  During the past half century, a major approximation was natural in the field
of light-matter interaction: the point-dipole model. It was assumed 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. As it is legitimate for visible light, the approximation does no
longer hold near plasmonic nanostructures, where the effective wavelength can
drop 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. Going
beyond the approximation requires intensive numerical efforts to compute the
photonic response over the spatial extent of the emitter, since the complete
Green's function is required. Here, we develop a general model that computes
the 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 local
breakdown of the selection rules, with quadrupolar transition rates becoming
100 times larger than dipolar ones.
