Scattering Theory of Bardeen's Formalism for Tunneling: New Approach to Near-Field Microscopy

We propose a new theoretical approach to near-field microscopy, which allows one to deal with scanning tunneling microscopy and scanning near-field optical microscopy with a unified formalism. Under the approximation of weak tip-sample coupling, we show that Bardeen's perturbation formula, originally derived for electron tunneling, can be derived from a scattering formalism which extends its validity to electromagnetic vector fields. This result should find broad applications in near-field imaging and spectroscopy.