  The non-Hermitian skin effect (NHSE) has been intensely investigated over the
past few years and has unveiled new topological phases, which have no
counterparts in Hermitian systems. Here we consider the hybridization between
the NHSE in an exciton-polariton waveguide and a localized defect mode. By
tuning the non-Hermiticity, we find that the resulting ground-state of the
system is both spatially extended and energetically separated from other modes
in the system. When polariton lasing occurs in the system, we find an enhanced
spatial coherence compared to regular waveguides, which is robust in the
presence of disorder.
