  Increasing the collection efficiency from solid-state emitters is an
important step towards achieving robust single photon sources, as well as
optically connecting different nodes of quantum hardware. A metallic substrate
may be the most basic method of improving the collection of photons from
quantum dots, with predicted collection efficiency increases of up to 50%. The
established 'method-of-images' approach models the effects of a reflective
surface for atomic and molecular emitters by replacing the metal surface with a
second fictitious emitter which ensures appropriate electromagnetic boundary
conditions. Here, we extend the approach to the case of driven solid-state
emitters, where exciton-phonon interactions play a key role in determining the
optical properties of the system. We derive an intuitive polaron master
equation and demonstrate its agreement with the complementary half-sided cavity
formulation of the same problem. Our extended image approach offers a
straightforward route towards studying the dynamics of multiple solid-state
emitters near a metallic surface.
