Probing individual phonon-polaritonic nanoparticle-on-mirror cavities by infrared nanospectroscopy

Abstract: Nanoparticle-on-mirror (NPoM) cavities enable extreme light confinement and strong light-matter interactions, but their realization with phonon-polariton materials in the mid-infrared spectral range remains largely unexplored. Here, we use nano-FTIR spectroscopy to study the near-field response of individual phononic NPoM cavities formed by gold nanoparticles on a quartz substrate supporting phonon-polaritons. By placing a metal tip on top of the NPoM and recording the tip-scattered field, we observe two reproducible cavity resonances, identified as the fundamental and a second-order antenna modes by numerical simulations. The calculations show that, in absence of the tip, the NPoM cavity exhibits ultrasmall mode volumes ($V \sim 10<sup>3$ nm$<sup>3$) and high quality factors ($Q \sim 100$), resulting in extraordinary field intensity enhancements ($F \sim 10<sup>4$) and Purcell factors ($P_F \sim 10<sup>9$). They also indicate that the nano-FTIR tip enables efficient excitation and readout of these phononic NPoM modes without perturbing them, while enhancing the intrinsic local field intensity in the NPoM gap by two orders of magnitude. Our results establish phononic NPoM cavities as a promising platform for mid-infrared nanophotonics and pave the way for ultrasensitive vibrational spectroscopy based on nano-FTIR measurements of individual cavities.

• The paper demonstrates the first nano-FTIR measurements of individual phonon-polaritonic nanoparticle-on-mirror cavities, resolving reproducible L₀₁ and L₀₂ modes in single 60 nm gold nanoparticles on quartz.
• Simulations estimate ultrasmall mode volumes of roughly 700–1,500 nm³, quality factors of 80–110, and Purcell factors approaching 7.3 × 10⁹, exceeding typical visible plasmonic NPoM performance.
• The nano-FTIR tip enhances gap intensity to approximately 7 × 10⁷ without significantly shifting, broadening, or spatially perturbing the cavity modes, enabling local infrared spectroscopy of ultrathin molecular layers.

Overview

This paper reports the first nano-FTIR spectroscopy of individual phonon-polaritonic nanoparticle-on-mirror (NPoM) cavities, formed by colloidal gold nanoparticles (AuNPs) drop-cast onto a c-cut quartz substrate that acts as a phonon-polaritonic mirror (2607.07941). Whereas conventional NPoM research has focused on plasmonic gaps in the visible, and prior mid-infrared phononic NPoM work on Ag nanocubes on SiC was restricted to ensemble measurements due to vanishingly small extinction cross-sections, this work demonstrates that an AFM-based nano-FTIR tip can excite and read out the cavity modes of a single phononic NPoM without perturbing them — while simultaneously boosting the gap field intensity by roughly two orders of magnitude.

Experimental approach

The NPoM geometry exploits the Reststrahlen band of quartz between its two transverse optical phonons at $\nu_{TO,1} = 1065\ \text{cm}^{-1}$ and $\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$, where $\operatorname{Re}\{\varepsilon_\perp\} < 0$ and supports surface phonon polaritons (SPhPs). The in-plane dielectric function is extracted from far-field reflectivity using a double Lorentz oscillator model; the authors deliberately restrict analysis to the monotonic portion of $\operatorname{Re}\{\varepsilon_\perp\}$ below $\nu_{TO,2}$, since its non-monotonic behavior near the second phonon complicates mode assignment. The ~1 nm citrate capping layer on the AuNPs defines the nanogap, and quartz's ability to be polished to sub-nanometer roughness is essential for achieving ultrasmall mode volumes comparable to plasmonic NPoMs.

Nano-FTIR spectra are acquired by positioning a PtIr tip (50 nm apex radius) atop individual 60 nm AuNPs, demodulating at higher harmonics ($n = 3, 4$) for background suppression, and normalizing to gold. Three independent particles show reproducible two-peak spectra at approximately 1090 cm$^{-1}$ and 1140 cm$^{-1}$. Control measurements — tip in contact with bare quartz, and tip retracted by 60 nm reconstructed from QCL retraction curves — yield only single broad peaks, confirming that the two peaks originate from the nanoparticle rather than direct tip–quartz coupling.

Mode identification and cavity figures of merit

Finite-element simulations reproduce the two resonances and identify them via near-field distributions and surface charge patterns as the fundamental longitudinal antenna mode L$_{01}$ (single azimuthal maximum, 1110 cm$^{-1}$ without tip) and a second-order axially symmetric mode L$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$0 (two concentric maxima, 1130 cm$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$1). The extracted cavity parameters are notable:

Mode	$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$2 (nm$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$3)	$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$4	$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$5	$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$6
L$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$7	~1300–1500	~$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$8	~80	$\nu_{TO,2} = 1160.7\ \text{cm}^{-1}$9
L$\operatorname{Re}\{\varepsilon_\perp\} < 0$0	~700	~$\operatorname{Re}\{\varepsilon_\perp\} < 0$1	~96–110	$\operatorname{Re}\{\varepsilon_\perp\} < 0$2

These quality factors exceed those of visible-range plasmonic NPoMs ($\operatorname{Re}\{\varepsilon_\perp\} < 0$3) at comparable normalized mode volumes, yielding Purcell factors around $\operatorname{Re}\{\varepsilon_\perp\} < 0$4 — a direct consequence of combining low-loss phonon-polariton materials with extreme gap confinement. Quality factors were cross-checked against four independent observables (field enhancement, LDOS, decay rate, background-subtracted Purcell factor), giving consistent values. A caveat: the Purcell spectrum is dominated by a quasi-continuum of higher-order modes, so the L$\operatorname{Re}\{\varepsilon_\perp\} < 0$5/L$\operatorname{Re}\{\varepsilon_\perp\} < 0$6 contributions appear as shoulders requiring background subtraction, introducing some spread in extracted $\operatorname{Re}\{\varepsilon_\perp\} < 0$7 (96–142).

Non-invasive role of the nano-FTIR tip

A central result is that the tip enhances but does not perturb the cavity. With the tip 2 nm above the NP, resonance positions, field distributions, and quality factors remain essentially unchanged ($\operatorname{Re}\{\varepsilon_\perp\} < 0$8, $\operatorname{Re}\{\varepsilon_\perp\} < 0$9 versus 81 and 96 without tip), and the lateral mode extent (~8 nm) changes by less than 3% for L$\operatorname{Re}\{\varepsilon_\perp\}$0. Meanwhile, the tip boosts the maximum field amplitude in the gap to $\operatorname{Re}\{\varepsilon_\perp\}$1, i.e., intensity enhancement $\operatorname{Re}\{\varepsilon_\perp\}$2, compared to $\operatorname{Re}\{\varepsilon_\perp\}$3 for the bare NPoM. This validates the tip-on-NPoM configuration as a stable platform for field-enhanced infrared spectroscopy of ultrathin layers placed in the gap.

The contrast with bare-quartz measurements is instructive: a static tip 1 nm above quartz also forms a phononic cavity supporting L$\operatorname{Re}\{\varepsilon_\perp\}$4 and L$\operatorname{Re}\{\varepsilon_\perp\}$5 modes, but during tapping-mode operation the oscillating tip samples a range of tip–quartz separations over which the resonances shift strongly (the L$\operatorname{Re}\{\varepsilon_\perp\}$6 mode blueshifts from 1105 to 1146 cm$\operatorname{Re}\{\varepsilon_\perp\}$7 as separation grows from 2 to 42 nm). Demodulation averages over this trajectory, merging the two resonances into one broad feature — consistent with both experiment and an analytical spheroid-tip model. In the NPoM geometry, by contrast, the particle–quartz gap is fixed independently of tip motion, so the cavity modes persist spectrally intact.

Size tuning

Spectra of NPoMs with 40, 60, and 80 nm AuNPs show that both L$\operatorname{Re}\{\varepsilon_\perp\}$8 and L$\operatorname{Re}\{\varepsilon_\perp\}$9 redshift with increasing particle diameter, mirroring trends known from plasmonic NPoMs and enabling spectral matching to specific molecular vibrations within the Reststrahlen band. Interestingly, the simulations reveal a discrepancy with plasmonic behavior regarding field enhancement: without the tip, $\nu_{TO,2}$0 increases with NP size as expected, but with the tip present it decreases. The authors attribute this to the growing tip–quartz separation for larger particles weakening tip–substrate coupling — a tip-induced effect, not intrinsic to the phononic cavity. Peak positions shift identically with or without the tip, confirming the redshift is intrinsic.

Limitations and open questions

The paper concedes several quantitative discrepancies between experiment and simulation: experimental peaks are broader and red-shifted relative to calculations, plausibly due to unmodeled geometrical factors such as the precise optical thickness of the citrate layer, NP facets, quartz anisotropy, or polishing-induced defects and strain. The isotropic treatment of quartz is justified post hoc — full-tensor simulations show only slight blueshifts and modest intensity changes — but relies on an estimated $\nu_{TO,2}$1 taken from literature rather than measured directly. Mode identification rests entirely on numerical simulation rather than an independent experimental observable, and the reported Purcell factors and mode volumes are simulated quantities for idealized spherical particles with a uniform 1 nm gap, not directly measured on the actual colloidal particles. Whether molecular ensembles placed in the gap reach vibrational strong coupling, and whether the tip-enhanced excitation suffices for nonlinear vibrational spectroscopy of minute quantities of matter, remain experimentally untested in this work.

Conclusion

This study establishes single-cavity infrared nanospectroscopy of phonon-polaritonic NPoMs, identifying reproducible L$\nu_{TO,2}$2 and L$\nu_{TO,2}$3 antenna modes with simulated mode volumes of ~700–1300 nm$\nu_{TO,2}$4, quality factors of ~80–110, and Purcell factors approaching $\nu_{TO,2}$5. The demonstration that the nano-FTIR tip serves as a non-invasive local excitation and readout probe — enhancing the gap field by more than an order of magnitude without shifting or broadening the cavity resonances — opens a route toward nanoscale SEIRA, vibrational strong coupling with small molecular ensembles, and nonlinear mid-infrared spectroscopy on individually addressable phononic cavities.