Probing nanoparticle substrate interactions with synchrotron infrared nanospectroscopy: Coupling gold nanorod Fabry-Pérot resonances with ${\mathrm{SiO}}_2$ and $h\text{−}\mathrm{BN}$ phonons

Spectroscopic interrogation of materials in the midinfrared with nanometer spatial resolution is inherently difficult due to the long wavelengths involved, reduced detector efficiencies, and limited availability of spectrally bright, coherent light sources. Technological advances are driving techniques that overcome these challenges, enabling material characterization in this relatively unexplored spectral regime. Synchrotron infrared nanospectroscopy (SINS) is an imaging technique that provides local sample information of nanoscale target specimens in an experimental energy window between 330 and 5000 ${\mathrm{cm}}^{-1}$. Using SINS, we analyzed a series of individual gold nanorods patterned on a ${\mathrm{SiO}}_2$ substrate and on a flake of hexagonal boron nitride. The SINS spectra reveal interactions between the nanorod photonic Fabry-Pérot resonances and the surface phonon polaritons of each substrate, which are characterized as avoided crossings. A coupled oscillator model of the hybrid system provides a deeper understanding of the coupling and provides a theoretical framework for future exploration.

Figure 1

(a) Schematic of the experimental SINS setup. The dashed box encloses the tip-sample interaction region. (b) Geometry of the idealized sample system and the model parameters used to build an analytical oscillator model of the tip-sample interaction (see text for details).

Figure 2

SINS line scans showing the normalized phase [(a) and (c)] and normalized magnitude [(b) and (d)] for 1.13 [(a) and (b)] and 2.18 [(c) and (d)] $\mu \mathrm{m}$ long nanorods on an ${\mathrm{SiO}}_2$ substrate as a function of distance from the nanorod center. AFM images of the nanorods scanned are included on the right, with each horizontal scale bar representing 100 nm. The unmixed $m=1$ FP mode is observed in the shorter nanorod, whereas the longer nanorod shows the mixing of the $m=1$ FP mode with the substrate phonon and the emergence of the unmixed $m=2$ FP mode. To better highlight these behaviors, SINS intensity information is displayed over a given range ($0.1–0.7\mathrm{rad}$ and $0.4–1.0\mathrm{V}$) so that data outside of it saturates the image.

Figure 3

SINS magnitude spectra from a series of nanorods ($L=0.7–10.0\mu \mathrm{m}$) obtained at the end (blue tones) or middle (red tones) of the nanorod on ${\mathrm{SiO}}_2$ (first column) and hBN (second column) substrates. The spectrum obtained from the shortest nanorod is plotted at the top in each panel with longer nanorod spectra vertically offset until the longest nanorod in each series is plotted at the bottom.

Figure 4

Avoided crossing diagram derived from the SINS magnitude measurements for the complete nanorod series on both ${\mathrm{SiO}}_2$ and hBN substrates. The $m=1$ (blue) and $m=2$ (red) FP modes are plotted versus inverse nanorod length. Dotted black lines are the asymptotic energies.

Figure 5

Comparison of experimentally collected [(a), (c)] and theoretically constructed [(b), (d)] SINS magnitude spectra $|A_2\left(\omega \right)|$ of the $m=1$ nanorod FP mode. The experimental spectra were obtained from a series of target gold nanorods of lengths varying from $L=0.7$ to $10.0\mu \mathrm{m}$, while the theoretical spectra were generated using a target spheroid of long axis radius $a_2=9\mu \mathrm{m}$, short-axis radius $b_2=550$ nm, plasma wave number ${\omega }_{p2}/2\pi c=1633$ ${\mathrm{cm}}^{-1}$, scattering wave number ${\gamma }_2/2\pi c=256.5{\mathrm{cm}}^{-1}$, and variable Lorentz wave number ${\omega }_2/2\pi c=805.5–2977{\mathrm{cm}}^{-1}$. The nanorods were mounted on ${\mathrm{SiO}}_2$ (a) and hBN (c) substrates, and these substrates were modeled theoretically [(b), (d)] with plasma wave numbers ${\omega }_{p3}/2\pi c=362.9$ and 1169 ${\mathrm{cm}}^{-1}$, damping wave numbers ${\gamma }_3/2\pi c=64.12$ and 92.75 ${\mathrm{cm}}^{-1}$, Lorentz wave numbers ${\omega }_3/2\pi c=1147$ and 1398 ${\mathrm{cm}}^{-1}$, and intraband dielectric constants ${\varepsilon }_{\infty 3}=1.2$ and 2.68, respectively [63, 64, 65]. Additionally, the spectral locations of the uncoupled nanorod dipole (${\overline{\nu }}_2$), uncoupled substrate SPhP (${\nu }_3$), and hybridized modes (${\nu }_{\pm }$) are superimposed on the spectra to demonstrate the effects of the nanorod-substrate coupling on the observable signal.