Second harmonic generation is one of the fundamental nonlinear optical processes that is at the heart of communication and sensing applications. Due to the underlying crystal symmetry, second harmonic generation in noble metal-nanostructures is dominated by metal/dielectric interfaces with only weak (magneto-dipole and quadrupolar) contributions coming from the bulk of the metal inclusions. Here we demonstrate that, in metamaterials, nonlinear contributions from individual plasmonic inclusions can add up together, resulting in the bulk nonlinear polarization. The resulting nonlinear response can be described in terms of volumetric second harmonic polarizability that relates unit-cell averaged nonlinear polarization to a product of unit-cell averaged fundamental fields. The amplitude of this effective nonlinear polarizability is comparable to that of common nonlinear crystals.
In order to analyze nonlinear response of the plasmonic nanowire arrays we compare experimental results to numerical solutions of Maxwell equations where second harmonic response is calculated using nonlinear hydrodynamic model. Numerical solutions of Maxwell equations are also used to analyze the spatial and spectral distributions of fundamental and nonlinear fields across the composites and, in the end, to guide and validate the development of analytical description of effective second harmonic polarizability. The developed analytical description of the second harmonic generation in plasmonic composites opens new avenues for engineering of nonlinear response.
Plasmonic nanowire metamaterials, arrays of aligned plasmonic nanowires grown inside an insulating substrate, have recently emerged as a flexible platform for engineering refraction, diffraction, and density of photonic states, as well as for applications in bio- and acoustic sensing. Majority of unique optical phenomena associated with nanowire metamaterials have been linked to the collective excitation of cylindrical surface plasmons propagating on individual nanowires. From the effective medium standpoint, this collective excitation can be described as an additional electromagnetic wave, emanating from nonlocal effective permittivity of metamaterial. The electromagnetic fields associated with such mode can are strongly inhomogeneous on the scale of the unit cell.
In this work we analyze the effect of the strong field variation inside nanowire metamaterial on second harmonic generation (SHG). We show that second harmonic generation is strongly enhanced in the frequency region where metamaterial is nonlocal. Overall, the composite is predicted to outperform its homogeneous metal counterparts by several orders of magnitude. Quantitative description of SHG in nanowire medium is developed. The results suggest that bulk second harmonic polarizability emerges as result of collective surface-enhanced SHG by individual components of the composite.
Hyperbolic plasmonic metamaterials provide numerous opportunities for designing unusual linear and nonlinear optical properties. Here we report a full vectorial numerical model to study SHG in a plasmonic nanorod metamaterial slab. Our frequency-domain implementation of the hydrodynamic model of the metal permittivity for conduction electrons provided a full description of the nonlinear susceptibility in a broad spectral range. We show that the modal overlap of fundamental and second-harmonic light in the plasmonic metamaterial slab results in the frequency tuneable enhancement of radiated second-harmonic intensity by up to 2 orders of magnitudes for TM- and TE-polarized fundamental light, compared to a smooth Au film under TM-polarised illumination. A double-resonant condition with both the enhancement of fundamental field and the enhanced scattering of the second-harmonic field can be realised at multiple frequencies due to the mode structure of the metamaterial slab. The nanostructured geometry of the Au nanorod metamaterial provides a larger surface area compared to the centrosymmetric crystal lattice of gold, which is needed for exploiting the intrinsic surface nonlinearity of gold. The numerical model allows us to explain experimental investigations on the spectral behaviour and radiation diagram of the second harmonic signal. In the experiments SHG generated under femtosecond excitation with varying wavelength, polarization, and angle of incidence, was characterized in backward and forward directions. We show that the excitation of plasmonic modes in the array can remarkably enhance the nonlinear response of the system, as predicted by the model. The results open up wide ranging possibilities to design tuneable frequency-doubling metamaterial with the goal to overcome limitations associated with classical phase matching conditions in thick nonlinear crystals.
We designed cylindrical AlGaAs-on-aluminium-oxide all-dielectric nanoantennas with magnetic dipole resonance at near-infrared wavelengths. Our choice of material system offers a few crucial advantages with respect to the silicon-oninsulator platform for operation around 1.55μm wavelength: absence of two-photon absorption, high χ<sup>(2)</sup> nonlinearity, and the perspective of a monolithic integration with a laser. We analyzed volume second-harmonic generation associated to a magnetic dipole resonance in these nanoantennas, and we predict a conversion efficiency exceeding 10<sup>-3</sup> with 1GW/cm<sup>2</sup> of pump intensity.