Graph Laplacian analysis of modulation instability in three-core optical coupler

Abstract This study explores modulation instability (MI) in a three-core optical coupler, utilizing a graph Laplacian framework to model the system's dynamics through coupled nonlinear Schrödinger equations (NLSE). By substituting the traditional continuous Laplacian with the graph Laplacian, the research investigates how the eigenvalues of the graph Laplacian influence MI through linear stability analysis. Notably, the findings reveal that real eigenvalues lead to a decrease in the instability band as their magnitude increases, suggesting a stabilizing effect. In contrast, when the eigenvalues are complex, the MI spectrum exhibits both upper and lower thresholds in amplitude ratio, with an enhancement in MI as the absolute value of these complex eigenvalues grows. These insights underscore the critical role of the graph Laplacian's spectral properties in shaping the stability and behavior of MI in three-core optical couplers, offering valuable implications for the design and optimization of such systems in optical communications and photonics applications.