  We investigated, both experimentally and theoretically, the reflection phase
shift (RPS) of one-dimensional plasmon polaritons. We launched 1D plasmon
polaritons in carbon nanotube and probed the plasmon interference pattern using
scanning near-field optical microscopy (SNOM) technique, through which a
non-zero phase shift was observed. We further developed a theory to understand
the nonzero phase shift of 1D polaritons, and found that the RPS can be
understood by considering the evanescent field beyond the nanotube end.
Interesting, our theory shows a strong dependence of RPS on polaritons
wavelength and nanotube diameter, which is in stark contrast to 2D plasmon
polaritons in graphene where the RPS is a constant. In short wave region, the
RPS of 1D polaritons only depends on a dimensionless variable -- the ratio
between polaritons wavelength and nanotube diameter. These results provide
fundamental insights into the reflection of polaritons in 1D system, and could
facilitate the design of ultrasmall 1D polaritonic devices, such as resonators,
interferometers.
