Logical Fallacy of using the Electric Field in Non-resonant Near-field Optics

We find that the electric field is not a suitable physical quantity to describe the response of a non-metallic material in the study of non-resonant near-field optics. In practice, we show the spin-less one-electron two-level system responds differently to longitudinal and transverse electric fields under the non-resonant condition. This difference originates from the non-relativistic nature of the system, and should exist in actual many-electron systems. For this type of system, it is a logical fallacy to use the constitutive equation in terms of the total electric field and the associated permittivity. Recognizing this fallacy, both experimental and theoretical progress is needed in the field of non-resonant near-field optics of non-metallic materials.