Second Harmonic Generation in Nanostructured Metamaterials.

The nonlinear dipolar second order third rank susceptibility tensor responsible of second harmonic generation (SHG) vanishes due to selection rules within centrosymmetric media, but a large second order dipolar polarization may be induced within a thin region close to their interfaces [1]. Thus, nanoparticles made up of centrosymmetrical materials could be sources of a large SH signal, given their large surface to volume ratio. For simple geometries which are themselves centrosymmetrical, the strong SH contributions from opposite sides of the particle cancel out, leaving only a multipolar SH signal [2]. The quadrupolar nature of the SH radiated by arrays of nanoparticles has been confirmed experimentally and techniques have been developed to enhance their SH signal [3]. If the geometry is not centrosymmetrical, the surface SH signal may not cancel out when adding contributions all around the particles. To study this case we extend a formalism previously used to efficiently calculate the macroscopic dielectric response of nanostructured metamaterials of arbitrary geometry and composition [4] using Haydock’s recursion. This method yields a set of states which allow the calculation of the microscopic electric field.