Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation

Year: 2017

Authors: Cardoso WB., Salasnich L., Malomed BA.

Autors Affiliation: Univ Fed Goias, Inst Fis, BR-74690900 Goiania, Go, Brazil;‎ Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy;‎ Univ Padua, CNISM, Via Marzolo 8, I-35131 Padua, Italy‎; CNR, INO, Sez Sesto Fiorentino, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy; Tel Aviv Univ, Fac Engn, Sch Elect Engn, Dept Interdisciplinary Studies, IL-69978 Tel Aviv, Israel;‎ ITMO Univ, Lab Nonlinear Opt Informat, St Petersburg 197101, Russia

Abstract: 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 selffocusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zerodimensional) 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 stability 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 numerical results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation.


Volume: 71 (5)      Pages from: 112-1  to: 112-10

DOI: 10.1140/epjd/e2017-80060-7

Citations: 5
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