Intra-cavity field dynamics near avoided mode crossing in concentric silicon nitride ring resonator

Understanding the intra-cavity field dynamics in passive microresonator systems has already been intriguing. It becomes fascinating when the system is complex, such as a concentric dual microring resonator that exhibit avoided mode crossing (AMC). In this work, we present a systematic study of intra-cavity oscillatory field dynamics near AMC in a concentric silicon nitride microring resonator with the help of the coupled Lugiato-Lefever equation (LLE). We identify two regions viz. weakly coupled region (WCR) and strongly coupled region (SCR) based on eigenfrequency separation of the two-hybrid modes, which originate from mode coupling near AMC. In WCR, the mode coupling effect is dominant, leading to intra-cavity power oscillation between these two modes in a periodic manner and non-identical variation of their phases. In SCR, the mode coupling effect reduces gradually with nearly identical characteristics of both the modes. We further verify our numerical findings with the semi-analytical variational method, leading to an in-depth understanding of the mode coupling induced dynamics. We finally analyze the polarization evolving state, and the polarization locked state with the help of Stokes parameters and Jones vectors in WCR and SCR, respectively.