Determining the orientation of the flexural modes of a thermally driven microwire cantilever

Mechanical resonators are excellent transducers for ultrasensitive detection applications. Recent advances such as vectorial force sensing and ultrahigh-resolution mass spectra rely on the identification of two flexural vibrational modes of a resonator. The orientations of the flexural modes with respect to the incident optical axis are crucial parameters for a cantilevered resonator. Previous methods have adopted complex experimental setups using quadrant photodetectors or have required simultaneous detection of two flexural modes of the cantilever. In this paper, we propose a method for determination of the orientations of the flexural vibrations of a cantilever using a microlens optical fiber interferometer that takes both the light interference and the lateral light scattering of the cantilever into account. We demonstrated the method by experimentally determining the orientation of the first three flexural vibrational modes of a thermally driven microwire. Our method can be used to characterize individual flexural modes with arbitrary orientations and thus provides a new tool for detecting vectorial forces.