  We discovered novel Anderson localization behaviors of pseudospin systems in
a 1D disordered potential. For a pseudospin-1 system, due to the absence of
backscattering under normal incidence and the presence of a conical band
structure, the wave localization behaviors are entirely different from those of
normal disordered systems. We show both numerically and analytically that there
exists a critical strength of random potential ($W_c$), which is equal to the
incident energy ($E$), below which the localization length $\xi$ decreases with
the random strength $W$ for a fixed incident angle $\theta$. But the
localization length drops abruptly to a minimum at $W=W_c$ and rises
immediately afterwards, which has never been observed in ordinary materials.
The incidence angle dependence of the localization length has different
asymptotic behaviors in two regions of random strength, with $\xi \propto
\sin^{-4}\theta$ when $W<W_c$ and $\xi \propto \sin^{-2}\theta$ when $W>W_c$.
Experimentally, for a given disordered sample with a fixed randomness strength
$W$, the incident wave with incident energy $E$ will experience two different
types of localization, depending on whether $E>W$ or $E<W$. The existence of a
sharp transition at $E=W$ is due to the emergence of evanescent waves in the
systems when $E<W$. Such localization behavior is unique to pseudospin-1
systems. For pseudospin-1/2 systems, there is a minimum localization length as
randomness increases, but the transition from decreasing to increasing
localization length at the minimum is smooth rather than abrupt. In both
decreasing and increasing regions, the $\theta$ -dependence of the localization
length has the same asymptotic behavior $\xi \propto \sin^{-2}\theta$.
