  Kagome magnet TbMn$_6$Sn$_6$ is a new type of topological material that is
known to support exotic quantum magnetic states. Experimental work has
identified that TbMn$_6$Sn$_6$ hosts Dirac electronic states that could lead to
topological and Chern quantum phases, but the optical response of the Dirac
fermions of TbMn$_6$Sn$_6$ and its properties remain to be explored. Here, we
perform optical spectroscopy measurement combined with first-principles
calculations on single-crystal sample of TbMn$_6$Sn$_6$ to investigate the
associated exotic phenomena. TbMn$_6$Sn$_6$ exhibits frequency-independent
optical conductivity spectra in a broad range from 1800 to 3000 cm$^{-1}$
(220-370 meV) in experiments. The theoretical band structures and optical
conductivity spectra are calculated with several shifted Fermi energy to
compare with the experiment. The theoretical spectra with 0.56 eV shift for
Fermi energy are well consistent with our experimental results. Besides, the
massive quasi-two-dimensional (quasi-2D) Dirac bands, which have linear band
dispersion in $k_x$-$k_y$ plane and no band dispersion along the $k_z$
direction, exist close to the shifted Fermi energy. According to tight-binding
model analysis, the quasi-2D Dirac bands give rise to a flat optical
conductivity, while its value is smaller than, about one tenth of, that from
the calculations and experiments. It indicates that the other trivial bands
also contribute to the flat optical conductivity.
