Nanoscale optical microscopy

Optical measurement techniques, and near-field optical microscopy in particular, exist in a broad variety of configurations. In the following we will derive an interaction series to understand and categorize different experimental configurations. The interaction series describes multiple scattering events between an optical probe and a sample and is similar to the Born series in light scattering. We will start out by discussing far-field microscopy first and then proceed with selected configurations encountered in near-field optical microscopy. The interaction series The interaction of light with matter can be discussed in terms of light scattering events [1, 2]. Figure 5.1 is a sketch of a generic geometry considered in the following. The sample and – in the case of near-field optical microscopy – also an optical probe, which is positioned in close proximity, are assumed to be described by dielectric susceptibilities η( r ) and χ( r ), respectively. An incident light field E i is illuminating the probe-sample region. E i is assumed to be a solution of the homogeneous Helmholtz equation (2.35). The incoming field causes a scattered wave E s , which is detectable in the far-field. The total field is then given by E = E i + E s . In a qualitative picture, there are several processes that can convert an incoming photon into a scattered photon. For example, the incoming photon may be scattered only at the probe or only at the sample before traveling into the far-field.