Modeling scanning near-field optical photons scattered from an atomic force microscope for quantum metrology

Scattering scanning near-field optical microscopy (s-SNOM) is a promising technique for overcoming Abbe diffraction limit and substantially enhancing the spatial resolution in spectroscopic imaging. The s-SNOM works by exposing an atomic force microscope (AFM) tip to an optical electromagnetic (EM) field, while the tip is so close to a dielectric sample that the incident beam lies within the near-field regime and displays nonlinear behavior. We suggest replacing the incident EM field by photons generated by a single photon emitter, and propose a theoretical model for the suggested system by employing electric-dipole approximation, image theory, and perturbation theory. The count rate of the scattered photons from the AFM tip is extracted through a single photon detector, which contains information about electrical permittivity of the dielectric material beneath the tip. The permittivity of the sample can be extracted through spectroscopic setups. Our proposed scheme is useful for enhancing the spatial resolution of the modern quantum spectroscopy configurations that utilize entangled single photons.