  The achievement of large values of the light-matter coupling in
nanoengineered photonic structures can lead to multiple photonic resonances
contributing to the final properties of the same hybrid polariton mode. We
develop a general theory describing multi-mode light-matter coupling in systems
of reduced dimensionality and we explore their novel phenomenology, validating
the predictions of our theory against numerical electromagnetic simulations. On
the one hand, we characterise the spectral features linked with the multi-mode
nature of the polaritons. On the other hand, we show how the interference
between different photonic resonances can modify the real-space shape of the
electromagnetic field associated with each polariton mode. We argue that the
possibility of engineering nanophotonic resonators to maximise the multi-mode
mixing, and to alter the polariton modes via applied external fields, could
allow for the dynamical real-space tailoring of subwavelength electromagnetic
fields.
