Second harmonic generation in planar two-dimensional photonic crystals without out-of-plane losses

We are making a study of the out-of-plane losses for the second harmonic generation process in planar two-dimensional photonic crystals made from Al_0.3Ga_0.7As. We found that for the rhombic symmetry of the lattice it can be obtained a structure in which the out-of-plane losses vanish for both fundamental and second harmonic waves in conditions of very small diffraction for the second harmonic wave and a diffraction close to the one obtained in homogeneous medium for the fundamental wave.