Giant optomechanical spring effect in plasmonic nano- and picocavities probed by surface-enhanced Raman scattering

Abstract

Molecular vibrations couple to visible light only weakly, have small mutual interactions, and hence are often ignored for non-linear optics. Here we show the extreme confinement provided by plasmonic nano- and pico-cavities can sufficiently enhance optomechanical coupling so that intense laser illumination drastically softens the molecular bonds. This optomechanical pumping regime produces strong distortions of the Raman vibrational spectrum related to giant vibrational frequency shifts from an optical spring effect which is hundred-fold larger than in traditional cavities. The theoretical simulations accounting for the multimodal nanocavity response and near-field-induced collective phonon interactions are consistent with the experimentally-observed non-linear behavior exhibited in the Raman spectra of nanoparticle-on-mirror constructs illuminated by ultrafast laser pulses. Further, we show indications that plasmonic picocavities allow us to access the optical spring effect in single molecules with continuous illumination. Driving the collective phonon in the nanocavity paves the way to control reversible bond softening, as well as irreversible chemistry.

Fig. 1. Theory of nonlinear vibrational coupling in plasmonic nanocavities.

a Schematic of 80 nm nanoparticle-on-mirror (NPoM) containing 1.3 nm-thick self-assembled monolayer (SAM) of biphenyl-4-thiol (BPT) molecules, showing benzene ring stretch at 1586 cm⁻¹. b Nanogap supports localized plasmon modes (red). BPT molecular Raman dipoles (s, s') interact via their image molecules (pink arrow) and through plasmon modes (blue arrow). c Complex self-interaction Green’s function ($\mathrm{Re}\left\{G\right\}$ = red, $\mathrm{Im}\left\{G\right\}$ = blue) for response produced by a vertical dipole in the gap centre. Scattering cross section (grey) shows dominant localized plasmonic (10) (lowest order) and (20) (second order) modes (vertical dashed) at λ₍₁₀₎ ≈ 830 nm, λ₍₂₀₎ ≈ 670 nm, and a peak in ImG at ${\lambda }_{PPM}\approx 520$ nm identified as the plasmon pseudo-mode (PPM), originating from overlapping higher order modes. Dashed curves show G when only a single-optical-mode is considered in the model. d Two-point Green’s function between spatially separated locations in the gap (separation ρ), at ${\lambda }_{\left(20\right)}$ = 670 nm as obtained numerically (solid line) and with an analytic model based on image dipoles (dashed lines, see Supplementary Note S3.1). Inset shows midgap electric near-field at ${\lambda }_{\left(20\right)}$, with a scale bar 10 nm.

Fig. 2. Origin of optical spring effect in molecular optomechanics.

a Optical spring effect vs laser wavelength for ${\omega }_{\nu 1}$ = 1586 cm⁻¹ mode in the NPoM gap, showing contributions of the Stokes $S^{+}$(blue) and anti-Stokes $S^{-}$ (red) optomechanical parameters to the total vibrational shift, ${\mathrm{\Delta }}_{\mathrm{os}}^1$, for a single molecule in the nanocavity centre. $S^{+}$ and $S^{-}$ scale linearly with laser intensity (shown here for 10⁷ $\mathrm{\mu }\mathrm{W}\mathrm{\mu }{\mathrm{m}}^{-2}$). Dashed curves show single-mode plasmonic cavity results. b Dependence of shift in the fundamental collective Raman bright mode ${\mathrm{\Delta }}_{\mathrm{os}}^N$ with the number of molecules N_m arranged in a lattice at the middle of gap (Stokes in blue, anti-Stokes in red) at 5 × 10⁷ $\mathrm{\mu }\mathrm{W}\mathrm{\mu }{\mathrm{m}}^{-2}$. c SERS emission from full multi-molecule model for the ${\omega }_{\nu 1}$ = 1586 cm⁻¹ mode with 633 nm CW pump intensity of 10⁵ $\mathrm{\mu }\mathrm{W}\mathrm{\mu }{\mathrm{m}}^{-2}$ (blue, multipled by 50) and 5 × 10⁷ μW μm⁻² (red). At the larger intensity the broad peak is down-shifted ${\mathrm{\Delta }}_{\mathrm{os}}^N~$170 cm⁻¹ from ${\omega }_{\nu }$ due to the dominant bright Raman collective phonon mode. Top inset shows the square array of 100 molecules spaced ρ = 0.58 nm apart and centred in the facet (dashed, radius 16 nm). Bottom inset shows each molecular contribution to the fundamental bright collective phonon mode. Other parameters are specified in Supplementary Note S5.

Fig. 3. Pulsed Raman scattering from plasmonic nanocavities.

a Dark-field spectrum of typical 80 nm nanoparticle-on-mirror (NPoM) containing BPT molecular SAM. Pump laser (red dashed) is spectrally tunable, shaded region shows range of SERS emission, with individual plasmon modes labelled. b Pulsed SERS experiment combined with white-light dark-field scattering on individual NPoMs. Spectrally-tuned 0.5 ps pump pulses excite individual NPoM (with white light off), and laser is filtered from the collected emission. c Pulsed Stokes SERS spectrum of BPT for three vibrational modes indicated. Blue shading shows 1586 cm⁻¹ peak area, grey shading shows region of softened mode + background (which is integrated for comparison).

Fig. 4. Saturation of pulsed Raman scattering from many NPoMs.

a–c Averaged power-normalized SERS spectra for increasing in-coupled average powers at different pump wavelengths ${\lambda }_l$. d–f Integrated SERS emission from ${\omega }_{\nu 1}$= 1586 cm⁻¹ mode (colours show laser power) and integrated background + softened spectral region (grey, x6), excited by pulsed laser at ${\lambda }_l$= 633, 658, 700 nm. Open points are averages of individual measurements in each power range. Insets show relative position of pump wavelength and plasmon resonances. g–i Integrated SERS normalized by in-coupled peak intensity and integration time, error bars indicate their standard deviation. The critical laser intensity for saturation is marked as I_c (indicated in the main text).

Fig. 5. Nonlinear vibrational coupling model vs expt.

a Experimental power-normalized SERS spectra at low (blue) and high (red) powers. Constant ERS background is estimated by dashed lines. b Corresponding theoretical results showing the SERS spectra vs CW illumination power, for 100 molecules arrayed around the gap centre. c, d Extracted Raman integrated in the region around the 1586 cm⁻¹ peak (blue line/symbols) and in the softened+background region between 1350–1500 cm⁻¹ (grey line/symbols) for theory and experiment (SERS normalized by power in d, as in Fig.4g–i). Experimental data are averages of many particles with error bars indicating standard deviation of individual measurements. In c, d, scaling of in-coupled power from theory by 0.24 is used to match with experiment. The transfer in weight from the 1586 cm⁻¹ peak to lower wavenumbers arises from the redistribution of emission to the red-shifted lowest-energy bright Raman collective mode.

Fig. 6. Optical spring shift in picocavities.

a Schematic of nanolens on NPoM (SPARK construct). b Generation of a picocavity when Au atom moves onto facet, enhancing field at a single BPT molecule. c Sawtooth modulation of 633 nm CW laser power from 60 to 300 μW at 50 Hz. d, e Fast spectral scans (0.5 ms integration time) of Stokes emission from the SPARK nanocavity (d), and after formation of a picocavity (e). f-h, Extracted fits to 1586 cm⁻¹ line in nanocavity (grey) and 1501 cm⁻¹ picocavity line (red). Peak area (f) is linear in laser power, while optical spring effect in the picocavity leads to a repeatable shift in position (g) and broadening (h) of the vibrational line. i, j Spectra of vibrational lines investigated in f-h averaged over 4 periods of laser modulation. Nanocavity line (i) shows constant width and position while picocavity line (j) shifts and broadens (colour gives laser power). k Optical spring shift ${\Delta }_{os}^1$ dependence on laser intensity for several vibrational lines in nano- and picocavities. Each picocavity vibration experiences a different optical spring magnitude.

Fig. 7. Optical spring shifts in optomechanics.

a Ratio of spring shift $\mathrm{\Delta }{\omega }_{\nu }$ to the vibrational linewidth Γ_tot mapped vs cavity linewidth ${\kappa }_c$ and detuning ${\omega }_l-{\omega }_c$ of laser ω_l from cavity ω_c, both normalized to vibrational frequency ω_ν, for single-mode cavities. Typical regimes for cold atoms and whispering gallery (WG) resonances are shown dashed. For each ${\kappa }_c$, the lowest intensity is used at which $\mid {\gamma }_{\nu }{-\mathrm{\Gamma }}_{\mathrm{tot}}\left(I_l\right)\mid ={\gamma }_{\nu }/2$ over the detuning range. Box shows the results for the NPoM including the full multimode plasmonic response, as considered in the simulations, and with ${\omega }_c$ fixed at the NPoM dark-field resonance of 800 nm, giving ~10-fold enhancement. b Comparison of spring shifts per cavity photon vs ω_ν for a range of systems.