Phase matched second harmonic generation is observed experimentally in
a centrosymmetric ne crystalline lattice of dielectric spheres of opt
ical dimensions. The inversion symmetry is broken locally at the surfa
ce of each sphere in such a way that the scattered second harmonic lig
ht interferes constructively leading to a nonvanishing macroscopic fie
ld. Phase matching of the fundamental and second harmonic waves in suc
h periodic lattice is observed to be naturally provided by the bending
of the photon dispersion curve at the edge of the Bragg reflection ba
nd of a given set of lattice planes. (C) 1997 American Institute of Ph
ysics.