光子晶体超棱镜是实现分色、滤波等功能的关键器件,而群延迟是衡量分波滤波效果的重要参量。为了获得更好的分光效果,一般采用级联法布里珀罗滤波器或者Gires-Tournois滤波器实现大而线性的群延迟。基于多镜理论提出了一种新的多腔滤波器群延迟计算方法,简化了计算过程,使得计算不再受实际材料的限制。并以四腔级联Gires-Tournois滤波器为例进行群延迟的模拟计算,得到的结果与薄膜传输矩阵基本吻合,证实了算法的正确性。最后分析了群延迟、线性范围与Gires-Tournois滤波器腔长之间的关系,指出了如何根据实际要求选择腔长的方向。

Photonic crystal superprism is the key device for the light deflection, filtering and so on, and the group delay is one of the most important parameters to judge light deflection and filtering performances. For the sake of achieving large shift separation, cascade Fabry-Pérot filters or Gires-Tournois filters are usually used to achieve large and linear group delay. A novel method for calculating group delay of multi-cavities filters based on multi-mirror theory is presented, which simplifies the calculation and is not restricted by the practicable materials. As an example, the group delay of a four-cavity Gires-Tournois filters is obtained, which is in excellent agreement with the result by transmission matrix method in optical thin film theory and proves its validity. Finally, the relationship between group delay, linear region and cavity length of Gires-Tournois filters is analyzed, and the suggestion on how to choose suitable cavity length is presented.