Toy model of second harmonic generation due to structuring of centrosymmetric films

We show how structuring of matter can lead to second order optical nonlinearity. Coulomb interactions involving bound electrons cause a nonlinear optical response at boundaries. We demonstrate that second order nonlinearity is proportional to the perimeter of a planar structure cut from a centrosymmetric lattice of harmonic oscillators. This proportionality and our model can instruct the design of dielectric nonlinear particles, surfaces and metamaterials for optical second harmonic generation.