  We propose two non-Hermitian arrays consisting of $N=2l+1$ waveguides and
exhibiting parity-time ($\mathcal{PT}$) or anti-$\mathcal{PT}$ symmetry for
investigating light transfer dynamics based on $N$th-order exceptional points
(EPs). The $\mathcal{PT}$-symmetric array supports two $N$th-order EPs
separating an unbroken and a broken phase with real and imaginary eignvalues,
respectively. Light transfer dynamics in this array exhibits radically
different behaviors, i.e. a unidirectional oscillation behavior in the unbroken
phase, an edge-towards localization behavior in the broken phase, and a
center-towards localization behavior just at $N$th-order EPs. The
anti-$\mathcal{PT}$-symmetric array supports also two $N$th-order EPs
separating an unbroken and a broken phase, which refer however to imaginary and
real eigenvalues, respectively. Accordingly, light transfer dynamics in this
array exhibits a center-towards localization behavior in the unbroken phase and
an origin-centered oscillation behavior in the broken phase. These nontrivial
light transfer behaviors and their controlled transitions are not viable for
otherwise split lower-order EPs and depend on the underlying $SU(2)$ symmetry
of spin-$l$ matrices.
