  We theoretically study high-order optomechanically-induced transparency
(OMIT) process in a nonlinear Kerr resonator. A frequency shift induced by the
Kerr effect, is identified for the optical cavity mode, which results in
asymmetric OMIT windows of the signal and its higher-order sidebands. We also
find that both the sideband amplitude and its associated group delay
sensitively depend on the strength of the Kerr nonlinearity. This indicates the
possibility to enhance or steer the performance of OMIT devices with various
nonlinear optical cavities.
