  We study a system made up of one or two two-level quantum emitters, coupled
to a single transverse mode of a closed waveguide, in which photon wavenumbers
and frequencies are discretized, and characterize the stable states in which
one excitation is steadily shared between the field and the emitters. We
unearth finite-size effects in the field-emitter interactions and identify a
family of dressed states, that represent the forerunners of bound states in the
continuum in the limit of an infinite waveguide. We finally consider the
potential interest of such states for applications in the field of quantum
information.
