【作者】 丁卫强；

【导师】 刘树田； 陈历学；

【作者基本信息】 哈尔滨工业大学 ， 光学， 2006， 博士

【摘要】 光子晶体，即光学参数(线性和／或非线性电极化率和／或磁导率)随空间位置周期变化的光学结构，是近二十年来发展最快的光学领域之一。由于其独特的光子禁带和光子局域效应，使光子晶体成为集成光学和全光通信领域中的研究热点。本论文利用数值模拟和理论分析的方法，研究一维和二维光子晶体耦合腔结构的局域特性，及其在光学器件中的应用。其中研究的耦合腔结构包括线性和Kerr非线性两种类型，所实现的功能包括宽频带光限幅器、宽频带和多模的双稳态开关以及耦合腔光波导。 论文提出光子晶体耦合腔结构具有两种不同的状态：其一是本征频率连续分布的状态，在这种状态下，各个腔内的电场局域强度近似相等，其行为可以利用已知的紧束缚理论描述。其二是本征频率离散分布的状态，在此状态下，不同腔内的电场局域强度不同。此时耦合腔行为不符合通常使用的紧束缚理论。为此，我们提出一种耦合模理论对离散本征态的耦合腔结构进行描述。利用该理论，求解出了本征模对应的本征频率、品质因子、以及电场本征态。虽然这两种状态可以通过耦合腔结构两端局域强度的调节而相互转换，但是这两种状态在耦合腔应用(包括线性和非线性器件)中表现出完全不同的特性。 当耦合腔结构处于连续模状态时，研究了整个连续本征频率带内的宽带光学双稳态开关和光限幅器。这两种功能是在具有连续本征频谱的耦合腔结构中引入Kerr型非线性介质而实现的。利用非线性传输矩阵方法和时域有限差分方法对限幅和开关的稳态及动态特性分别进行了研究。结果表明，通过入射光所激发的Kerr效应对腔折射率的动态调节，改变了腔之间的耦合强度与耦合效率，从而造成了整个连续透射带内高低透射状态的动态转换，进而实现了宽频带的全光双稳态开关和限幅功能。 当耦合腔结构处于离散模工作状态时，在一维结构中研究了均匀低阈值的多模光学双稳态开关。通过分析耦合腔内电场的局域特性以及腔受到微扰时对本征频率的影响特性，得出在适当的腔内引入Kerr介质，通过入射光自泵浦，可以实现所有本征频率的移动，并且基于此实现了低阈值的双稳态开关。利用耦合模理论分析，得出所有信道的开关阈值都相等的条件，并且在数值模拟结果中得到了验证。在二维结构中，我们研究了二维耦合腔阵列的更多还原

【Abstract】 Photonic crystal (PC), in which optical parameters (such as the linear and/or nonlinear electric permittivity and/or magnetic permeability) change periodically in space, is one of the most fruitful optical fields in the last two decades. Due to the merits of photonic band gap and strong localization, PCs exhibit promising future in optical integrated circuits (OIC) and all optical communication systems. In this dissertation, using both theoretical analysis and numerical simulation methods, we investigate the localization properties and potential applications of photonic crystal coupled cavity (CC) structures in one- and two-dimensions. The CC structures include linear and Kerr nonlinear cavities, and the functionalities realized include broad band and multimode optical bistable switchings, broad band optical limiting and optical waveguiding.Our studies show that there are two different types of states for the CC structures: The first one is continuous eigenmode state. In this state, the eigenfrequencies form a continuous band, and the field localization intensities in all the cavities are approximately the same. This state can be described properly by the well known tight binding (TB) theory. The other is discrete eigenmode state. In this state, the eigenfrequencies are completely separated (discrete), and the localizations in various cavities are completely different, and TB theory is invalid in this case. Therefore, we developed a coupled mode theory (CMT) to describe the discrete mode states, and the eigenfrequencies, quality factors and the electric eigenfields of the states are derived. Although the two states can be converted to each other by tuning the confinements to the two ends, the two states show very different properties in both the linear and nonlinear devices.When the coupled cavity structure operates in the continuous mode state, broad band optical bistable switching and limiting in the whole band of the CC structures are realized by introducing Kerr medium into one (or more) of the cavities. Due to the Kerr effects excited by the incident light, the coupling strength between the cavities are tuned, then high and low transmissions are realized dynamically. Therefore, all optical limiting and bistable switching are achieved successfully.更多还原