  Hyperbolic polaritons exhibit large photonic density of states and can be
collimated in certain propagation directions. The majority of hyperbolic
polaritons are sustained in man-made metamaterials. However, natural-occurring
hyperbolic materials also exist. Particularly, natural in-plane hyperbolic
polaritons in layered materials have been demonstrated in MoO3 and WTe2, which
are based on phonon and plasmon resonances respectively. Here, by determining
the anisotropic optical conductivity (dielectric function) through optical
spectroscopy, we predict that monolayer black phosphorus naturally hosts
hyperbolic exciton-polaritons due to the pronounced in-plane anisotropy and
strong exciton resonances. We simultaneously observe a strong and sharp ground
state exciton peak and weaker excited states in high quality monolayer samples
in the reflection spectrum, which enables us to determine the exciton binding
energy of ~452 meV. Our work provides another appealing platform for the
in-plane natural hyperbolic polaritons, which is based on excitons rather than
phonons or plasmons.
