Charge reservoir as a design concept for plasmonic antennas

TL;DR

This study interrogates whether increasing the charge reservoir in plasmonic antennas—via larger cross-sections—enhances the electromagnetic response when the resonance energy and end-curvature are held fixed. Using a combination of focused-ion-beam fabricated gold PAs, electron energy loss spectroscopy, and boundary-element method simulations, the authors show that larger reservoirs primarily boost radiative losses, which suppress near-field enhancement, even as the total plasmon charge scales with PA volume. The analysis of optical response functions indicates that only the scattering cross-section benefits from a bigger reservoir, while the plane-wave excited near-field is only partially enhanced and spectral integrals remain largely unchanged. These findings suggest using the charge reservoir concept to optimize coupling to radiative channels rather than to maximize local field intensities, informing design strategies for plasmonic antennas with targeted radiative properties.

Abstract

Plasmonic antennas exploit localized surface plasmons to shape, confine, and enhance electromagnetic fields with subwavelength resolution. The field enhancement is contributed to by various effects, such as the inherent surface localization of plasmons or the plasmonic lightning-rod effect. Inspired by nanofocusing observed for propagating plasmons, we test the hypothesis that plasmonic antennas with a large cross-section represent a large charge reservoir, enabling large induced charge and field enhancement. Our study reveals that a large charge reservoir is accompanied by large radiative losses, which are the dominant factor, resulting in a low field enhancement.

Figures (9)

• Figure 1: (a) A scheme of a dipole LSPR supported by a plasmonic nanorod. The current is represented by the black arrow, thickened in the central part of the PA to mark the antinode of the current wave. The antinodes of the induced charge at the peripheral parts of the PA are labeled by $+$ and $-$ symbols. (b) Conceptual explanation of the charge reservoir. From left to right, the cross-section of PAs decreases, resulting in expectedly lower magnitudes of induced charge (represented by decreased size of $+$ and $-$ symbols). (c) The design of the study. From left to right, a diamond PA is transformed through a tapered-diamond PA into a nanorod PA and then to a dumbbell PA by a sequential thinning of the central part, accompanied by a reduction in the charge reservoir. The black circles at the peripheral part of all PAs demonstrate that the radius of curvature is preserved for all PAs. (d) Two sets of PAs not suitable for studying the charge reservoir effect. Top: The nanorods of different widths also differ in the radius of curvature. Bottom: Three bowtie PAs (full, contour, and fractal) differ in the charge oscillation patterns.
• Figure 2: EELS of a set of PAs with a length $L=300$ nm, a radius $R=50$ nm, and widths $W$ between 300 nm and 40 nm. (a) HAADF STEM image of two PAs with the widths $W=300$ nm and 40 nm. (b) Experimental loss function spectra for PAs with widths $W$ of 40 nm (golden line, dumbbell shape), 100 nm (salmon line, rod shape), 183 nm (maroon line, tapered diamond shape), and 300 nm (indigo line, symmetric diamond shape). The insets above the spectra also indicate the correspondence between the spectra and the shapes. The spectra were averaged over the electron beam positions corresponding to a square next to the left edge of the PA, as schematically indicated in the right inset. (c) Experimental loss function maps recorded for PAs from panel a for the loss energy corresponding to the dipole LSPR (represented by a peak in the corresponding spectra in panel b between 1.0 and 1.4 eV). (d) Theoretical loss function spectra analogous to panel b. The electron beam position, 20 nm from the left edge of PAs, is indicated in the right inset. The dashed lines represent raw simulated spectra, the solid lines show the spectra convolved with a Gaussian with a full width at half maximum (FWHM) of 0.15 eV representing the instrumental broadening of our EELS setup. (e) Theoretical loss function maps analogous to panel c.
• Figure 3: Calculated magnitude of the induced electric field of PAs illuminated with a plane wave at the energy of the dipole LSPR (1.2 eV). (a) A planar cross-section in the middle of the PA height for PAs with the widths of 385 nm (indigo line, symmetric diamond shape), 204 nm (maroon line, tapered diamond shape), 100 nm (salmon line, rod shape), and 40 nm (golden line, dumbbell shape). (b) A linear cross-section along the long axis of PAs (indicated in the inset) for the same PAs as in panel a. The distance from the PA edge is labeled $x$. (c) The magnitude of the field at a distance of 25 nm from the PA edge (blue) or averaged over a cube with a side of 50 nm centered at a distance of 25 nm from the PA edge (green). The fields are normalized to the amplitude of the incident plane wave. The inset shows the position/area where the field is evaluated. The symbols in panel c corresponding to the PAs included in panel b are enlarged and displayed using corresponding colors.
• Figure 4: Calculated optical response of a set of PAs with a length adjusted for the energy of the dipole LSPR of 1.2 eV, a radius $R=50$ nm, and widths $W$ between 385 nm and 40 nm. (a) Absorption cross-section for PAs with widths $W$ of 40 nm (golden line, dumbbell shape), 100 nm (salmon line, rod shape), 204 nm (maroon line, tapered diamond shape), and 385 nm (indigo line, symmetric diamond shape). The insets on the right side of the spectra also indicate the correspondence between the spectra and the shapes. (b) Scattering cross-section for the same set of PAs. (c) Q factor. (d) Integral absorption cross-section (IACS). The symbols in panels c and d corresponding to the PAs included in panels a and b are enlarged and displayed using corresponding colors.
• Figure 5: Total charge (in units of $10^8$ elementary charges) involved in plasmon oscillations according to the generalized harmonic oscillator model Kats:11 as a function of the PA width (left) and the PA volume (right) for sets of PAs with the dipole LSPR energy fixed at 1.2 eV (red symbols), 0.8 eV (blue symbols), and 1.7 eV (green symbols).