Extreme Optical Field Confinement and Enhancement in a Plasmonic Picopatch within a Nanoparticle-on-Mirror Resonator

Abstract: Plasmonic resonances in metallic nanogaps can confine light into nanometric regions, but reaching modes of volume $\approx 1$ nm$<sup>3$ remains challenging. Here we present a detailed theoretical analysis of the optical modes of a nanoresonator that contains a picopatch formed by the lifting of a few gold atoms in the gap of a Nanoparticle-on-Mirror (NPoM) structure. This configuration is motivated by recent experiments that suggest that local lifting of an atomic monolayer from metallic substrates can occur randomly due to optical or thermal forces. We show through classical simulations that the plasmonic modes associated with the picopatch geometry can confine light to extremely small regions and are highly sensitive to the size and shape of the picopatch, enabling broad tunability. Furthermore, these modes can couple strongly with other nanocavity modes of the structure, as identified by the presence of a clear anti-crossing of the resulting polaritonic resonances. Remarkably, up to $\approx 2000$-fold electric field enhancement in the middle of the picopatch and tiny effective mode volumes that approach $\approx 1$ nm$<sup>3$ are obtained. We also confirm that changing the morphology of the picopatch does not modify the qualitative findings, and verify that increasing the absorption losses in the classical simulations, to mimic quantum (non-local) effects in the metal permittivity, decreases the electric field enhancement only moderately. Compared to the standard picocavities formed by single-atom protrusions, this work shows that picopatches are an intriguing alternative to reach extreme optical field confinement and enhancement in plasmonic cavities.

• The paper demonstrates that integrating plasmonic picopatches into nanoparticle-on-mirror resonators yields over 2000× electric field enhancement and mode volumes as small as ~1 nm³.
• It employs full-wave COMSOL simulations validated by quantum calculations to reveal strong mode hybridization, with coupling strengths up to 80 meV and clear spectral anti-crossing.
• The findings highlight tunable and robust optical confinement, paving the way for applications in ultra-strong plasmon-exciton coupling, SERS, nonlinear optics, and nanophotonic device miniaturization.

Extreme Optical Field Confinement in Plasmonic Picopatches: Analysis of Nanoparticle-on-Mirror Resonators

Introduction

The study provides a comprehensive theoretical investigation into plasmonic picopatches embedded within nanoparticle-on-mirror (NPoM) resonators, focusing on their ability to confine and enhance optical fields at sub-nanometric scales. The work is motivated by experimental evidence suggesting random lifting of atomic monolayers through optical or thermal forces, yielding local geometries—i.e., picopatches—fundamentally distinct from single-atom picocavities. The manuscript systematically characterizes the electromagnetic properties, mode hybridization phenomena, tunability, and robustness of these picopatch structures, employing full-wave classical simulations validated by recent quantum mechanical calculations.

Optical Mode Structure and Dispersion Analysis

The authors begin by embedding the picopatch scenario in the broader context of plasmonic waveguide theory, relating the complex NPoM+pico configurations to laterally infinite Metal-Insulator-Metal (MIM) and Metal-Insulator-Metal-Insulator (MIMI) waveguides. The classical treatment reveals that the picopatch, due to its sub-atomic thickness and lateral dimension ($r_\mathrm{slot}\sim 1$–$2$ nm), supports unique MIMI plasmonic modes. These modes exhibit in-plane wavevectors nearly two orders of magnitude larger than free photons ($q\sim 100k_0$), resulting in extreme light confinement and field localization. The dispersion is corroborated by prior quantum ab-initio calculations, indicating classical theory is sufficient for modeling picopatch plasmonics down to separations of $\sim 0.2$ nm, with only moderate discrepancies in peak broadening due to quantum loss mechanisms.

Nanoresonator Response and Mode Hybridization

Full-wave simulations performed with COMSOL Multiphysics® unveil the optical response of bare NPoM and NPoM structures containing picopatches. For bare NPoM, Fabry-Pérot-like transverse cavity plasmons (TCPs) are resolved, with pronounced maxima in field enhancement ($|E/E_0|\sim 200$) and scattering/absorption spectra, notably the fundamental longitudinal antenna plasmon and multi-order TCPs.

Picopatch incorporation induces strong mode hybridization, especially when the picopatch TCP resonance (e.g., $s'_{01}$) is spectrally aligned with a nanocavity TCP mode (e.g., $S_{01}$). The anti-crossing behavior is evident, and fitting to a coupled harmonic oscillator model yields robust coupling strengths ($g=50$–$80$ meV), surpassing both quarter and half-damping thresholds for strong coupling. The splitting of resonance peaks in scattering and absorption illustrates clear polaritonic hybridization. Importantly, the inclusion of a picopatch, with only $\sim 3.8$ nm$2$0 added geometry, results in an order-of-magnitude enhancement of the local electric field ($2$1).

Extreme Mode Volume and Field Localization

Spatial field distributions demonstrate that the strongest enhancements occur at the picopatch slot, with fields confined within volumes approaching 1 nm$2$2, far below the diffraction limit and comparable to atomic-sized picocavity scenarios. The effective mode volume ($2$3), calculated via both quasi-normal mode integration and Purcell factor extraction, is shown to reach the $2$4–$2$5 nm$2$6 regime for optimal hybrid modes. The picopatch configuration, therefore, provides a geometrically robust alternative to atomic protrusion picocavities for extreme field localization. Fields not only concentrate within the vacuum slot but significantly penetrate into the lifted gold monolayer, supporting hypotheses explaining short-lived fluorescence flares observed experimentally.

Tunability, Robustness, and Practical Considerations

Systematic variation of picopatch parameters (e.g., slot radius $2$7) reveals broad tunability of the hybrid mode wavelength across the visible and near-IR spectrum. The qualitative features—strong hybridization, field enhancement, and small mode volume—are shown to be robust against picopatch morphological changes (e.g., semi-ellipsoidal versus flat geometry), with only minor modifications in coupling strength or enhancement factor. Simulations mimicking increased absorption losses, potentially arising from quantum nonlocal effects, indicate moderate reductions in enhancement but retention of qualitative behavior, maintaining enhancements several times higher than bare NPoM.

Implications and Prospects

This study highlights the transformative potential of plasmonic picopatches in achieving ultra-small mode volumes ($2$8 nm$2$9) and extraordinary electric field enhancements ($q\sim 100k_0$0) in realistic, experimentally-accessible gap configurations. The implications for quantum nanophotonics are significant, including the possibility for ultra-strong plasmon-exciton coupling, highly efficient SERS and SEFS, nonlinear optics, optomechanics, and photonic device miniaturization. Practically, the robust nature of picopatch-induced modes with respect to fabrication uncertainty and quantum losses stresses their feasibility for advanced applications.

In theoretical terms, the strong-coupling regime realized at atomic-scale geometries challenges the boundaries between classical and quantum plasmonics and invites further investigation into quantum loss mechanisms, mode lifetimes, and controllability. The ability to engineer the plasmonic landscape at the level of a few atoms suggests new directions for manipulating light-matter interaction at ultimate limits and for coupling external quantum emitters with optical nanocavities under ambient experimental conditions.

Conclusion

The theoretical analysis demonstrates that NPoM resonators containing picopatches achieve extreme optical confinement and enhancement by hybridizing highly localized MIMI slot modes with nanocavity TCP modes. The resulting field localization reaches effective mode volumes near the atomic scale and enhancement factors exceeding 2000, robust against variations in morphology and increased quantum losses. This geometry broadens the toolkit for nanophotonic device engineering, opening avenues toward atomic-scale optics, quantum plasmonics, and practical devices exploiting the extreme field localization inherent to plasmonic picopatch nanostructures (2605.22780).