  The energy transfer between different subsystems or different vibration modes
is always one of the most interested problems in the study of the resonance
phenomena in coupled nonlinear dynamical systems. With an optomechanical system
operating in the regime of unresolved sideband, where its mechanical frequency
is lower than the cavity field damping rate, we illustrate the existence of a
special nonlinear resonance phenomenon. This type of previously unknown
resonance manifests an organized pattern of the coupled cavity field and
mechanical oscillation, so that the cavity field precisely pushes the
mechanical oscillator within an appropriate small time window in each
mechanical oscillation period and the mechanical energy will increase by a jump
of almost fixed amount after each oscillation cycle. The scenario is realized
at a resonance point where the frequency difference of two driving fields
matches the mechanical frequency of the system, and this condition of
drive-frequency match is found to trigger a mechanism to lock the two
subsystems of an unresolved-sideband optomechanical system into a highly
ordered energy transfer as the above mentioned. Due to a significantly enhanced
nonlinearity in the vicinity of the resonance point, optical frequency combs
can be generated under pump powers of thousand times lower, as compared to the
use of a single-tone driving field for the purpose. An unresolved sideband
system under the drives without satisfying the resonance condition also
demonstrates other interesting dynamical behaviors. Most of all, by providing a
realistic picture for the nonlinear optomechanical dynamics in unresolved
sideband regime, our study points to a direction to observe novel dynamical
phenomena and realize other applications with the systems of less technical
restrictions.
