  We consider a periodic chain of oscillating dipoles, interacting via
long-range dipole-dipole interactions, embedded inside a cuboid cavity
waveguide. We show that the mixing between the dipolar excitations and cavity
photons into polaritons can lead to the appearance of new states localized at
the ends of the dipolar chain, which are reminiscent of Tamm surface states
found in electronic systems. A crucial requirement for the formation of
polaritonic Tamm states is that the cavity cross-section is above a critical
size. Above this threshold, the degree of localization of the Tamm states is
highly dependent on the cavity size, since their participation ratio scales
linearly with the cavity cross-sectional area. Our findings may be important
for quantum confinement effects in one-dimensional systems with strong
light-matter coupling.
