This work explores the stochastic dynamics and important diagnostics of a mechanical resonator (nanobeam) used in cavity optomechanical sensors for atomic force microscopy. Atomic force microscopy (AFM) is a tool to image surface topology down to the level of individual atoms. Conventional AFM has been an essential tool for micro and nanoscale studies in physics, chemistry, and biology. Cavity optomechanical sensors for AFM extend the utility of conventional AFM into a new regime of high sensitivity k is approximately 1 N/m and high frequency f0 is approximately 10 MHz. Cavity optomechanical sensors for AFM are unique because they use near field optics to transduce the position of a nanobeam. The nanobeam is not able to be transduced by more conventional AFM techniques, such as laser interferometry, because the nanobeam is smaller than the spot size of the laser.

This work determines the noise spectrum G of a nanobeam in water and in air. Also important diagnostics of the nanobeam are determined in air and in water. These important diagnostics include the quality factor Q and natural frequency in fluid omega_f. It is found that the nanobeam is overdamped in water. However, the nanobeam is underdamped in air and has quality factor of Q is approximately 4. The noise spectrum is determined from deterministic numerical calculations and the Fluctuation-Dissipation Theorem. This is possible because the same molecular processes, Brownian motion, cause both the fluctuations of the nanobeam and the dissipation of the nanobeam.