Detecting the motion of a microresonator via mode-mode interaction

We demonstrate that a flexural resonance mode of a clamped-clamped beam resonator can be measured by using another resonance mode of the same resonator as a detector. The detector mode and the mode to be detected are coupled through the beam displacement. Displacement of the resonance mode to be measured introduces tension in the beam, which gives rise to an upwards shift in the resonance frequency of the detector mode. We experimentally show that this mechanism can be used to detect the first and second resonance mode of a silicon beam resonator. The modal interaction can also be used to increase the dynamic range of the resonator.