Strong multipolar transition enhancement with graphene nanoislands

For a long time, the point-dipole model was a central and natural approximation in the field of photonics. This approach assumes that the wavelength is much larger than the size of the emitting atom or molecule so that the emitter can be described as a single or a collection of elementary dipoles. This approximation no longer holds near plasmonic nanostructures, where the effective wavelength can reach the nanometer-scale. In that case, deviations arise and high-order transitions, beyond the dipolar ones, are not forbidden anymore. Typically, this situation requires intensive numerical efforts to compute the photonic response over the spatial extent of the emitter wavefunctions. Here, we develop an efficient and general model for the multipolar transition rates of a quantum emitter in a photonic environment by computing Green’s function through an eigen permittivity modal expansion. A major benefit of this approach is that the position of the emitter and the permittivity of the material can be swept in a rapid way. To illustrate, we apply the method on various forms of graphene nanoislands, and we demonstrate a local breakdown of the selection rules, with quadrupolar transition rates becoming 100 times larger than dipolar ones.