Even nanomechanical modes transduced by integrated photonics

We demonstrate the actuation and detection of even flexural vibrational modes of a doubly clamped nanomechanical resonator using an integrated photonics transduction scheme. The doubly clamped beam is formed by releasing a straight section of an optical racetrack resonator from the underlying silicon dioxide layer, and a step is fabricated in the substrate beneath the beam. The step causes uneven force and responsivity distribution along the device length, permitting excitation and detection of even modes of vibration. This is achieved while retaining transduction capability for odd modes. The devices are actuated via optical force applied with a pump laser. The displacement sensitivities of the first through third modes, as obtained from the thermomechanical noise floor, are 228 fm Hz^−1/2, 153 fm Hz^−1/2, and 112 fm Hz^−1/2, respectively. The excitation efficiency for these modes is compared and modeled based on integration of the uneven forces over the mode shapes. While the excitation efficiency for the first three modes is approximately the same when the step occurs at about 38% of the beam length, the ability to tune the modal efficiency of transduction by choosing the step position is discussed. The overall optical force on each mode is approximately 0.4 pN μm⁻¹ mW⁻¹, for an applied optical power of 0.07 mW. We show a potential application that uses the resonant frequencies of the first two vibrational modes of a buckled beam to measure the stress in the silicon device layer, estimated to be 106 MPa. We anticipate that the observation of the second mode of vibration using our integrated photonics approach will be useful in future mass sensing experiments