Fig. 3: Near-field spectroscopic measurement of field-enhanced molecular scattering.

a Experimental (s-SNOM) amplitude spectra, \({s}_{3}\left(\omega \right)\), obtained with a PDMS-contaminated AFM tip (O) that interacts with a metal nanorod (A) of different lengths, \(L\) (solid lines). Shaded areas show the numerically calculated near-field spectra, \({s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)\), from (b) but scaled to the experimental data (Supplementary Note 1). b Numerically calculated (FDTD) amplitude spectra, \({s}_{3}\left(\omega \right)\), (solid lines), where the AFM tip is described as a core-shell nanoparticle with a 50 nm radius Au core and a 10 nm thick PDMS shell, and aspects of tip vibration and signal demodulation were taken into account (Supplementary Note 1). Shaded areas show the calculated amplitude spectra, \({s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)\), assuming a non-absorbing dielectric shell. Dashed lines show the magnitude of field-enhanced molecular scattering, \(|{E}_{{{\rm{AOA}}}}\left(\omega \right)|\), (Eq. 18, no demodulation considered, scaled to the calculated data). c, d Isolated spectral signature of the molecular vibrations, \(\Delta {s}_{3}\left(\omega \right)={s}_{3}\left(\omega \right)-{s}_{3}^{{{\rm{bkg}}}}\left(\omega \right)\), from the data in (a, b) (curves are offset for clarity). The magnitude of the polarizability of the core-shell nanoparticle considered in (b), \(|{\alpha }_{{{\rm{O}}}}\left(\omega \right)|\), is shown for reference (black solid line in (d)). e Parametric representation of the spectral signature of the 1258 cm⁻¹ (Si-CH₃) molecular vibration of PDMS, \(\Delta {s}_{3}^{{{\rm{pp}}}}\), as obtained from panels (a, b), normalized to maximum and plotted against the calculated field enhancement, \({|f|}\), at 1258 cm⁻¹. f Experimental (s-SNOM) and g numerically calculated (FDTD) phase spectra, \({\varphi }_{3}\left(\omega \right)\), (solid lines). The dotted lines in (g) show the calculated phase spectra, \({\varphi }_{3}^{{{\rm{bkg}}}}\left(\omega \right)\), assuming a non-absorbing dielectric shell. Black dashed lines show the phase of field-enhanced molecular scattering, \({\varphi }_{{{\rm{AOA}}}}\left(\omega \right)\) (Eq. 19). h, i Baseline-corrected phase spectra, \(\Delta {\varphi }_{3}\left(\omega \right)={\varphi }_{3}\left(\omega \right)-{\varphi }_{3}^{{{\rm{bkg}}}}\left(\omega \right)\) from the data in (f, g) (curves are offset for clarity). The phase of the polarizability of the core-shell nanoparticle, \({{\rm{Arg}}}\{{\alpha }_{{{\rm{O}}}}\left(\omega \right)\}\), is shown for reference in (i) (black solid line). j Parametric representation of the spectral signature of the molecular vibration (Si-CH₃) of PDMS, \({\varphi }_{3}^{{{\rm{pp}}}}\), as obtained from panels (h, i), plotted against the calculated field enhancement, \(f\), at 1258 cm⁻¹. Error bars in (e, j) describe the uncertainty owing to experimental noise (see Methods). Supplementary Fig. 5 shows the spectra for each antenna individually, Supplementary Note 2 details the corresponding spectrally integrated near-field images. The PDMS shell of the core-shell nanoparticle in (b) was modeled using tabulated data, and the non-absorbing dielectric shell with constant \(\varepsilon=1.8\). The polarizability of the core-shell nanoparticle was evaluated analytically using Eq. 2 in Supplementary Note 1.