In terms of the coupled mode theory and the transfer matrix technique, novel formulas of the transfer functions are presented for a 2D microring resonator (MRR) array, which consists of two straight buslines, N parallel-cascaded columns, each of which contains M series-coupled rings. By using these formulas, the parameters are optimized, and the transmission characteristics including the transmission spectrum and the insertion loss are analysed for such a 2D SiN/SiO2 MRR array. By properly selecting the distance between adjacent columns, the amplitude coupling ratio between the busline and the ring and that between adjacent rings, as well as the number of the rows and that of the columns, the box-like spectral response is successfully obtained, the passband is precipitous, and the non-resonant light and crosstalk are weak.
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机译：根据耦合模式理论和传递矩阵技术，给出了二维微环谐振器（MRR）阵列传递函数的新公式，该矩阵由两条直线，N个平行级联的列组成，每个列包含M个系列耦合环。通过使用这些公式，可以优化参数，并分析这种2D SiN / SiO2 MRR阵列的透射特性，包括透射光谱和插入损耗。通过适当选择相邻列之间的距离，总线和环之间以及相邻环之间的幅度耦合比以及行数和列数，可以成功获得盒状光谱响应，通带陡峭，非谐振光和串扰微弱。
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