【作者】 康学亮；

【导师】 李永平；

【作者基本信息】 中国科学技术大学 ， 光学， 2010， 博士

【摘要】 光子作为信息和能量的载体,具有高速性、大容量、抗干扰和低能耗等特点。所以,人们希望制造出集成光路来控制光子。作为集成光路中最为基本的组成元件,光子晶体和光学微腔应此需求被提出,正吸引着越来越多的科研工作者的兴趣。光子晶体是一种具有周期结构的光学介质。由于其具有光子禁带和光局域性等独特的性质和潜在的应用前景,在二十世纪八十年代末一经提出,就得到了人们的重视。如今,光子晶体的理论基础已经趋于完善,设计能够实现特定功能的光子晶体器件成为研究重点。光学微腔是指至少有一个方向上尺度在光波长量级的谐振腔。它在量子计算、传感器、低阈值窄线宽激光器以及全光通讯滤波器件等方面有巨大优势。目前,研究人员一直在尝试着设计出具有高品质因子、小模式体积、方向性辐射等特性以及无模式简并、可调谐的微腔。正是在这样的背景下,本论文研究了光子晶体中的负折射现象和电各向异性圆形光学微腔的模式特性。主要工作及创新点如下：1.分别就光子晶体中介质柱半径和介质柱位置具有均匀随机误差两种情况,用时域有限差分方法研究了光子晶体同一能带的正负折射效应对这两种工艺误差的宽容度,为实验上制备光子晶体提供指导。2.针对光子晶体同一能带的正负折射效应的一系列缺点,提出并采用平面波展开法、等频面方法和时域有限差分方法研究了基于光子晶体交叠能带的正负折射效应。在这一种新的正负折射效应中,入射光束在入射界面上和出射界面上均只在传统反射方向上有反射,因而透过率更高；在出射界面上,正、负折射光束均只激发了一种模式的透射光,故从光子晶体透射出来的光场便于后续器件接收和耦合；由于负、正折射分别独立地发生于第二和第三能带,故基于此效应的分束器既有宽容的工作入射角,也利于用入射角度实现分束效果的调谐。更重要的是,这种思想提供了一种利用光子晶体的交叠能带控制光传输的新颖机制。3.开发了完整的分析二维各向异性微腔的数值计算平台,包括推导出了主轴坐标系下电各向异性介质中二维时域有限差分算法的迭代公式,引入体积平均有效介电常数近似来处理微腔边界,利用基于Baker算法的Pade近似将时域信号转换为高精度的频谱。利用此平台求得的各向同性圆形微腔数值解与其解析解的高度一致性,证明了此平台用于二维微腔分析的有效性。4.提出了各向异性光学微腔的概念,分析了二维电各向异性圆形微腔的模式特性,包括频谱控制、方向性辐射和对高阶径向模式的抑制。在各向异性微腔中,各回音壁模式的谐振频率随微腔介质的各向异性变化而线性平移,平移幅度正比于介质的两主折射率之相对差；微腔因圆形几何结构而具有的轴对称性被介质的各向异性所破坏,导致明显的方向性辐射；Q值随各向异性增大呈指数衰减；另外,各向异性微腔有效地抑制了高阶径向模式,因而更易实现单模工作。各向异性微腔的这种调谐机制将在波长可调低阈值微型激光器,可调谐滤波器,高灵敏度传感器等领域发挥重要作用。更多还原

【Abstract】 As a carrier of information and energy, photon has a high speed, huge capability, and low power, and is interference-free. Therefore people intend to make a kind of integrated optics circuit to control the photons. Photonic crystals and optical microcavtity, which are the basis elements of integrated optics circuit, are proposed to meet this need, and have attracted an increasing interest of scientists.Photonic crystal is a kind of optical media whose refractive index is periodically modulated. Due to its unique properties, such as photonic band-gap and photonic localization, photonic crystal has received a lot of attention since it was proposed in 1980s. Today their theoretical basis is almost consummate, and the research focus is designing of photonic crystals devices with special function.Optical microcavity is those cavities with dimension of optical wavelength in one direction at least. They have important potential in many field including quantum computing, sensor, low-threshold narrow-line-width laser and full optical communication filter. Now the researchers are trying to design microcavities with high quality factor, a small mode-volume, directional emission, no mode degeneracy and tunability.In the above background, this thesis studies the negative refraction in two-dimensional photonic crystals, and the mode character of cylindrical microcavity made of electric anisotropic medium. The primary research and achievement are as follows:1. The influence of radius-error and position-error of dielectric-rod on the properties of beam splitter, which is based on positive-negative refraction within a single band in a two dimensional photonic crystal, were both investigated by the frequency-difference time-domain method, respectively. This study is instructive to fabricate the photonic crystal devices experimentally.2. In order to solve the drawbacks of beam splitter based on positive-negative refraction within a single band in a photonic crystal, positive-negative refraction based on overlapping bands in a two dimensional photonic crystal is proposed and studied by the plane-wave expansion method, the equifrequency contours method and the finite-difference time-domain method. In the later positive-negative refraction effect, the transmittance is improved in respect that there is only one reflected beam in traditional reflective direction at both input interface and output interface. Either positive or negative refracted beam launching onto the output interface will excite only one transmitted beam in air. Therefore it will be more convenient to receive these transmitted beams or couple them into the next optical devices. Since negative and positive refraction is induced by the second and third band, respectively and separately, the beam splitter based on this effect has a flexible incident angle to operate properly, and its splitting effect can be manipulated by adjusting the incident angle. In addition, this thought provides a novel mechanism to control light propagation by overlapping bands in photonic crystals.3. A complete numerical simulation system to deal with microcavity made of electric anisotropic medium is explored, including deduced iterative formula of the 2D finite-difference time domain method for electric anisotropic medium in its principal axis coordinate system, and introducing a volume-average effective permittivity approximation to deal with the microcavity boundary, transferring the time-domain signal to accurate spectrum by Pade approximation with Baker’s algorithm. The validity of these numerical methods in solving the microcavity problem is demonstrated by the consistency of the analytical solution with the numerical solution for isotropic cylindrical microcavity.4. Cylindrical microcavity made of electric anisotropic medium is proposed, and its mode characters, such as spectrum control, directional emission, and suppression to higher radial number mode, are studied. For this anisotropic cylindrical microcavity, the following conclusions is reached:the resonant frequency for different whispering-gallery modes has a similar shift in direct proportion to the relative difference of two principal refractive indices; The axial symmetry as cylinder geometry configuration have destroyed by anisotropy and thus results to a significant directional emission from the microcavity; The quality factors decay exponentially due to increasing directional emission when the anisotropy increases; The anisotropic microcavity can efficiently suppress those modes with larger radial mode number and thus operates conveniently in single-mode. This novel tuning characteristic of anisotropic cylindrical microcavity will play an important role in many areas, such as low threshold microlaser with tunable wavelength, tunable filter and sensitive sensor.更多还原