  Prototypical three-dimensional (3D) topological Dirac semimetals (DSMs), such
as Cd$_3$As$_2$ and Na$_3$Bi, contain electrons that obey a linear
momentum-energy dispersion with different Fermi velocities along the three
orthogonal momentum dimensions. Despite being extensively studied in recent
years, the inherent \emph{Fermi velocity anisotropy} has often been neglected
in the theoretical and numerical studies of 3D DSMs. Although this omission
does not qualitatively alter the physics of light-driven massless
quasiparticles in 3D DSMs, it does \emph{quantitatively} change the optical
coefficients which can lead to nontrivial implications in terms of
nanophotonics and plasmonics applications. Here we study the linear optical
response of 3D DSMs for general Fermi velocity values along each direction.
Although the signature conductivity-frequency scaling, $\sigma(\omega) \propto
\omega$, of 3D Dirac fermion is well-protected from Fermi velocity anisotropy,
the linear optical response exhibits strong linear dichroism as captured by the
\emph{universal} extinction ratio scaling law, $\Lambda_{ij} = (v_i/v_j)^2$
(where $i\neq j$ denotes the three spatial coordinates $x,y,z$, and $v_i$ is
the $i$-direction Fermi velocity), which is independent of frequency,
temperature, doping, and carrier scattering lifetime. For Cd$_3$As$_2$ and
Na$_3$Bi$_3$, an exceptionally strong extinction ratio larger than 15 and
covering broad terahertz window is revealed. Our findings shed new light on the
role of Fermi velocity anisotropy in the optical response of Dirac semimetals
and open up novel polarization-sensitive functionalities, such as
photodetection and light modulation.
