  Domain walls separating regions of AB and BA interlayer stacking in bilayer
graphene have attracted attention as novel examples of structural solitons,
topological electronic boundaries, and nanoscale plasmonic scatterers. We show
that strong coupling of domain walls to surface plasmons observed in infrared
nanoimaging experiments is due to topological chiral modes confined to the
walls. The optical transitions among these chiral modes and the band continua
enhance the local ac conductivity, which leads to plasmon reflection by the
domain walls. The imaging reveals two kinds of plasmonic standing-wave
interference patterns, which we attribute to shear and tensile domain walls. We
compute the electronic structure of both wall varieties and show that the
tensile wall contain additional confined bands which produce a
structure-specific contrast of the local conductivity. The calculated plasmonic
interference profiles are in quantitative agreement with our experiments.
