Reciprocity theory of apertureless scanning near-field optical microscopy with point-dipole probes.

Near-field microscopy offers the opportunity to reveal optical contrast at deep subwavelength scales. In scanning near-field optical microscopy (SNOM), the diffraction limit is overcome by a nanoscopic probe in close proximity to the sample. The interaction of the probe with the sample fields necessarily perturbs the bare sample response, and a critical issue is the interpretation of recorded signals. For a few specific SNOM configurations, individual descriptions have been modeled, but a general and intuitive framework is still lacking. Here, we give an exact formulation of the measurable signals in SNOM which is easily applicable to experimental configurations. Our results are in close analogy with the description Tersoff and Hamann have derived for the tunneling currents in scanning tunneling microscopy. For point-like scattering probe tips, such as used in apertureless SNOM, the theory simplifies dramatically to a single scalar relation. We find that the measured signal is directly proportional to the...