  We study the optical response of bilayer graphene with a kink potential
composed of a domain wall separating two AB regions with opposite interlayer
bias. The band structure and the local optical conductivity in real space are
investigated in details based on a continuum model. We find that the
one-dimensional chiral states localized at the domain wall contribute
significantly to the local optical conductivity, which shows a clear
distinction in different regions. The effects of domain wall states on optical
conductivity can be detected by spatially and frequency resolved spectroscopic
features. From the spectrum at various Fermi energies, important features in
the band structure such as the energy separation between two chiral states can
be directly measured. When the domain wall region is broad, the spatial
distribution of local optical conductivity can provide important information on
the bound states as well as the topological domain wall states.
