Mode matching for second-harmonic generation in photonic crystal waveguides

The influence of localized photonic eigenstates on the second-harmonic generation efficiency in planar photonic crystal waveguides is studied with a simple, yet realistic model. We show that $>~{10}^6$ enhancements in the external conversion efficiency in specular reflection can be achieved due to a combination of “generalized phase-matching” and strong local fields in these periodically textured, nonlinear dielectric structures. The second-harmonic response involving the resonant modes of these membranelike photonic crystals is essentially a resonant cavity effect, and hence is strongly influenced by the modal quality factor.