|
Metal nanoparticles demonstrate unique optical properties that are mostly due to localized surface plasmon resonances (LSPRs). In addition, when nanoparticles are arranged in arrays (metasurfaces), their responses can be modified by the presence of the neighboring particles. As a result, sharp spectral features can be observed. Such features, called surface lattice resonances (SLRs), are related to the appearance of diffraction orders in the optical response. Both types of resonances can lead to local-field enhancement and thereby boost nonlinear optical effects. For the particular case of second-harmonic generation (SHG) the sample needs to be also non-centrosymmetric. This condition is fulfilled when, for example, V-shaped nanoparticles are used in the array. Increasing the number of particles typically increases the optical density, which should increase the nonlinear response with the square of the particle density. This approach, however, has its limitations because, when the particles are too close to each other, the quality of the LSPRs decreases leading to an effect opposite to the desired. Here, we will show the counterintuitive effect that the nonlinear response can be enhanced by reducing the number of particles in the array.
In order to verify our idea, we use two arrays of V-shaped gold nanoparticles fabricated on a glass substrate by electron-beam lithography and lift-off methods. The particles are distributed in 500 x 500 nm2 square arrays in two configurations: i) all lattice points are filled with particles (V1) or ii) every other particle in the lattice is removed in a way that the remaining particles form a rotated (by 45°) square array with a pitch of 707 nm (V2). Both samples have two eigenpolarizations: one along the symmetry axis (y) of the V shape and other in the perpendicular direction (x).
In the SHG experiments, the incident beam from an optical parametric oscillator was incident on the sample. Polarizers and a half-wave plate were used to control the polarization of the fundamental (1000 – 1300 nm) and second-harmonic beams. The SHG signal was collected by a photon counting system.
The sample V2, that has reduced (by a factor of 2) density of particles in the array, shows the expected decrease in the strength of the resonance peak (1151 nm) and a slight redshift of the resonance wavelength with respect to the sample V1 (1081 nm). In order to achieve fair comparison of the nonlinear signals, we tuned the incident wavelength to the position of approximately equal losses for both samples (1135 nm). The sample V2 is found to have, by a factor of 7, stronger response than sample V1. Such enhancement in the nonlinearity is related to the improvement in the quality of the resonance for sample V2, for which the width of the resonance is reduced by ~30% compared to V1. This is due to SLRs that are present for sample V2. Our results are in good agreement with calculations by using an approach based on the discrete-dipole approximation.
|
