Exactly solvable model of surface 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.

Multipolar analysis of the second harmonic generated by dielectric particles

We studied the second harmonic generation (SHG) by two-dimensional dielectric particles made of a centrosymmetric high-index material. The calculated scattered fields at the fundamental and harmonic frequencies are decomposed on a multipolar basis, allowing the evaluation of the relative strengths of the multipolar resonances excited at the particle. With these tools, we studied the strength of the multipoles that produce the second harmonic field and the role played by those excited at the fundamental frequency.

Lorentz Nanoplasmonics for Nonlinear Generation

While past works have suggested that the Lorentz magnetic contribution to second harmonic generation from metal nanostructures is negligible as compared to other terms, here we demonstrate a dominant Lorentz contribution from T-shaped apertures in a gold film. The apertures are designed to have overlapping magnetic and electric near-field intensities at the plasmonic resonance. This gives 65% greater nonlinear generation from the Lorentz term than the sum of the other two terms. We demonstrate this effect experimentally by milling of nanoapertures of different size and orientation in a metal film and measuring their second harmonic generation. Good agreement is seen between the experiments and comprehensive calculations. In the development of highly efficient nonlinear metasurfaces, careful optimization of the Lorentz contribution should be considered in addition to all other contributions. Following the approach of this work, the Lorentz contribution may also be optimized for THz 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.

Second Harmonic Excitation Spectroscopy of Silver Nanoparticle Arrays

Frequency-scanned excitation profiles of coherent second harmonic generation (SHG) were measured for silver nanoparticle arrays prepared by nanosphere lithography. The frequency of the fundamental beam did not coincide with the localized surface plasmon resonance (LSPR) of the nanoparticles and was tuned so that the coherent second harmonic (SH) emission was in the region of the LSPR at 720-750 nm. The SH emission from the arrays was compared with a smooth silver film to identify an enhancement of SH emission efficiency that peaks near approximately 650 nm for nanoparticles 50 nm in height. The polarization and orientation dependence of this enhancement suggests that it is related to a dipolar LSPR mode polarized normal to the plane of the substrate. Linear extinction spectra are dominated by in-plane dipoles and do not show this weak out-of-plane LSPR mode. The nanoparticle arrays are truncated tetrahedrons symmetrically oriented by nanosphere lithography to cancel SH from in-plane dipoles which allows observation of the weak out-of-plane component.

Near-field second-harmonic generation induced by local field enhancement

The field near a sharp metal tip can be strongly enhanced if irradiated with an optical field polarized along the tip axis. We demonstrate that the enhanced field gives rise to local second-harmonic (SH) generation at the tip surface thereby creating a highly confined photon source. A theoretical model for the excitation and emission of SH radiation at the tip is developed and it is found that this source can be represented by a single on-axis oscillating dipole. The model is experimentally verified by imaging the spatial field distribution of strongly focused laser modes.