根据波导耦合方程,导出了串联微环谐振器的传输矩阵,并分析了环数、环间耦合系数以及损耗对串联微环谐振器输出特性的影响。数值模拟表明,串联微环谐振器具有光子带隙的特征。当环数增加时,通带内满足谐振条件的波长数增加; 当环间耦合系数增加时,可使通带带宽加宽; 通过适当选择环数和环间耦合系数,可以实现滤波和波分复用(WDM)的功能。选用脉冲宽度为50 ps的高斯型激光脉冲注入微环谐振器,发现当环间耦合系数较小时,出射脉冲相对于入射脉冲具有光学延迟的效果,并且随着环数的增加,延迟时间逐渐增大,而当环间耦合系数较大时,光学延迟效果不明显。

The transfer matrix of the series-coupled microring resonators is derived in detail based on the coupled mode theory of waveguides. The influence of the coupling coefficients, the number of the rings and loss on the transmission spectrum of the resonators are analyzed. Numerical simulation indicates that the bandwidth of the pass band will increase with the coupling coefficient, and at the same time, the number of the resonant wavelength in the pass band will also increase with the number of the rings. The microring resonator can act as filters or wavelength division multiplexer (WDM) in appropriate condition. Additionally, we find that the structure has the performance of optical delay when we launch a 50 ps (full-width at half maximum, FWHM) long Gaussian-shaped pulse into the structure. The larger the number of the rings, the more group delay we can achieve when the coupling coefficients is rather small, however, no delay effect can be observed when the coupling coefficient between the rings is strong.