Recovery of permittivity and depth from near-field data as a step toward infrared nanotomography

The increasing complexity of composite materials structured on the nanometer scale requires highly sensitive analytical tools for nanoscale chemical identification, ideally in three dimensions. While infrared near-field microscopy provides high chemical sensitivity and nanoscopic spatial resolution in two dimensions, the quantitative extraction of material properties of three-dimensionally structured samples has not been achieved yet. Here we introduce a method to perform rapid recovery of the thickness and permittivity of simple 3D structures (such as thin films and nanostructures) from near-field measurements, and provide its first experimental demonstration. This is accomplished via a novel nonlinear invertible model of the imaging process, taking advantage of the near-field data recorded at multiple harmonics of the oscillation frequency of the near-field probe. Our work enables quantitative nanoscale-resolved optical studies of thin films, coatings, and functionalization layers, as well as the structural analysis of multiphase materials, among others. It represents a major step toward the further goal of near-field nanotomography.