  We investigate the optical property of monolayer and layered BiI$_3$ and
reveal the presence of exciton only in the monolayer crystal. We evaluate the
energy spectrum of a dielectric function by using time-dependent density
functional theory. Bulk crystal of BiI$_3$ is an atomic layered semiconductor
with the band gap corresponding to the frequency of visible light. The
numerical result for the bulk crystal is confirmed to be consistent with the
previous experimental results and it does not depend on the number of layers
except the monolayer. We reveal the excitons appearing below the resonant peak
associated with the inter-band excitation in the monolayer crystal. The unique
optical property can be directly observed in the optical absorption or
differential reflectance spectrum and distinguish the monolayer crystal from
the stacked BiI$_3$.
