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During the past half century, a major approximation was natural in the fieldof light-matter interaction: the point-dipole model. It was assumed that thewavelength is much larger than the size of the emitting atom or molecule, sothat the emitter can be described as a single or a collection of elementarydipoles. As it is legitimate for visible light, the approximation does nolonger hold near plasmonic nanostructures, where the effective wavelength candrop below 10 nm. In that case deviations arise from the approximate model.First, the emitter spatial extent influences the far-field spectrum. Second,high-order transitions beyond the dipolar ones are not forbidden anymore. Goingbeyond the approximation requires intensive numerical efforts to compute thephotonic response over the spatial extent of the emitter, since the completeGreen's function is required. Here, we develop a general model that computesthe multipolar transition rates of a quantum emitter in a photonic environment,by computing the Green's function through an eigenpermittivity modal expansion.We apply the method on graphene nanoislands, and we demonstrate a localbreakdown of the selection rules, with quadrupolar transition rates becoming100 times larger than dipolar ones.

Strong multipolar transition enhancement with graphene nanoislands