in the slab. The enhanced SH signal is observed in the form of resonant peaks, unlike in linear reflectance spectra. The observations are in very good agreement with a full 3D calculation of the anisotropic mode dispersion in the photonic crystal slab. The present results open the way towards realizing the extraordinary enhancement of SHG which was recently predicted [A. R. Cowan and J. F. Young, Phys. Rev. B $65,$ 085106 (2002)], and also demonstrate the potential of SHG as a nonlinear spectroscopic tool for optical studies of photonic crystals.