Probing nanoparticle substrate interactions with synchrotron infrared nanospectroscopy: Coupling gold nanorod Fabry-Pérot resonances with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>SiO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi><mml:mtext>?</mml:mtext><mml:mi>BN</mml:mi></mml:math> phonons

Spectroscopic interrogation of materials in the midinfrared with nanometer spatial resolution is inherently difficult due to long wavelengths involved, reduced detector efficiencies, and limited availability spectrally bright, coherent light sources. Technological advances are driving techniques that overcome these challenges, enabling material characterization this relatively unexplored spectral regime. Synchrotron infrared nanospectroscopy (SINS) an imaging technique provides local sample information nanoscale target specimens experimental energy window between 330 5000 ${\mathrm{cm}}^{\ensuremath{-}1}$. Using SINS, we analyzed a series individual gold nanorods patterned on ${\mathrm{SiO}}_{2}$ substrate flake hexagonal boron nitride. The SINS spectra reveal interactions nanorod photonic Fabry-P\'erot resonances surface phonon polaritons each substrate, which characterized as avoided crossings. A coupled oscillator model hybrid system deeper understanding coupling theoretical framework for future exploration.