2017/04/11 by Wesley B. Cardoso, Luca Salasnich, Boris A. Malomed
Computer Science · Physics and Astronomy · #Field (mathematics) #Limit (mathematics) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Orbital Angular Momentum in Optics #Phase (matter) #Simple (philosophy) #Spiral (railway) #Stability (learning theory) #Vortex #Vorticity #nlin.PS #physics.optics
paper · pdf · doi:10.1140/epjd/e2017-80060-7
published as Eur. Phys. J. D (2017) 71: 112 · 11 pages, 15 figures, Eur. Phys. Journal D, in press (Topical Issue "Theory and Applications of the Lugiato-Lefever Equation")
arxiv created 2017/04/11 · openalex publication_date 2017/05/01 · openalex created_date 2017/05/12 · arxiv updated 2017/05/26 · openalex updated_date 2026/08/05
We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self- focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad sta- bility areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numeri- cal results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation.