  Inspired from perturbative calculations, this work introduces imaginary
($\Omega_{\rm I}$) and real ($\Omega$) rotation effects to the pure $SU(3)$
gauge potentials simply through variable transformations: The empirical
Polyakov loop (PL) potentials can be rewritten as functions of the imaginary
chemical potentials of gluons and ghosts $(q_{\rm ij})$, and the
transformations are taken as $q_{\rm ij}\rightarrow q_{\rm ij}\pm\Omega_{\rm
I}/T$ and $q_{\rm ij}\rightarrow q_{\rm ij}\pm i\,\Omega/T$, respectively. For
the PL potential of Fukushima $(V_1)$, a smaller imaginary rotation
$\Omega_{\rm I}$ tends to suppress PL at all temperature and the deconfinement
transition keeps of first order. However, for the PL potential of Munich group
$(V_2)$, $\Omega_{\rm I}$ tends to enhance PL at low temperature $T$,
consistent with lattice simulations; but suppress PL at high $T$, consistent
with perturbative calculations. Moreover, the deconfinement alters from first
order to crossover with increasing $\Omega_{\rm I}$ as is expected from lattice
simulations. On the other hand, the real rotation $\Omega$ tends to enhance PL
at relatively low $T$ for both potentials, and the (pseudo-)critical
temperature decreases with $\Omega$ as expected. Therefore, we find that
analytic continuation of the phase diagram from imaginary to real rotation is
not necessarily valid in the non-perturbative region. Finally, we apply the
more successful PL potential $V_2$ to the Polyakov--Nambu-Jona-Lasinio (PNJL)
model and discover that $\Omega_{\rm I}$ tends to break chiral symmetry while
$\Omega$ tends to restore it. Especially, the modified model is even able to
qualitatively explain the lattice result that a larger $T$ would catalyze
chiral symmetry breaking for a large $\Omega_{\rm I}$.
