【作者】 陶佳；

【导师】 陶智勇；

【作者基本信息】 哈尔滨工程大学 ， 光学工程， 2021， 硕士

【摘要】 相对于传统的Bragg共振,周期结构中模式更加复杂的Non-Bragg共振及其带隙内的缺陷态和局域化现象同样具有重要的研究意义和应用价值,可以实现各种光学功能器件如滤波器、全光开关、光纤传感和光纤通讯等的设计和应用。本文通过数值模拟和实验研究等方式对周期侧壁矩形起伏波导中模式相互作用和谱带结构的变化进行了研究和探讨。论文的主要内容如下:1、从波动方程出发,将侧壁周期起伏水槽类比二维矩形波导,借鉴晶体中的带隙机理来分析周期波导的谱带结构和色散关系。分别用微扰法和平面波展开法对侧壁周期小起伏波导(侧壁余弦变化)和大起伏剧烈变化的波导(矩形起伏)进行了理论分析,得到发生Bragg共振和Non-Bragg共振的条件,并对不同情况下的禁带分布进行了详细的讨论。之后基于有限元思想,对数值仿真软件中侧壁周期起伏波导的建模过程进行了详细的介绍和说明。并搭建了一套振动激发和检测的实验系统,给出了实验系统详细的工作流程说明和优化方案,使其能够满足科学实验的要求。2、基于傅立叶分析和Floquet定理,推导了周期性起伏侧壁的波导中的色散关系,从侧壁对称性出发,推导给出了一种共振选择规则以识别禁带的特征,从而对共振发生的条件和种类进行描述,并利用平面波展开法对该选择规则进行了验证和分析。随后通过仿真模拟、数值计算和实验检测三种方法分别对侧壁结构的起伏相位差和占空比对波动传播特性的影响进行了研究和分析。结果表明,侧壁相位差的变化会导致低频Bragg禁带和高频Non-Bragg禁带不同的变化规律。当占空比变化时,Bragg禁带和Non-Bragg禁带的宽度都经历了产生、增强、衰减和消失的过程,但Non-Bragg禁带的中心频率会随占空比的增加向高频移动,而Bragg禁带的中心频率则不会发生改变。3、对侧壁起伏波导中引入缺陷元素后产生的缺陷态模式进行了分析和研究。通过Bragg缺陷态和Non-Bragg缺陷态的横向对比,分析研究了其中的谱带变化和这两种缺陷态的特性。研究结果表明,缺陷长度对于两种缺陷态的调控具有相似的频移特性。相比于Bragg缺陷态,Non-Bragg缺陷态存在于更小的禁带范围内,且Non-Bragg缺陷态对于水表面波的能量局域特性要比Bragg缺陷态更强烈,缺陷范围内所能局域的能量也更多。这种特殊的能量分布性质有益于波浪控制工程和海岸保护技术的应用。本文通过数值模拟和实验检测的方法对二维矩形波导中波的传播特性及缺陷态的调控进行了细致的分析和研究,研究结果对光学、声学、微波和太赫兹波等领域有重要参考价值,同时也为波控制工程中各种功能性设备的创新设计铺平道路。更多还原

【Abstract】 Compared with the traditional Bragg resonance,the more complex Non-Bragg resonance in the periodic structures and the defect state and localization phenomenon in the band gap also have important research significance and application value,which can realize the design and application of various optical functional devices such as filters,all-optical switches,optical fiber sensing and optical fiber communications.In this paper,numerical simulation and experimental research are used to study and discuss the mode interaction and the changes of the band structure in the rectangular waveguide with corrugated sidewalls.The main content of the paper is as follows:1.Starting from the wave equation,the sidewall periodic undulating channel is analogous to a two-dimensional rectangular waveguide,and the band gap mechanism in the crystal is used to analyze the band structure and dispersion relationship of the periodic waveguide.The perturbation method and the plane wave expansion method are used to theoretically analyze the waveguide with small periodic undulations on the sidewalls(cosine change of the sidewall)and the waveguide with large undulations and drastic changes(rectangular undulation),and the conditions for Bragg resonance and Non-Bragg resonance are obtained.And the distribution of the forbidden band in the waveguide under different conditions was discussed in detail.Then,based on the finite element idea,the modeling process of the waveguide with corrugated sidewalls in the numerical simulation software is introduced and explained in detail.A set of experimental system for vibration excitation and detection was built,and a detailed work flow description and optimization plan of the experimental system were given to enable it to meet the requirements of scientific experiments.2.Based on Fourier analysis and Floquet’s theorem,the dispersion relationship of wave propagation in the waveguide with periodically undulating sidewalls is derived.Starting from the symmetry of the sidewalls,we derive a resonance selection rule to identify the characteristics of the band gap.Thus,the conditions and types of resonance occurrence are described,and the selection rule is verified and analyzed by the plane wave expansion method.Simulation,numerical calculation and experimental testing were used to study and analyze the influence of the undulating phase difference and duty cycle of the sidewall structure on the wave propagation characteristics.The results show that the change of the sidewall phase difference will cause different changes of the low-frequency Bragg band gap and the highfrequency Non-Bragg band gap.When the duty cycle changes,the width of the Bragg forbidden band and the Non-Bragg forbidden band have undergone the process of generation,enhancement,attenuation and disappearance,but the center frequency of the Non-Bragg forbidden band will move to high frequency with the increase of duty cycle,and the center frequency of the Bragg forbidden band will not change.3.The defect states mode were analyzed and studied after introducing defect elements in the sidewall undulating waveguide.The band changes and the characteristics of the two defect states are analyzed and studied through the lateral comparison of Bragg defect state and NonBragg defect state.The research results show that defect length has similar frequency shift characteristics for the regulation of two defect states.Compared with the Bragg defect state,the Non-Bragg defect state exists in a smaller forbidden band,and Non-Bragg defect state has stronger energy localization characteristics for the water surface wave than the Bragg defect state and the local energy within the defect range is also more than the Bragg defect state.This special energy distribution property is beneficial to the application of wave control engineering and coastal protection technology.In this paper,numerical simulation and experimental detection methods are used to analyze and study the wave propagation characteristics and defect state control in a twodimensional rectangular waveguide.The research results not only have crucial references value to the fields of optics,acoustics,microwaves,and terahertz waves,but also pave the way for the innovative design of various functional equipment in wave control engineering.更多还原