Abstract
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.
Highlights
The second-order nonlinear interaction of two waves in a medium can generate a third wave at a combinational frequency, underpinning the phenomena of second harmonic generation, optical rectification, parametric down conversion, sum- and difference frequency generation
Second harmonic is generated in crystals with symmetry lacking an inversion centre, centrosymmetric media can generate second harmonic waves in the presence of inhomogeneity associated with interfaces [1,2,3,4,5,6,7,8,9], optical field gradients [9,10,11] or chirality [12]
A considerable effort is focused on artificial nonlinear materials that can be manufactured by top-down nanofabrication processes: second harmonic can be efficiently generated in structured metallic and dielectric films, as well as metasurfaces with asymmetric patterns even if the bulk of the constituent materials is centrosymmetric [13,14,15,16,17,18,19,20,21,22]
Summary
The second-order nonlinear interaction of two waves in a medium can generate a third wave at a combinational frequency, underpinning the phenomena of second harmonic generation, optical rectification, parametric down conversion, sum- and difference frequency generation. A considerable effort is focused on artificial nonlinear materials that can be manufactured by top-down nanofabrication processes: second harmonic can be efficiently generated in structured metallic and dielectric films, as well as metasurfaces with asymmetric patterns even if the bulk of the constituent materials is centrosymmetric [13,14,15,16,17,18,19,20,21,22]. In this paper we report a classical oscillator model that gives rise to second-order nonlinearity in a structured dielectric film made of a centrosymmetric dielectric material. We show that flakes of such structured films can generate second harmonic where nonlinearity emerges from the Coulomb interactions of charges of neighbouring optical electrons and nuclei in the confined anisotropic environment of the flake. The model leads to the following scaling rules: for a particle of a given shape and orientation (relative to the driving field), the first order polarizability is proportional to the particle surface while the second order polarizability is proportional to the particle perimeter
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