  We study the dynamics of a driven optomechanical cavity coupled to a charged
nanomechanical resonator via Coulomb interaction. We find the tunable switch
between slow-and fast- light in double-mode can be observed from the output
field by adjusting the laser-cavity detuning in this coupled system. Moreover,
the requencies of signal light can be tuned by Coulomb coupling strength. The
proposal may have potential application in optical communcation and nonlinear
optics.
