Quantitative model for infrared nano-spectroscopy in liquid

Nanoscale spectroscopy at the liquid-solid interface has recently been developed by combining scattering-scanning near-field optical microscopy (<i>s</i>-SNOM) with total internal reflection (TIR) geometry illumination. Despite experimental success, existing theoretical models lack physical description of the probe geometry and rely on quasistatic approximations of scattering. We demonstrate a numerical model based on near-to-far-field transformation of optical fields calculated by a Maxwell's equation solver. We observe the signal is directional, as expected with breakdown of the quasistatic approximation at the prism surface. We find compelling agreement between calculated and experimentally measured signal in approach curves. We model near-field vibrational spectroscopy of thin-film proteins and quantify thickness-dependent signal and associated spectral shifts. Our far-field reconstruction approach enables quantitative interpretation of TIR <i>s</i>-SNOM spectroscopy, and we expect it to become a reliable method for <i>s</i>-SNOM nanospectroscopy in a range of optical geometries and sample morphologies.