The properties of the square array of coupled Microring Resonators (MRRs) with interstitial rings are studied. Dispersion behavior of the interstitial square coupled MRRs is obtained through the transfer matrix method with the Floquet-Bloch periodic condition. Analytical formulas of the eigen wave vectors, band gaps and eigen mode vectors are derived for the special cases of the interstitial square coupled MRRs array with identical couplers and the regular square coupled MRRs array without the interstitial rings. Then, the eigen modes’ field distribution are calculated for each of the four eigen wave vectors for a given frequency through the secular equation. Finally, numerical simulation is performed for an interstitial square coupled MRRs array with identical couplers and a regular square coupled MRRs array. The simulation result verifies the analytical analysis. Finally, the loaded quality factors of the interstitial 5-ring configuration, the regular 4-ring configuration and the 1-ring configuration are obtained. It is found that the loaded quality factor of the interstitial 5-ring configuration is >20 times and >8 times as high as those of the 1-ring configuration and the regular 4-ring configuration respectively, making it attractive in applications like selective filters, ultra-sensitive sensor and four-wave mixing quantum entangled photon pair sources.

中文翻译：

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高 Q 间隙方形耦合微环谐振器阵列

研究了具有间隙环的耦合微环谐振器 (MRR) 方阵的特性。通过具有 Floquet-Bloch 周期条件的传递矩阵方法获得间隙方形耦合 MRR 的色散行为。针对具有相同耦合器的间隙方形耦合MRRs阵列和没有间隙环的规则方形耦合MRRs阵列的特殊情况，推导出了本征波矢量、带隙和本征模式矢量的解析公式。然后，通过长期方程为给定频率的四个本征波向量中的每一个计算本征模式的场分布。最后，对具有相同耦合器的间隙方形耦合MRRs阵列和规则方形耦合MRRs阵列进行了数值模拟。仿真结果验证了解析分析。最后，得到了间隙 5 环配置、规则 4 环配置和 1 环配置的加载质量因子。发现间隙 5 环配置的负载品质因数分别是 1 环配置和常规 4 环配置的 20 倍以上和 8 倍以上，使其在选择性过滤器等应用中具有吸引力，超灵敏传感器和四波混合量子纠缠光子对源。