Anisotropy
in low-dimensional materials offers an extra degree
of freedom to understand and tune the peculiar or potential properties
to design novel electronic, optical, thermal, and optoelectronic devices.
However, most research attention has been paid to qualitatively observing
anisotropic phenomena, lacking quantitatively revealing optical anisotropy,
in particular, and deeply digging for the physical mechanism. In this
work, for the first time to our knowledge, the complete dielectric
tensor of quasi-one-dimensional ZrTe5 is determined by
Mueller matrix spectroscopic ellipsometry (MMSE) to quantitatively
and comprehensively investigate the giant optical anisotropy, and
the underlying physical mechanism is revealed by combination with
the first-principle calculations. The ZrTe5 demonstrates
giant dispersive birefringence and dichroism, and the birefringence
(Δn = 0.58) outperforms many other low-dimensional
and conventional birefringent materials, showing great potential and
advantages in fabricating miniature and integrated polarization-sensitive
devices. By combining the critical point (CP) analysis and first-principle
calculations, the specific interband transitions related to the CPs
in dielectric function spectra along three crystal axes of ZrTe5 are identified, revealing the physical essence of the optical
anisotropy from the perspective of quantum mechanics. The proposed
method is general and can be easily extended to quantitatively investigate
the optical anisotropies in other novel low-symmetry materials.