  We present a Hamiltonian model describing two pairs of mechanical and optical
modes under standard optomechanical interaction. The vibrational modes are
mechanically isolated from each other and the optical modes couple
evanescently. We recover the ranges for variables of interest, such as
mechanical and optical resonant frequencies and naked coupling strengths, using
a finite element model for a standard experimental realization. We show that
the quantum model, under this parameter range and external optical driving, may
be approximated into parametric interaction models for all involved modes. As
an example, we study the effect of detuning in the optical resonant frequencies
modes and optical driving resolved to mechanical sidebands and show an optical
beam splitter with interaction strength dressed by the mechanical excitation
number, a mechanical bidirectional coupler, and a two-mode mechanical squeezer
where the optical state mediates the interaction strength between the
mechanical modes.
