Near-field optical techniques exploit light-matter interactions at small length scales for mechanical sensing and actuation of nanomechanical structures. Here, we study the optical interaction between two mechanical oscillators - a plasmonic nanofocusing probe-tip supported by a low frequency cantilever, and a high frequency nanomechanical resonator - and leverage their interaction for local detection of mechanical vibrations. The plasmonic nanofocusing probe provides a confined optical source to enhance the interaction between the two oscillators. Dynamic perturbation of the optical cavity between the probe-tip and the resonator leads to nonlinear modulation of the scattered light intensity at the sum and difference of their frequencies. This double-frequency demodulation scheme is explored to suppress unwanted background and to detect mechanical vibrations with a minimum detectable displacement sensitivity of 0.45 pm/Hz1/2, which is limited by shot noise and electrical noise. We explore the demodulation scheme for imaging the bending vibration mode shape of the resonator with a lateral spatial resolution of 20 nm. We also demonstrate the time-resolved aspect of the local optical interaction by recording the ring-down vibrations of the resonator at frequencies of up to 129 MHz. The near-field optical technique is promising for studying dynamic mechanical processes in individual nanostructures.
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