Isolation of optomechanical nonlinearities in nanomechanical cantilevers

Abstract

In this paper we study the nonlinearities present in a nano-optomechanical system consisting of a cantilever coupled to a racetrack resonator. We show that higher-order harmonics in the mechanical frequency spectrum are indicative of a readout nonlinearity and we connect these harmonics to the optical cavity transmission with detuning function and its derivatives. We also show that there are optical force nonlinearities that cause a Duffing-type response in the driven mechanical signal. The Duffing-type nonlinearity produces a nonlinear softening when the probe laser is blue detuned, and a nonlinear stiffening when the probe laser is red detuned. The optical force and readout nonlinearities are difficult to separate using a purely experimental approach. We demonstrate the use of a numerical model of the pump-and-probe system to analyze the nonlinearities independently. The numerical model also allows us to estimate the amplitude of the system, predicting the exact detuning where nonlinearities cancel each other to produce higher critical amplitude, and ultimately gives a prospective mass sensitivity level of $83\phantom{\rule{0.28em}{0ex}}\mathrm{yg}/{\mathrm{Hz}}^{1/2}$. The numerical model provides a rich understanding of the complexities of the nano-optomechanical system and is much needed for the development of sensors with increased dynamic range and overall performance.