无序耦合谐振腔光波导的光学特性研究

A new kind of micro-/nano-photonic device based on the coupling of nearest-neighbor optical micro-resonators, the coupled resonator optical waveguide (CROW), has great and potential practical applications in slow-light delay lines, all-optical buffer, enhancement of light-matter interactions, etc. However, the unavoidable imperfections such as off-diagonal disorder, emerging from the random variation of coupling coefficients between two neighboring micro-resonators, and correlated disorder, emerging from correlated randomness in size and coupling coefficients of micro-resonators, greatly affected the performance of CROWs and hence restricted the popularization and batch production of CROWs. The aims of this proposal are to study the effect of off-diagonal disorder and correlated disorder on the optical properties of large-scale CROWs constructed by several hundreds microspherical resonators and to investigate the role of disorder in optical transport in CROWs. To this end, in this proposal, starting from the perspective of Mie scattering theory and considering the coupling between Whispering Gallery Modes with different angular mode numbers, we intend to theoretically construct tight-binding models for the situation of off-diagonal disorder and the situation of correlated disorder respectively. We then intend to derive some analytical expressions which characterize the optical properties of CROWs and thereby to numerically study the CROWs' optical properties such as slow light effect, transmission efficiency of light, and localization of light. By analyzing and comparing our results with other groups' experimental results, we try to find the reasons which restrict the improvement of CROWs' related performance and hence provide theoretical basis and guiding principles to the production of optical integration devices based on CROWs.

新型的微纳光子器件耦合谐振腔光波导（CROW）在慢光、全光缓存、增强光物相互作用等方面蕴藏着巨大的潜在应用价值，但相邻微谐振腔之间的耦合系数随机变化导致的非对角无序以及微谐振腔的尺寸之间、耦合系数之间的关联无序等各种无序的存在显著降低了CROW的相关性能，制约了CROW的推广和批量生产。为了研究非对角无序和关联无序对由几百个微球谐振腔构成的大尺寸CROW的光学特性的影响，探讨光在CROW中传播时无序在其中所起的作用，本项目拟从Mie散射理论出发，考虑微球谐振腔中的不同角模数所对应的光波之间的相互耦合，从理论分析上分别建立非对角无序和关联无序作用下的紧束缚理论模型，给出表征CROW的光学特性的各种解析表达式，对CROW的慢光效应、光的传输效率、光的局域化等光学特性进行研究并与相关实验结果进行分析和对比，寻求制约CROW相关性能提升的原因，为制备基于CROW的高精度的光学集成器件提供理论依据。

为了寻求制约耦合谐振腔光波导(CROW)的光学性能提升的原因，为制备基于CROW的高精度的光学集成器件提供理论依据，本项目在CROW中引入非对角无序和关联无序，研究了各种无序对CROW的光学特性的影响，同时为了尽最大可能减少各种无序因素的制约，我们还研究了如何利用新型微谐振腔来构造CROW以提升CROW的光学性能。通过本项目的研究，我们取得了以下几个方面的主要研究成果：1. 在CROW中引入多模耦合近似条件，我们得出了相应的描述光波沿CROW传播的紧束缚理论模型，推导出了表征光波在CROW中传播时的光学特性的各种解析表达式，发展了一套能够在多模耦合近似下研究各种无序存在时CROW光学特性的理论方法。2. 我们研究了非对角无序即耦合系数之间的随机变化对CROW的光学特性的影响，结果表明非对角无序因素作用在不同的CROW上时会产生不同的效应，既能增强CROW的散射、消光作用，也能减弱CROW的散射、消光作用，即存在双重效应，同时由于非对角无序因素的存在，单个谐振腔的共振态被CROW的集体光学激发模式所取代并逐渐消失。3. 我们研究了谐振腔的尺寸之间、耦合系数之间的关联无序对CROW的光学特性的影响，结果表明关联无序对CROW的光学特性的影响与相同无序强度下非对角无序对CROW的光学特性的影响几乎是一样的，即存在关联与否并不额外产生新的效应。4.我们首次提出并研究了两种新型的高性能微谐振腔——H型微谐振腔和鱼骨型微谐振腔。H型微谐振腔具有极高的品质因子和极小的模体积，鱼骨型微谐振腔同时支持横电(TE)模和横磁(TM)模，并且这两种模式也都具有极高的品质因子、极小的模体积和极大的储能因子。这两种微谐振腔都具有非常小的体积，非常适合用来级联成CROW. 如果以这些新型的微谐振腔来构造CROW，必将极大的提升CROW的光学性能。

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