传输矩阵法分析多环高阶谐振滤波器特性

Transfer Matrix Method for Analyzing the Characteristics of Multiple-Ring Higher Order Microring Resonators

与输入/输出波导耦合的环型谐振腔能形成结构简洁、性能良好、集成度高的信道滤波器。为实现通带内频率响应平坦度高、滚降时间快的滤波效果,采用多环结构形成的高阶滤波器。利用传输矩阵法推导了环与环间通过串联耦合和并联耦合两种方式形成的多环高阶谐振滤波器的传输函数公式。对于并联耦合结构,通过优化直接影响下话路滤波特性的环与环间直波导的长度,实现了下话路光谱的对称性。对于串联结构,影响其特性的主要因素为环与环间的耦合系数,要实现最大平坦的通带特性,通过数值计算得出各个环间耦合系数必须从中间到两侧对称增加的特性。

The microring resonator coupled with the input/output channel waveguides can be applied in filter due to its compactness, functionality, and the possibility of dense integration. In order to achieve flatter tops and sharper rolloff in the passband, the multiple-ring higher order structure is employed. Both the transfer functions of series-coupled and parallel-coupled multi-ring high order filters are derived using the transfer matrix method. For the parallel-coupled structure, the symmetric spectral response is achieved by optimizing the ring distance, while for the series-coupled structure, the performance is determined by the coupling coefficients between the ring and ring. In order to obtain maximally flat response passbands, the numerical results show that the proper coupling coefficients should be symmetric and smaller in the middle of the structure.