Second harmonic generation in a photonic crystal

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Abstract
Phase matched second harmonic generation is observed experimentally in a centrosymmetric crystalline lattice of dielectric spheres of optical dimensions. The inversion symmetry is broken locally at the surface of each sphere in such a way that the scattered second harmonic light interferes constructively leading to a nonvanishing macroscopic field. Phase matching of the fundamental and second harmonic waves in such periodic lattice is observed to be naturally provided by the bending of the photon dispersion curve at the edge of the Bragg reflection band of a given set of lattice planes.