  We consider an optomechanical cavity made by two moving mirrors which
contains a Kerr-down conversion nonlinear crystal. We show that the coherent
oscillations of the two mechanical oscil- lators can lead to splitting in the
electromagnetically induced transparency (EIT) resonance, and appearance of an
absorption peak within the transparency window. In this configuration the
coher- ent induced splitting of EIT is similar to driving a hyperfine
transition in an atomic Lambda-type three-level system by a radio-frequency or
microwave field. Also, we show that the presence of non- linearity provides an
additional flexibility for adjusting the width of the transparency windows. The
combination of an additional mechanical mode and the nonlinear crystal suggests
new possibilities for adjusting the resonance frequency, the width and the
spectral positions of the EIT windows as well as the enhancement of the
absorption peak within the transparency window.
