Relationship between phase measured using a scattering SNOM (s-SNOM) and the Local Density of Optical States (LDOS)
EMN Meeting on Photonics 2016
We theoretically discuss the link between the phase measured using a scattering SNOM (s-SNOM) and the Local Density of Optical States (LDOS). One of the main results is that the LDOS information is directly proportional to the phase of the probe. In a given trans-scattering configuration, the transmitted phase, is the sum of the phase of the total Green function which propagate the field from the probe position up to the detector, the phase of the polarizability tensor, and the phase of the local field. Therefore by monitoring the spatial variation of the trans-scattering phase, we locally measure the phase modulation associated with the probe and the phase associated with the optical paths. We demonstrate numerically that a technique involving simple two phase imaging of a sample with two different sized tips should allow us to obtain the image the pLDOS directly by normalization and subtraction. For this novel imaging method, numerical comparison with extinction probe measurement show crucial qualitative and quantitative improvement.