| Contemporary scientists are continuing to eclipse imagination in the minuteness of structures that they can engineer. This trend is true also in the discipline of physical sensors, where smaller sensors respond to minute changes in conditions. The more susceptible that devices are to effects which are intended to be measured, so are they to effects of randomness. At the nano- and micro- scale these converging trends reveal a complex trade-off. In the sensor community, sensitivity is paramount. Will noise effects limit the sensitivity inherent in smaller devices? This work explores a class of devices, cantilevers, which have been instrumental to the progress of resonant sensors. Resonance is the amplification of a signal due to a strong disposition of a structure to respond to certain frequencies. The great majority of work in this area assumes the operating range limited to amplitudes at which linear effects greatly dominate nonlinear effects. With some exceptions, the description of these nonlinearities can be approximated by a cubic nonlinearity. This work questions the prejudice that sensitivity of resonant cantilevers and even resonators in general, is maximized in the regime of relatively small amplitude oscillations where the non-linear terms can be ignored. One such method of operation that oversteps linear limits is so called parametric resonance. This is the time periodic variation of a system parameter that, under certain conditions, creates a linear instability. The instability results in oscillation amplitudes that are limited only by system nonlinearities and can produce oscillations far greater in magnitude than predominant linear sensing techniques. The fundamental limit to stochastic processes in such systems is accepted as being thermomechanical fluctuations. It is in this limit that we analytically examine the benefits of using the intrinsically nonlinear spectral features of parametric resonance as a sensing technique. Experimentally, upon demonstrating a cantilever design which exhibits parametric resonance and can be driven and sensed electronically, we present convincing results that testify to the promise of using such a nonlinear sensing technique. That is, we report 1 part in 10 million frequency resolution, or the resolution to which one can measure the resonant frequency of an oscillator. |
