【作者】 李静；

【导师】 吴福根；

【作者基本信息】 广东工业大学 ， 电子科学与技术， 2015， 硕士

【摘要】 声子晶体,作为一种新型的人工周期结构,它是在天然晶体和光子晶体的研究基础上提出的新概念。目前在机械振动、集成声学及声通信等领域有着极其广泛的应用前景。最近几年,光子晶体的异常色散引起了研究工作者的极大兴趣,主要包括负折射、声聚焦和自准直等效应。其中,自准直效应因其低损耗、无通道等优点,为集成光学器件的声波操控提供了一种新方法。基于自准直效应的光子晶体波导、分束器、干涉仪等器件的研究已取得重要进展,而声子晶体自准直效应方面的理论和应用探索才刚刚开始。针对目前光子晶体及声子晶体中自准直效应的研究现状,本文主要对自准直效应相关概念进行了介绍,并对其在二维声子晶体中的应用进行了系统分析和深入研究。采用有限元方法,本文主要完成以下几方面的工作。(1)从两个基本概念原理(群速度与等频线的联系、Snell波矢守恒定律)出发,分析了在倒格矢空间中光波的折射,从而引入自准直效应的原理。分析光子晶体中光波的自准直传播和自准直光波发生90°转弯的三个机理。(2)提出并设计了两种声子晶体自准直声波分束器,分别采用了圆形钢柱置于水中(模型一)和正方钢柱置于水中(模型二)两种声子晶体模型。首先在模型一中通过改变对角线方向圆形钢柱的尺寸引入线缺陷结构,设计了第一种声子晶体声波分束器。接着在模型二中改变对角线方向方形钢柱的方位构成线缺陷结构,设计了第二种声子晶体声波分束器。结果显示,改变缺陷圆柱体的半径或者缺陷方柱体的方位,均可实现声波分束效率的大范围调节。设计的两种分束器结构紧凑,声波分束方式更灵活。对于方柱体模型,我们另外研究了方柱体的边长对声传播特性的影响：当边长在一定范围内增大时,声传播的全反/透射范围减小/增大,且半反半透点与边长呈近线性的关系。(3)研究了基于自准直效应的定向辐射：基元方位对定向辐射频率的影响。首先基于自准直效应确定了定向辐射源的定向频率。然后改变基元方位,研究了基元方位的变化对等频线的影响。计算结果表明,定向辐射频率值随基元方位不断变化,但其对应的等频线的法线方向却保持不变。而后通过声场分布直观地验证了这一性质。这一特点的潜在应用是声波器件的调频。除此之外,我们还探究了对所提出结构进行剪裁之后对声场分布的影响。当沿+45°方向剪裁声子晶体的一角,发现基元方位取定θ=450时,剪裁一角的出射声波能够明显压制其他三个角的出射声波,而在其他基元方位处则无此现象。这将帮助我们进一步加深对声子晶体中定向辐射的理解。以上三方面的研究,将自准直效应的研究推广到声子晶体中。通过理论分析和有限元仿真,进一步证明了自准直效应在声子晶体中的有效性和可行性,为异常色散在声子晶体中的理论及应用研究提供了新的思路。更多还原

【Abstract】 As a kind of new artificial periodic material, phononic crystal was proposed by analogy with natural crystal and photonic crystal. It has potential application prospects in many fields such as mechanical vibration, integrated acoustics and acoustic communication. In recent years, the anomalous dispersion in photonic crystal has attracted lots of interest, due to their unique properties in passing band. The unique properties include negative refraction, sonic focusing, and self-collimation effect. Of which, the latter provides a new method to manipulate the light waves in integrated optical device. Compared with the conventional waveguides, self-collirnation-based wave propagation is much better, because of no coupling and reflection losses. Great progress has been made in designing light devices based on self-collimation effect, such as channelless waveguide, beam splitter and interferometers. However, the researches of theory and application on self-collimation effect in phononic crystal are just beginning.According to the present research situation on photonic crystal and phononic crystal, we analyze the self-collimation effect systematically in the paper. Meanwhile, we explore the possible applications of self-collimation effect in phononic crystal. Using finite element method, we have studied the following several aspects in this paper.(1) Proceeded from two basic conceptions (group velocity and equi-frequency contour line) at first, we analyze the refraction phenomena of light waves in the reciprocal lattice space. The principle of self-collimation effect is then introduced. We analyze the propagation of self-collimation-based light waves in photonic crystal.(2) Two kinds of acoustic beam splitters are proposed. The two-dimensional (2D) PC employed herein comprises rigid steel rods arranged in a square lattice and immersed in water. Circular and square steel rods are respectively adopted in model 1 and model 2. The acoustic beam splitter is formed by changing the rods’radius along with the diagonal direction of model 1, or changing the rods’orientation along with the diagonal direction of model 2. The calculated results show that the splitting efficiency of two splitters can be controlled by changing the radii of the circle rods or the orientations of the square rods. The two splitters we proposed are compact-sized and flexible to split. Moreover, for model 2, we have discussed the acoustic propagation phenomenon when the length of the square rods is changed. The results show that the total transmission/reflection range decreases/increases as the side length increases. In addition, there is a quasi-linear relationship between the orientation of the transflective point and the square rods’length.(3) We investigate the acoustic directional radiation based on self-collimation effect How the rods’orientation affects the directional radiation frequency. Firstly, we calculate the equi-frequency contour line with different rods’orientations. The results show that the directional radiation frequency changed with the changing of rods’orientation. But the corresponding normal direction keeps steady in the changing process which means the propagation direction of acoustic waves keeps unchanging. We can see the results clearly through the acoustic field distributions. The finding will apply to tuning the frequency of acoustic wave device. Besides, we also study the effect of structure truncating on acoustic fields distribution. We truncate the corner of the structure along +45° direction with different orientation cases. The results show that when rods’rotating angle θ=45°, the radiation branch along+45° suppresses other three branches while there are no similar results in other rotating angle. The finding will help us understand the acoustic directional further.These three aspects of the study illustrated that it is possible to research the self-collimation in phononic crystal. The theory analysis and the simulation results demonstrated that this subject is effective and feasible. The paper provides a new idea for the research of anomalous dispersion in phononic crystal.更多还原