Near-field enhancement by a metasurface at octupole plasmon resonance in periodic disc dimers

TL;DR

The paper addresses near-field enhancement in plasmonic metasurfaces by leveraging higher-order multipole resonances, focusing on octupole excitations coupled to surface-lattice resonances in a periodic gold-disc dimer array. It develops an analytical framework based on the scattering-current multipole expansion to derive effective dipole and octupole polarizabilities, and introduces a practical numerical method (validated with COMSOL) to extract these polarizabilities for single particles and arrays. The key finding is that, as the array period decreases, the dipole polarizability vanishes while the octupole polarizability grows, enabling exceptionally strong, densely packed hot spots at the octupole resonance in the visible range, especially when hybridized with lattice modes. The work demonstrates, both analytically and numerically, that higher-order multipoles in periodic plasmonic structures can be harnessed for enhanced sensing, spectroscopy, and nonlinear applications, and points to future explorations of alternative shapes, unit cells, and waveguide integration to further exploit these resonances.

Abstract

Local intensity enhancement by plasmonic nanoparticles is widely used in optics and photonics. However, the effect is usually based on dipole resonances in the particles. Recently, it has been shown that quadrupole and octupole resonances can exhibit comparable, or even higher near-field enhancement. In this work, we focus on the near-field enhancement by a metasurface composed of gold-disc dimers arranged in a rectangular array. We find that, owing to an octupole plasmon resonance coupled to a surface lattice resonance, exceptionally high near-field enhancement in the dimer gaps can be achieved in the visible spectral range. To gain insight into the effect, we develop an analytical model for the effective dipole and octupole polarizabilities of the particles in an array, and discover, that at decreasing array periods, the dipole polarizability tends to vanish, while the octupole polarizability rapidly increases. Hence, octupole resonances can find applications in high-density arrays of plasmonic resonators. We propose a method to numerically evaluate multipole polarizabilities of a single particle, applying it to the gold dimer that we consider. The influence of the array on the effective polarizabilities is then verified by numerical calculations and a good agreement is obtained. Our results may open new avenues for investigating the properties of periodic plasmonic structures based on higher-order multipole resonances and their applications.

Figures (9)

• Figure 1: (a) The spectrum of the scattering cross section $C_s$ (red line) of a gold disc dimer shown in the inset. The contribution to $C_s$ of the electric dipole, electric quadrupole, electric octupole, magnetic dipole, and magnetic quadrupole are shown by the blue, black, magenta, brown, and green lines, respectively. (b) Intensity enhancement factor (solid black line) and scattering current density (red dashed line). (c) The squared absolute values of the dipole (blue line) and octupole (red line) current densities in the dimer. The red dashed line marks the wavelength of 672 nm.
• Figure 2: The spectra of the numerically calculated polarizabilities (a) $\alpha_x$, (b) $\gamma_{xxx}$, and (c) $\gamma^{\text{(iii)}}_{xxx}$ for the considered dimer. The blue and red lines represent the real and imaginary parts of the polarizabilties, respectively. The inset in (c) shows the illumination of the dimer by two interfering plane waves for calculating $\gamma^{\text{(iii)}}_{xxx}$. The vertical dashed black line marks the wavelength of 672 nm.
• Figure 3: (a) Point scatterers (red dots) in an infinite periodic array. The dashed lines show schematically the fields scattered by the particles. (b) The magnitude of the effective dipole polarizability ($\tilde{\alpha}_x$; blue line) at $\lambda$ = 1184 nm and the sum $\tilde{\alpha}_x+2\tilde{\gamma}_{xxx}/x_\text{e}^2$ (red line) at $\lambda$ = 672 nm.
• Figure 4: The interaction geometry of the considered gold-dimer metasurface with an incident $x$-polarized plane wave.
• Figure 5: (a) The spectra of the near-field intensity enhancement factor (solid black line) and the squared absolute value of the normalized current density (dashed red line) calculated for a dimer in an optimized array. The inset shows the electric field amplitude distribution at the peak wavelength of 692 nm. (b) The total scattering cross section (red line) of a dimer in the array and the contributions to it from the constituent multipoles (blue, black, magenta, brown, and green lines corresponding to the electric dipole, electric quadrupole, electric octupole, magnetic dipole, and magnetic quadrupole). (c) The squared absolute value of the dipole (blue line) and octupole (red line) contributions to the scattering current density. The dashed line marks the wavelength of 672 nm.