  The light-matter coupling between electromagnetic modes guided by a
semiconductor nanowire and excitonic states of molecules localized in its
surrounding media is studied from both classical and quantum perspectives, with
the aim of describing the strong coupling regime. Weakly guided modes (bare
photonic modes) are found through a classical analysis, identifying those
lowest-order modes presenting large electromagnetic fields spreading outside
the nanowire, while preserving their robust guided behavior. Experimental fits
of the dielectric permittivity of an organic dye that exhibits excitonic states
are used for realistic scenarios. A quantum model properly confirms through an
avoided mode crossing that the strong coupling regime can be achieved for this
configuration, leading to Rabi splitting values above 100 meV. In addition, it
is shown that the coupling strength depends on the fraction of energy spread
outside the nanowire, rather than on the mode field localization. These results
open up a new avenue towards strong coupling phenomenology involving
propagating modes in non-absorbing media.
