Second Harmonic Scattering from Sites of a Crystalline Lattice

Experimental evidence of second harmonic generation in a macroscopically centrosymmetric lattice formed by spherical particles of optical dimensions is presented. Second harmonic light is scattered from the surface of these spherical particles. A simple theoretical model based on scattering in the Rayleigh-Gans approximation indicates constructive interference of light scattered at the second harmonic frequency leads to a plane wave front propagating in the direction of the incident beam. The implications of the addition of defects in a controlled manner will be discussed in the framework of the photonic band gap theory. Along these lines we will discuss in detail the simple case of a truncated periodic lattice in one dimension. We will present additional experimental results showing enhancement and suppression of the radiation of a dipole sheet oscillating at the second harmonic frequency embedded in a 1-dimensional periodic structure with a defect.