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

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dc.creatorCardoso, Wesley Bueno
dc.creatorSalasnich, Luca
dc.creatorMalomed, Boris A.
dc.date.accessioned2024-07-15T12:34:21Z
dc.date.available2024-07-15T12:34:21Z
dc.date.issued2017
dc.description.abstractWe 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 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.
dc.identifier.citationCARDOSO, Wesley B.; SALASNICH, Luca; MALOMED, Boris A. Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation. European Physical Journal D, Berlim, v. 71, p. 112, 2017. DOI: 10.1140/epjd/e2017-80060-7. Disponível em: https://link.springer.com/article/10.1140/epjd/e2017-80060-7. Acesso em: 1 jun. 2023.
dc.identifier.doi10.1140/epjd/e2017-80060-7
dc.identifier.issn1434-6060
dc.identifier.issne- 1434-6079
dc.identifier.urihttps://link.springer.com/article/10.1140/epjd/e2017-80060-7
dc.language.isoeng
dc.publisher.countryAlemanha
dc.publisher.departmentInstituto de Física - IF (RMG)
dc.rightsAcesso Restrito
dc.titleZero-dimensional limit of the two-dimensional Lugiato-Lefever equation
dc.typeArtigo

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