2024/01/28 by Yifan Sun, Sun, Yifan, Pedro Parra‐Rivas +5 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS) #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2401.15689
openalex publication_date 2024/01/28 · openalex created_date 2024/01/31 · openalex updated_date 2026/07/28
In this work, we study the bifurcation structures and the stability of multidimensional localized states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and 3D systems. Based on symmetric considerations, we transform higher-dimensional models into a single 1D model with a dimension parameter. This transformation not only yields a substantial reduction in computational complexity, but also enables an efficient examination of how dimensionality impacts the system dynamics. In the absence of nonlinearity, we analyze the eigenstates of the linear systems. This allows us to uncover a heightened concentration of the eigenmodes at the center of the potential well, while witnessing a consistent equal spacing among their eigenvalues, as the dimension parameter increases. In the presence of nonlinearity, our findings distinctly reveal that the stability of the localized states diminishes with increasing dimensionality. This study offers an approach to tackling high-dimensional problems, shedding light on the fundamental dimensional connections among radially symmetric states across different dimensions, and providing valuable tools for analysis.