Browsing by Author "Epstein, Stephen David"

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    The stochastic dynamics of a nanobeam near an optomechanical resonator in a viscous fluid
    Epstein, Stephen David; Paul, Mark R. (American Institute of Physics, 2013-10-14)
    We quantify the Brownian driven, stochastic dynamics of an elastic nanobeam immersed in a viscous fluid that is partially wrapped around a microdisk optical resonator. This configuration has been proposed as an optomechanical and nanoscale analog of the atomic force microscope [Srinivasan et al., Nano Lett. 11, 791 ( 2011)]. A small gap between the nanobeam and microdisk is necessary for the optomechanical transduction of the mechanical motion of the nanobeam. We compute the stochastic dynamics of the nanobeam in fluid for the precise conditions of the laboratory using deterministic finite element simulations and the fluctuation dissipation theorem. We investigate the dynamics of a nanobeam in water and in air and quantify the significance of the fluid-solid interaction between the nanobeam and the optical resonator. Our results in air show that, despite the complex geometry of the nanobeam, it can still be represented approximately as a damped simple harmonic oscillator. On the other hand, when the nanobeam is immersed in water there are significant deviations from the dynamics of a simple harmonic oscillator. The small gap between the nanobeam and the microdisk is found to be a significant source of additional dissipation. In air, the quality factor of the mechanical oscillation of the nanobeam is reduced by an order of magnitude due to the presence of the microdisk, however, the dynamics remain underdamped even in the presence of the microdisk. On the other hand, when placed in water, the dynamics without the microdisk is underdamped and with the microdisk the dynamics become strongly over damped. (C) 2013 AIP Publishing LLC.
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    The Stochastic Dynamics of Optomechanical Sensors for Atomic Force Microscopy
    Epstein, Stephen David (Virginia Tech, 2013-08-28)
    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.