Quantitative infrared nanoscopy: Probe-cavity eigenmodes and nano-gap polaritons for strongly coupled nanoscale optics
Optical nanoscopies including near-field optical microscopy and spectroscopy circumvent the diffraction limit of conventional optics thanks to the nanoscale light focus emerging at the apex of a sharp irradiated probe. However, while strong optical coupling between the apex and its dielectric environment affords both enhanced nanoscopic measurement sensitivity and potentially ultra-strong fields within a nano-gap cavity, the conditions for this coupling remain poorly quantified by prevailing analytic models. Here we present a robust formalism of probe-cavity eigenmodes that fully describes how mutual near-field interactions between probe and environment produce a composite response to external fields qualitatively distinct from that of its distinct components. This "EigenProbe" model identifies the fundamental excitations of realistic optical nanoscopies as nano-gap polaritons, which provide an elegant basis to accurately predict near-field microscopy and spectroscopy experiments especially when probe-sample interactions are non-perturbative. Through comparison to carefully controlled nanoscopies of polar phonons and molecular vibrations alike, we show how nano-gap polaritons are both realized and utilized for reliable and rapid "inversion" of local optical constants. This advance demands both a careful understanding of the probe response through quantitative calibration, and our efficient semi-analytic description of cavity eigenmode scattering at the probe apex. Our EigenProbe formalism sets the stage for maturing diverse and proliferating optical nanoscopies into precision metrologies of nano-scale optical environments, and guides future use of nano-gap cavities to manipulate local excitations of quantum materials and to achieve strong coupling over photonic emitters.