Coherent characterisation of a single molecule in a photonic black box

Extinction spectroscopy is a powerful tool for demonstrating the coupling of a single quantum emitter to a photonic structure. However, it can be challenging in all but the simplest of geometries to deduce an accurate value of the coupling efficiency from the measured spectrum. Here we develop a theoretical framework to deduce the coupling efficiency from the measured transmission and reflection spectra without precise knowledge of the photonic environment. We then consider the case of a waveguide interrupted by a transverse cut in which an emitter is placed. We apply that theory to a silicon nitride waveguide interrupted by a gap filled with anthracene that is doped with dibenzoterrylene molecules. We describe the fabrication of these devices, and experimentally characterise the waveguide coupling of a single molecule in the gap.