Vertically confined phase matched second harmonic generation in sub-diffractive planar two-dimensional photonic crystals

Working with narrow beams (with width of few wavelengths) implies mechanisms that are limiting the efficiency of the second harmonic (SH) generation. One of them is diffraction, as narrow beams are broadening over a short propagation distance and their peak intensity decreases. The second one is the phase mismatch, since narrow beams have broad distributions in the wave-vector space and simultaneous phase matching (PM) of all these components is difficult. In addition, in the planar photonic crystals, the out-of-plane losses for both fundamental wave (FW) and SH decrease the efficiency of the nonlinear process. Also, it is needed a good nonlinear coupling of the interacting Bloch modes. Simultaneous optimization of all these conditions is an extraordinary challenge in the design of a photonic crystal.