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.

Journal/Review: EUROPEAN PHYSICAL JOURNAL D

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

More Information: W.B.C. acknowledges the financial support from the Brazilian agencies CNPq (grant # 458889/2014-8) and the National Institute of Science and Technology (INCT) for Quantum Information. L.S. acknowledges for partial support the 2016 BIRD project Superfluid properties of Fermi gases in optical potentials of the University of Padova. The work of B.A.M. is supported, in part, by grant No. 2015616 from the joint program in physics between NSF (US) and Binational (US-Israel) Science Foundation.
KeyWords: Ground-state; Light; Dynamics; Patterns
DOI: 10.1140/epjd/e2017-80060-7

ImpactFactor: 1.393
Citations: 8
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