  We provide a simple semi-classical formalism to describe the coupling between
one or several quantum emitters and a structured environment. Describing the
emitter by an electric polarizability, and the surrounding medium by a Green
function, we show that an intuitive scattering picture allows one to derive a
coupling equation from which the eigenfrequencies of the coupled system can be
extracted. The model covers a variety of regimes observed in light-matter
interaction, including weak and strong coupling, coherent collective
interactions, and incoherent energy transfer. It provides a unified description
of many processes, showing that different interaction regimes are actually
rooted on the same ground. It can also serve as a basis for the development of
more refined models in a full quantum electrodynamics framework.
