  Exceptional points (EPs), i.e., non-Hermitian degeneracies at which
eigenvalues and eigenvectors coalesce, can be realized by tuning the gain/loss
contrast of different modes in non-Hermitian systems or by engineering the
asymmetric coupling of modes. Here we demonstrate a mechanism that can achieve
EPs of arbitrary order by employing the non-reciprocal coupling of spinning
cylinders sitting on a dielectric waveguide. The spinning motion breaks the
time-reversal symmetry and removes the degeneracy of opposite chiral modes of
the cylinders. Under the excitation of a linearly polarized plane wave, the
chiral mode of one cylinder can unidirectionally couple to the same mode of the
other cylinder via the spin-orbit interaction associated with the evanescent
wave of the waveguide. The structure can give rise to arbitrary-order EPs that
are robust against spin-flipping perturbations, in contrast to conventional
systems relying on spin-selective excitations. In addition, we show that
higher-order EPs in the proposed system are accompanied by enhanced optical
isolation, which may find applications in designing novel optical isolators,
nonreciprocal optical devices, and topological photonics.
