【作者】 姚凌江；

【导师】 彭景翠；

【作者基本信息】 湖南大学 ， 理论物理， 2005， 硕士

【摘要】 1987年Yablonovitch和John同时提出光子晶体这一概念，Yablonovitch指出有可能实现光子频率带隙和局域缺陷模以及许多光电技术方面的应用，John则讨论了在无序光子晶体中电磁波的强烈局域现象，并预言在光子晶体中存在许多有趣的量子光学现象，诸如光子局域态，自发辐射的非指数衰减。自1987年以来，很多研究人员试图去实现光子晶体中频率带隙和局域缺陷模以及其它一些光学特性。由于光子晶体是人造晶体，因此设计和制造光子晶体就成了研究的焦点。人们往往借助计算机进行精确的计算，来设计光子晶体结构，并致力于制造新的光子晶体并测试它们的特性。 这篇论文分析了二维方型光子晶体的带结构特性，因为二维方型光子晶体较容易制作并且很合适制作各种波导器件。 首先，对二维光子晶体的电磁波理论及周期介质中的Bloch波解作了详细的推导，给出了光子晶体中的禁带存在的理论依据，同时以正方晶格的二维光子晶体为例，用平面波展开方法计算了正方格子式二维光子晶体的频率带结构，并且分析了禁带随介质填充因子的变化关系，讨论了禁带随介质填充因子，介电常数的变化。并且在光子晶体中引入缺陷后，完全光子禁带中就出现相应的局域模，引入平面波导就能导光，给出了二维方型光子晶体的波导的TM模的电场分布。 其次，设计了一种二维方型旋转正四边形直柱光子晶体，这种结构降低了光子晶体的对称性。通过运用平面波展开方法以及有限差分时域(FDTD)方法进行分析，可以明显地发现，在低频和高频区域增大了光子晶体的光子禁带。在填充率f=0.5左右的情形下，计算了空气中的A1材料的旋转四边形直柱光子晶体的带结构。我们发现，在f=0.5才存在完全光子禁带，旋转角度为45度时，完全光子禁带最大，旋转角度为0度时，光子禁带位于高频区域。还运用FDTD方法检验了计算结果，并分析了旋转角旋转角度为45度时，正四边形直柱光子晶体的波导特性以及TM模的电场分布。 利用平面波方法分析了二维光子晶体的波导特性(色散关系和态密度)，得到二维光子晶体线缺陷所形成的波导模式的色散关系。由于波导边界的周期性，某些波长的光会被波导反射回去，还会出现微禁带。通过恰当地构建波导边界和波导宽度，就可实现光子晶体的导光和滤波作用。更多还原

【Abstract】 In 1987, a remarkble step was made by Yablonovitch and John, who pointed out the possibility of the realization of photonic band gaps, localized defect modes, and their applications to various optoelectronic devices, and by John who discussed the strong localization of electromagnetic waves in disordered photonic crystals and also predicted many interesting quantum optical phenomena that can be realized in photonic crystals such as the bound state of photons and non-exponential decay of spontaneous emission. Since 1987, many researchers have been engaged in the realization of photonic band gaps, localized defect modes, and other optical properties peculiar to the photonic crystals. Because photonic crystals are artificial crystals, it is our studying issue to design and fabricate the photonic crystals. Many accurate numerical calculations could be performed thanks to the development of computing facilities. These calculations were really useful for the design of the photonic crystal structures. As for the experiment studies, many researchers in various fields have been collaborating to make new photonic crystals and measure their properties.Two-dimensional photonic crystals have been studied, since they are easier to fabricate and may be employed in waveguide configurations. First, we give a complete deduction for the electromagnetic wave theory of photonic crystal of two dimensions and Bloch wave solution in stratified periodic dielectric, offer the academic foundation of the existence of band gap. Second, we demonstrate that dielectric pods in air background can generate a common band gap, which is called absolute photonic band gap, for both orthogonal TE and TM mode. At last, we design a U-waveguide, and give the energy distribution of the TM mode.Designing a two-dimensional photonic crystal of square lattice with rotating square cylinders, which the structural symmetry is reduced, we have found a larger absolute band gap in the low and high frequency. By using the plane wave expansion and finite-different time-domain (FDTD) methods, we can find a larger absolute band gap in the low and high frequency. When/is about 0.5, we get the photonic band structure of a two-dimensional photonic crystals of square lattice with rotating square cylinders. There is a band gap when f=0.5. A maximum absolute PBG exists while θ = 45° and the absolute PBG lies in the high frequency range for θ = 0°. Furthermore, the FDTD method is applied for examining and analyzing the waveguide characteristics and theelectric field distribution of TE mode of 2-D photonic crystals created by a square lattice with square cylinders while θ = 45°.The characteristics (dispersion relation and photonic density of states) of thewaveguide modes of photonic crystal are investigated using plane-wave method. We obtain the dispersion relation and photonic density of states for the waveguide modes created in a two dimension photonic crystals. Because of the periodic nature of the waveguide boundary, photonic crystal waveguide exhibits the behavior similar to fiber Bragg gratings, in that the particular wavelengths can be strongly reflected from the waveguide. They have been termed "mini-stop bands". Thus by correct engineering of the periodicity of the side walls and the waveguide width, both waveguiding and filtering action can be achieved.更多还原