The Lightning Rod Model: a Genesis for Quantitative Near-Field Spectroscopy

Near-field infrared spectroscopy has the proven ability to resolve optical contrasts in materials at deeply sub-wavelength scales across a broad range of infrared frequencies. In principle, the technique enables sub-diffractional optical identification of chemical compositions within nanostructured and naturally heterogeneous samples. However current models of probe-sample optical interaction, while qualitatively descriptive, cannot quantitatively explain infrared near-field spectra, especially for strongly resonant sample materials. We present a new first-principles model of near-field interaction, and demonstrate its superb agreement with infrared near-field spectra measured for thin films of silicon dioxide and the strongly phonon-resonant material silicon carbide. Using this model we reveal the role of probe geometry and surface mode dispersion in shaping the measured near-field spectrum, establishing its quantitative relationship with the dielectric properties of the sample. This treatment offers a route to the quantitative determination of optical constants at the nano-scale.