Homogenization and Scattering Analysis of Second-Harmonic Generation in Nonlinear Metasurfaces

We propose an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) which are used to model the electromagnetic responses of nonlinear metasurfaces. The GSTCs are solved both in the frequency domain, assuming an undepleted pump regime, and in the time-domain, assuming dispersionless material properties but a possible depleted pump regime. Based on these two modeling approaches, we derive the general second-harmonic reflectionless and transmissionless conditions as well as the conditions of asymmetric reflection and transmission. We also discuss and clarify the concept of nonreciprocal scattering pertaining to nonlinear metasurfaces

Ultrasensitive Optical Shape Characterization of Gold Nanoantennas Using Second Harmonic Generation

Second harmonic generation from plasmonic nanoantennas is investigated numerically using a surface integral formulation for the calculation of both the fundamental and the second harmonic electric field. The comparison between a realistic and an idealized gold nanoantenna shows that second harmonic generation is extremely sensitive to asymmetry in the nanostructure shape even in cases where the linear response is barely modified. Interestingly, minute geometry asymmetry and surface roughness are clearly revealed by far-field analysis, demonstrating that second harmonic generation is a promising tool for the sensitive optical characterization of plasmonic nanostructures. Furthermore, defects located where the linear field is strong (e.g., in the antenna gap) do not necessarily have the strongest impact on the second harmonic signal

Detecting the trapping of small metal nanoparticles in the gap of nanoantennas with optical second harmonic generation

The second harmonic generation from gold nanoparticles trapped into realistic and idealized gold nanoantennas is numerically investigated using a surface integral equations technique. It is observed that the presence of a nanoparticle in the nanoantenna gap dramatically modifies the second harmonic intensity scattered into the far-field. These results clearly demonstrate that second harmonic generation is a promising alternative to the conventional linear optical methods for the detection of trapping events at the nanoscale

Mode Coupling in Plasmonic Heterodimers Probed with Electron Energy Loss Spectroscopy

While plasmonic antennas composed of building blocks made of the same material have been thoroughly studied, recent investigations have highlighted the unique opportunities enabled by making compositionally asymmetric plasmonic systems. So far, mainly heterostructures composed of nanospheres and nanodiscs have been investigated, revealing opportunities for the design of Fano resonant nanostructures, directional scattering, sensing and catalytic applications. In this article, an improved fabrication method is reported that enables precise tuning of the heterodimer geometry, with interparticle distances made down to a few nanometers between Au–Ag and Au–Al nanoparticles. A wide range of mode energy detuning and coupling conditions are observed by near field hyperspectral imaging performed with electron energy loss spectroscopy, supported by full wave analysis numerical simulations. These results provide direct insights into the mode hybridization of plasmonic heterodimers, pointing out the influence of each dimer constituent in the overall electromagnetic response. By relating the coupling of nondipolar modes and plasmon–interband interaction with the dimer geometry, this work facilitates the development of plasmonic heterostructures with tailored responses, beyond the possibilities offered by homodimers

Universal scaling of plasmon coupling in metal nanostructures: Checking the validity for higher plasmonic modes using second harmonic generation

The universal scaling of plasmon coupling in metallic nanostructures is now a well-established feature. However, if the interaction between dipolar plasmon modes has been intensively studied, this is not the case of the coupling between higher order ones. Using Mie theory extended to second harmonic generation, we investigate the coupling between quadrupolar plasmon modes in metallic nanoshells. Like in the case of dipolar plasmon modes, a universal scaling behavior is observed in agreement with the plasmon hybridization model

Revealing a Mode Interplay That Controls Second-Harmonic Radiation in Gold Nanoantennas

In this work, we investigate the generation of second- harmonic light by gold nanorods and demonstrate that the collected nonlinear intensity depends upon a phase interplay between di ff erent modes available in the nanostructure. By recording the backward and forward emitted second-harmonic signals from nanorods with various lengths, we fi nd that the maximum nonlinear signal emitted in the forward and backward directions is not obtained for the same nanorod length. We con fi rm the experimental results with the help of full-wave computations done with a surface integral equation method. These observations are explained by the multipolar nature of the second- harmonic emission, which emphasizes the role played by the relative phase between the second-harmonic modes. Our fi ndings are of particular importance for the design of plasmonic nanostructures with controllable nonlinear emission and nonlinear plasmonic sensors as well as for the coherent control of harmonic generations in plasmonic nanostructure

Second harmonic scattering from silver nanocubes

The second harmonic light scattered from silver nanocubes dispersed in an aqueous suspension is investigated. The first hyperpolarizability is determined and corrected for resonance enhancement. It is shown to be similar to that of silver nanospheres with a comparable volume. The polarization-resolved analysis of the scattered harmonic intensity exhibits a surface response strongly modulated by the different multipolar field contributions. As a result, the shape does not play a leading role anymore for nanoparticles with a centrosymmetric shape when retardation must be considered. Comparing the right angle and forward-scattered polarized intensity responses, the unequal balance of the eight nanocube corners' contribution to the total response is revealed despite the high degree of centrosymmetry of the cubic shape. It is then demonstrated with a simple model that the nanocubes' first hyperpolarizability exhibits an octupolar tensorial symmetry. The surface integral equation method calculations are finally provided to investigate further the role of the corners’ and edges’ rounding