Wide-field stroboscopic imaging of topologically protected phononic modes

Imaging spatial mode profiles is important for understanding the behavior of mechanical resonators. The recent development of phononic circuits has increased the demand for a fast imaging method based on principles of coherent detection. However, it becomes complicated to perform measurements on a large surface area. Here, we present a frequency-detuned collimated-beam interferometry measurement scheme with in-plane spatial resolution of about 6 um, which can provide information about the phase dynamics of the entire mechanical oscillation cycle on a time scale of a few seconds. We employ a stroboscopic pulse probing method to resolve high-frequency vibrational motion with a standard CMOS camera. We use this setup to image megahertz frequency resonant mode profiles present in a Valley-Hall topological triangular cavity, over an area of more than 20 mm2. We relate the obtained data to numerical simulations of the topological edge modes to reveal the relation between backscattering and the mode profile distribution. The presented protocol can become a staple for characterizing mesoscopic mechanical resonators.