声光子晶体尺度效应对声光耦合影响机理研究

The phoxonic crystal can open phononic and photonic band gaps simultaneously. It has broad application prospects in the field of quantum computing, quantum communications and high precision sensors. How to obtain high quality factor and high light-sound coupling rate is a hot and difficult problem to be solved in the research of phoxonic crystal. The introduction of nanoscale defect, including cavity and waveguide, can enhance light-sound coupling. Up to now, study of phoxonic crystal was limited to one-way light-sound coupling. Moreover, size effect of nanoscale defects on light-sound interaction has not been involved. Therefore, mechanism of light-sound interaction enhanced by defects was still lack of accurate and quantitative analysis. Based on nonlocal elastic theory and nonlocal electromagnetic theory, this research will propose governing equations on two-way light-sound interaction with high-order nonlinearity for the phoxonic crystal with nano period and nano defects. The finite element model with weak form is further built basing on the principle of virtual displacement and variational method. The high-order nonlinearity and size effect are calculated by multiple time scale method and moving mesh method. The influence of size effect on light-sound interaction will be studied. The coupling theory and numerical methods will be developed. Taking quality factor and light-sound coupling rate as the target functions, the parameters of the model will be optimized by pixel method and energy method. The study aims to seek inherent mechanism of light-sound interaction enhanced by defects, and to provide a theoretical basis for designing phoxonic crystals with high performance.

声光子晶体具有声光子双谱带隙，在量子计算、量子通讯和高精密传感器等领域有广阔的应用前景。如何获得高品质因子和高声光耦合率是声光子晶体研究亟待解决的热点和难点问题。将纳米缺陷（腔体或波导）引入声光子晶体可增强声光耦合。但目前声光子晶体研究局限于声对光的单向耦合，且没有涉及尺度效应对声光耦合作用的影响，纳米缺陷对声光耦合作用增强机理尚缺乏准确的定量分析。本课题将基于非局部弹性理论和非局部电磁理论，建立研究纳米周期和纳米缺陷声光子晶体的声光高阶非线性双向耦合方程。应用虚位移原理和变分法，建立弱形式的有限元模型，应用多时间尺度法和动网格法，计算声光高阶非线性双向耦合效应和尺度效应。研究尺度效应对声光耦合作用的影响，发展相应的耦合理论和数值计算方法。结合像素法和能量法，以品质因子和声光耦合率为目标函数优化模型参数。寻求纳米缺陷增强声光耦合作用的内在机理，为设计高性能的声光子晶体提供理论基础。

声光子晶体具有声光子双谱带隙，在光致冷却、光诱导透明、高品质因子谐振器和高精密传感器等领域具有广阔的应用前景。如何获得高品质因子和高声光耦合率是声光子晶体研究亟待解决的热点和难点问题。将纳米缺陷（腔体或波导）引入声光子晶体可使得声子和光子局限于缺陷中相互作用，从而增强声光耦合。但目前声光子晶体研究没有涉及尺度效应对声光子能带及声光耦合作用的影响，纳米缺陷对声光耦合作用增强机理尚缺乏准确的定量分析。.本项目基于非局部弹性理论和电磁理论，建立了超宽带隙的声光子晶体模型，研究了缺陷模态的对称性。阐明了二维声光缺陷态的对称性对声光耦合的影响规律。优化设计了强声光耦合的声光子晶体腔结构。确定了三维声光子晶体最优厚度。.阐明了联合对称性对线性和非线性声光耦合作用的影响规律。提出了摄动理论和有限元法高精高效的声光耦合计算方法。发现了缺陷层厚度具有模态对称性调节作用的现象。阐明了缺陷层厚度调节光学缺陷态频率的规律。揭示了缺陷层厚度调节二次非线性耦合强度的机理，阐明了波数对耦合强度的影响规律。.设计了室温下工作的高Q值GHz纳米机械谐振器。提出了渐变型光力腔的设计方法。揭示了声光谐振器室温下高Q值的产生机理。.推导了基于非局部应变梯度理论的声子晶体偏微分波动方程。建立了求解非局部波动方程的有限元模型。阐明了尺度效应对声子晶体能带结构的影响规律。揭示了尺度效应和厚度效应对第一带隙的影响机制。阐明了尺度效应对缺陷态的影响规律。.给出了七大晶系32种点群晶体的独立和非独立材料常数分量之间的关系。揭示了晶体三阶压电常数和介电常数为0的机理。建立了研究温度引起频率漂移的压电控制方程。设计了一个具有温度补偿层的SAW谐振器模型，降低了器件的频率-温度系数。提出了获得声表面波器件COM参数的方法。推导了二次超谐波效应的控制方程。揭示了声表面波器件非线性行为的产生机理。发明了一种步进型压电驱动器。提出了Workbench和APDL联合计算模拟的新方法。

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