Theoretical Modeling of Frequency Combs Generated in Piezoelectric Nanomechanical Resonators
Author(s)
Fang, Yifan
Advisor(s)
Ansari, Azadeh
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Abstract
Frequency combs have been widely used for optical spectroscopy, atomic clocks and quantum optics. While most of the previous work had focused on optical or optomechanical frequency combs, recent research shows great interest in phononic frequency combs, with a fully-mechanical signal generation process. The proposed research is the theoretical modeling of the experimentally-observed phononic frequency combs in the piezoelectric NEMS membrane resonator using two coupled resonance modes.
Beginning with a physical interpretation of the generation of cubic geometric nonlinearity term from the Euler-Bernoulli equation, the nonlinearity coefficient of our fixed dimension membrane resonator is calculated in mode (0,1) and mode (1,1). The numerical solution of a single mode forced cubic duffing nonlinear oscillation is used for fitting the experimental data. By applying the pumping frequency that equals to the summation of two coupled resonant frequencies, multiple frequency combs with wide frequency range are generated. In addition, an evolution of the signal pattern and the relationship between the frequency spacing (∆f) and the pumping power are observed, which are also demonstrated in the experiments.
It is proven that equations with cubic geometric nonlinearity terms and simple coupling terms can describe the dynamic of phononic frequency combs in the piezoelectric NEMS membrane resonators. Using the Newtonian method that utilizes the physical meaning of each term, a better understanding of the piezoelectric NEMS membrane resonator is achieved in this work.
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Date
2023-05-02
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