Simple model of second-harmonic generation

Toy model of harmonic and sum frequency generation in 2D dielectric nanostructures

Optical nonlinearities of matter are often associated with the response of individual atoms. Here, using a toy oscillator model, we show that in the confined geometry of a two-dimensional dielectric nanoparticle a collective nonlinear response of the atomic array can arise from the Coulomb interactions of the bound optical electrons, even if the individual atoms exhibit no nonlinearity. We determine the multipole contributions to the nonlinear response of nanoparticles and demonstrate that the odd order and even order nonlinear electric dipole moments scale with the area and perimeter of the nanoparticle, respectively.

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.

Goos-Hänchen shifts in harmonic generation from metals

We present the first calculation of the Goos-Hänchen shifts in the context of the nonlinear generation of fields. We specifically concentrate on shifts of second harmonic generated at metallic surfaces. At metallic surfaces the second harmonic primarily arises from discontinuities of the field at surfaces which not only result in large harmonic generation but also in significant Goos-Hänchen shifts of the generated second harmonic. Our results can be extended to other shifts like angular shifts and Fedorov-Imbert shifts.