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We present a Hamiltonian model describing two pairs of mechanical and opticalmodes under standard optomechanical interaction. The vibrational modes aremechanically isolated from each other and the optical modes coupleevanescently. We recover the ranges for variables of interest, such asmechanical and optical resonant frequencies and naked coupling strengths, usinga finite element model for a standard experimental realization. We show thatthe quantum model, under this parameter range and external optical driving, maybe approximated into parametric interaction models for all involved modes. Asan example, we study the effect of detuning in the optical resonant frequenciesmodes and optical driving resolved to mechanical sidebands and show an opticalbeam splitter with interaction strength dressed by the mechanical excitationnumber, a mechanical bidirectional coupler, and a two-mode mechanical squeezerwhere the optical state mediates the interaction strength between themechanical modes.

Optical coupling control of isolated mechanical resonators