【作者】 田野；

【导师】 Joel Moser；

【作者基本信息】 苏州大学 ， 光学工程（专业学位）， 2021， 硕士

【摘要】 纳米机械谐振器对外界激发具有独特而有趣的响应,因此引起了人们的广泛关注。即使在激发力较弱的情况下,谐振器的弹性系数和阻尼率都取决于它们的振动幅度。这种行为可以用一个运动方程来模拟,在这个方程中,保守回复力和耗散力都可以表示为振动振幅的多项展开式,其中具有不可忽略的高阶系数。这种非线性响应可以应用于多种实际需求中,例如利用非线性纳米机械的共振现象对微弱信号进行放大,以及在纳米机械相位态中进行信息编码等。非线性响应也有助于探索复杂非线性物理学中的基本问题,因为研究者可以对单个隔离良好的非线性振动模式进行按需设计和操控。本论文的研究对象是参数纳米机械谐振器的非线性响应。我们重点研究了基模在共振驱动力和线性弹簧参数调制共同作用下的非线性响应,所使用的参数调制频率接近纳米谐振器谐振频率的两倍。具体研究内容如下:(1)通过对快速波动进行平均和对在衰荡时间尺度上的慢响应进行计算,得出了谐振器的理论响应特征。并使用一个理论模型来分析参数谐振器的非线性响应情况,该谐振器中的振动元件是悬浮的石墨烯薄片。提出了一种在石墨烯器件中进行信息编码的方法,该方法利用参数状态的迟滞响应来控制非线性振动的相位。(2)基于悬浮的数层石墨烯薄膜,制备出了纳米机械器件。器件的特点是在石墨烯下面布置了一个局部电极,该电极既可以作为栅极来驱动石墨烯发生振动,又可以作为薄膜振动的光学检测方案中的一个高反射镜。(3)测量了石墨烯谐振器的非线性响应,并对参数谐振器的响应进行了初步测量。更多还原

【Abstract】 Nanomechanical resonators have attracted much attention because of their unusual and interesting ways of responding to excitations.Namely,their spring constant and their damping rate both depend on the amplitude of their vibrations,even where the exciting force is weak.This behavior can be modeled by an equation of motion in which both the conservative restoring force and the dissipative force are polynomial expansions of the vibrational amplitude with nonnegligible higher order coefficients.Such a nonlinear response can be used to answer practical needs,including the amplification of weak signals using nonlinear nanomechanical resonances and the encoding of information in nanomechical phase states.The nonlinear response is also useful to explore fundamental problems in complex nonlinear physics,because single and well isolated nonlinear vibrational modes can be engineered and controlled.The topic of this work is the response of a nonlinear parametric nanomechanical resonator.Namely,we focus on the nonlinear response of the fundamental mode in the presence of a resonant driving force and a parametric modulation of the linear spring constant near twice the resonant frequency of the mode.The research contents are as followings:(1)We derive the theoretical response of the resonator by averaging fast fluctuations and calculating the slow response on a time scale of the ringdown time.We use our calculations to model a nonlinear parametric resonator where the vibrating element is a suspended graphene sheet.We propose a method to encode information in our graphene device.The latter is based on controlling the phase of nonlinear vibrations using the hysteretic response of parametric states.(2)We nanofabricate nanomechanical devices based on suspended few layer graphene.The specificity of our devices is the presence of a local electrode underneath graphene that we use both as a gate electrode to drive vibrations and as a highly reflective mirror for optical measurement of vibrations.(3)We present preliminary measurements of nonlinear response of the graphene resonators and the these devices used as parametric resonators.更多还原