Even nanomechanical modes transduced by integrated photonics

Abstract

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.

Single laser modulated drive and detection of a nano-optomechanical cantilever

“…17 The SLMDD setup operates similarly to a traditional NOMS pump/probe system, but instead of using a separate probe laser with a constant output power this probe laser is power modulated to coherently drive the nanomechanical resonator through an optical gradient force. 6,18 This is distinct from dynamic backaction mechanical amplification where a single laser uses the relationship between optical radiation pressure and mechanical deformation of the cavity to transfer power to the mechanical mode. 19,20 SLMDD has the advantage that the resonator can be driven at a broader range of laser detuning values.…”

Optical forces through the effective refractive index

“…Due to their computational simplicity, the two expressions based on derivative of the effective index have been largely applied to calculate the optical force in nano-optomechanical devices; for instance, Eq. ( 9) was used in [5,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and Eq. ( 13) in [6-9, 16, 33-46].…”

“…(9) was used in [5,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and Eq. (13) in [6-9, 16, 33-46].…”

Intermodal Coupling as a Probe for Detecting Nanomechanical Modes

“…For instance, at higher frequencies, readout schemes tend to get inefficient, e.g., due to increased parasitic capacitive coupling [26]. Moreover, the motion of particular modes may fail to induce a discernible change in the readout transducer; for instance, the readout signal for even-parity modes is canceled out in magnetomotive [27] and optomechanical [28] detection techniques.…”