  The nonlinear component of the optomechanical interaction between light and
mechanical vibration promises many exciting classical and quantum mechanical
applications, but is generally weak. Here we demonstrate enhancement of
nonlinear optomechanical measurement of mechanical motion by using pairs of
coupled optical and mechanical modes in a photonic crystal device. In the same
device we show linear optomechanical measurement with a strongly reduced input
power and reveal how both enhancements are related. Our design exploits
anisotropic mechanical elasticity to create strong coupling between mechanical
modes while not changing optical properties. Additional thermo-optic tuning of
the optical modes is performed with an auxiliary laser and a
thermally-optimised device design. We envision broad use of this enhancement
scheme in multimode phonon lasing, two-phonon heralding and eventually
nonlinear quantum optomechanics.
