Quantitative Analytical Model for Scattering-type Scanning Near-field Optical Spectroscopy

Scattering-type scanning near-field optical microscopy (s-SNOM) is a versatile technique in nanooptics, enabling local probing of optical responses beyond the diffraction limit from vis to THz frequencies. Its theoretical modeling based on tip-sample interactions typically relies on computationally intensive numerical methods or phenomenological models with empiric fitting parameters, complicating spectral analysis and interpretation. Developing a rigorous quantitative analytical model remains a significant challenge in near-field microscopy. Here, we introduce an accurate analytical solution for the prolate spheroid model of s-SNOM in the quasi-electrostatic limit. We validate our solution through comparisons with numerical simulations and experimental spectra. Due to its higher computational efficiency compared to numerical simulation and higher accuracy compared to phenomenological solutions, our solution for spheroid model facilitates spectrum prediction and interpretation for homogeneous bulk samples, enables systematic exploration of parameter effects, and supports data generation for machine learning applications. Furthermore, the generality of our approach allows straightforward extension to more complex nanostructures.