翻译更正并且检查下面这句话让它符合sci科技论文结论书写要求：综上所述我们采用传递矩阵的方法推导了带有MRU的MRR结构的共振线形变化。该模型考虑了MRR中双向传输的光和MRU的大小对共振线形和共振强度的影响并通过严格的分析纠正了先前理论的不足。此外我们演示了Fano线形在单纳米粒子传感中的应用并从耦合的角度说明了纳米粒子引起的线形移动和分裂机理。我们希望我们的理论工作将使具有MRU结构的微环谐振

In conclusion, we have derived the resonance line shape variation of the MRR structure with MRU using the transfer matrix method. The model takes into account the influence of bidirectional light transmission in the MRR and the size of the MRU on the resonance line shape and intensity. It has addressed the limitations of previous theories through rigorous analysis. Additionally, we have demonstrated the application of Fano line shape in single nanoparticle sensing and explained the mechanisms of line shape shifting and splitting caused by nanoparticle coupling. We believe that our theoretical work will enable the wider application of micro-ring resonators with MRU structures in sensing and also facilitate the development of more efficient optical isolators to reduce the impact of potential reflection on lasers and other on-chip devices