Fig. 3: Vibrational characterization of μHSRs.

a Schematic of the experimental setup for piezoelectric driving and optical sensing of the μHSR. b The amplitude and phase spectrum of the μHSR without a metal coating in the range of 2 to 10 kHz, showing different resonance modes and corresponding simulation results of eigenfrequencies. c Ring-down plot of the μHSR without a metal coating and its envelope fitting. d Frequencies of the \(m=2\) degenerate modes and the split (\(\Delta f\)) between them; the insets on the right show their mode shapes simulated by COMSOL Multiphysics software. To better illustrate the difference between the primary and secondary modes in the direction of vibration, the exact same angle is inserted into the background of the graph. e Ring-down plot of the μHSR with a metal coating and its envelope fitting