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. / Master of Science

Magnetic sensors are widely used in the field of mineral, navigational, automotive, medical, industrial, military, and consumer electronics. Many magnetic sensors have been developed that are generated by specific laws or phenomena: such as search-coil, fluxgate, Hall Effect, anisotropic magnetoresistance (AMR), giant magnetoresistance (GMR), magnetoelectric (ME), magnetodiode, magnetotransictor, fiber-optic, optical pump, superconducting quantum interference device (SQUID), etc. Each of these magnetic field sensors has their merits and application areas. For low power consumption (<10uW), quasi-static frequency (<10Hz) and high sensitivity (<nT) application, magnetoelectric laminate sensors offer the best potential capability and thus are the topic of my dissertation. Here, in this thesis, I have focused on designs and optimizations of magnetoelectric sensor units (i.e., sensors and circuit). To achieve my goals, I have developed some useful rules for ME sensor and detection circuit design. For ME sensor optimization, designs should consider both frequencies far away from resonance and at resonance. For the former one, both internal and external noise contribution must be considered, as one of them will limit practical applications. With regards to the internal noise sources, I have developed two design optimization methods, designated as ”'scale effect” and “ME array”. I showed that they have the ability to increase the magnetic field detection sensitivity, which was verified by experiments. With regard to external noise consideration, I have investigated how the fundamental extrinsic noise sources (temperature fluctuation, vibration, etc) affect ME laminate sensors. A concept of separating signal and noise modes into difference is put forward. Optimization with this concept in mind required us to redesign the internal structure of ME laminate sensors. At the resonant frequency, the ME voltage coefficient α_ME is the most important parameter. To enhance resonant gain in α_ME, I have developed a three phase laminate concept, which is based on increasing the effective mechanical factor Q while reducing the resonant frequency. A ME voltage coefficient of α_ME ~40V/cm.Oe has been achieved at resonance, which is about 2x higher than that of a conventional bending mode. Investigations of detection circuit optimization were also performed. Component selection strategies and a new charge topology were considered. Proper component values were required to optimize the charge detection scheme. It was also found, under some specific conditions to satisfy the circuit stability, that if the lowest required measurement frequency of the charge source was f1, then that it was not necessary to make the high corner frequency <i>f</i>_p of the charge amplifier lower than <i>f</i>₁: as doing so would decrease the system's signal-to-noise ratio (SNR). A high pass, high order filter placed behind the charge amplifier was found to increase the charge sensitivity, as it narrows the intrinsic noise bandwidth and decreases the output noise contribution, while only slightly affecting the signal's output amplitude. Prototype ME unit were also constructed, and their noise level simulated by Pspice. Experimental results showed that prototypes ME unit can reach their detection limit. In addition, a new magneto-electric coupling mechanism was also found, which had a giant ME effect. / Ph. D.