Probe phase shift: Relationship with the Local Density Of Optical State (LDOS)

The rate of spontaneous emission of a fluorescent emitter is determined both by the internal electronic states and the Local Density Of State (LDOS) [1]. Luminescence, i.e., emission of light by a source, can therefore be tailored trough the environment thanks to nanofabrication, modifying the LDOS. Due to its tremendous technological impact at the nanoscale, new application developments were designed. This is notably true for energy consumption, allowing to enhance energy extraction for local source such as LED [2], OLED [3] and also for integrated local photon source [4, 5] which is of rising interest in the field of Telecom Information Communication for Quantum Information Processing. Thus imaging the LDOS of fabricated samples becomes essential to characterize optical device, together with deeper understanding of light-matter interaction. Here, we will present a new theoretical relationship between the Local Density of Optical States (LDOS) and phase sensitive near field probe. Based on this finding, we propose a new pathway to determine the LDOS in a more quantitative way, i.e., in order to get a much better signature than the extinction measurement, or emitter lifetime decay rate.