  It is well known that for ordinary one-dimensional (1D) disordered systems,
the Anderson localization length $\xi$ diverges as $\lambda^m$ in the long
wavelength limit ($\lambda\rightarrow \infty$ ) with a universal exponent
$m=2$, independent of the type of disorder. Here, we show rigorously that
pseudospin-1 systems exhibit non-universal critical behaviors when they are
subjected to 1D random potentials. In such systems, we find that $\xi\propto
\lambda^m$ with $m$ depending on the type of disorder. For binary disorder,
$m=6$ and the fast divergence is due to a super-Klein-tunneling effect (SKTE).
When we add additional potential fluctuations to the binary disorder, the
critical exponent $m$ crosses over from 6 to 4 as the wavelength increases.
Moreover, for disordered superlattices, in which the random potential layers
are separated by layers of background medium, the exponent $m$ is further
reduced to 2 due to the multiple reflections inside the background layer. To
obtain the above results, we developed a new analytic method based on a stack
recursion equation. Our analytical results are in excellent agreements with the
numerical results obtained by the transfer-matrix method (TMM). For
pseudospin-1/2 systems, we find both numerically and analytically that
$\xi\propto\lambda^2$ for all types of disorder, same as ordinary 1D disordered
systems. Our new analytical method provides a convenient way to obtain easily
the critical exponent $m$ for general 1D Anderson localization problems.
