Stabilizing single- and two-color vortex beams in quadratic media by a trapping potential

Hidetsugu Sakaguchi, Boris A. Malomed

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    We consider two-dimensional (2D) localized modes in the second-harmonic-generating (X(2)) system with the harmonic-oscillator (HO) trapping potential. In addition to its realization in optics, the system describes the mean-field dynamics of mixed atomic-molecular Bose-Einstein condensates (BECs). The existence and stability of various modes is determined by their total power, N, topological charge, m/2 [m is the intrinsic vorticity of the second-harmonic (SH) field], and X(2) mismatch, q. The analysis is carried out in a numerical form and, in parallel, by means of the variational approximation (VA), which produces results that agree well with numerical findings. Below a certain power threshold, N ≤ Nm (q), all trappedmodes are of the single-color type, represented by the SH component only, while the fundamental frequency (FF) one is absent. In contrast with the usual situation, where such modes are always unstable, we demonstrate that they are stable, for m = 0, 1, 2 (the mode with m = 1 may be formally considered as a semivortex with topological charge m/2 = 1 /2), at N ≤ Ncm(q), and unstable above this threshold. On the other hand, Ncm(q) = 0 at q = qmax (in our notation, qmax = 1); hence the single-color modes are unstable in the latter case. At N = Nc(m), the modes with m = 0 and m = 2 undergo a pitchfork bifurcation, which gives rise to two-color states, which remain completely stable for m = 0. The two-color vortices with m = 2 (topological charge 1) have an upper stability border, N = Nc2(q). Above the border, they exhibit periodic splittings and recombinations, while keeping their vorticity. The semivortex does not bifurcate; at N = Nc(m=1), it exhibits quasi-chaotic oscillations and a rotating "groove" resembling a screw-edge dislocation induced by the semi-integer vorticity.

    Original languageEnglish
    Pages (from-to)2741-2748
    Number of pages8
    JournalJournal of the Optical Society of America B: Optical Physics
    Volume29
    Issue number10
    DOIs
    Publication statusPublished - Oct 1 2012

    Fingerprint

    trapping
    vortices
    color
    vorticity
    borders
    harmonics
    thresholds
    screw dislocations
    edge dislocations
    Bose-Einstein condensates
    grooves
    harmonic oscillators
    integers
    coding
    optics
    oscillations
    approximation

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Atomic and Molecular Physics, and Optics

    Cite this

    Stabilizing single- and two-color vortex beams in quadratic media by a trapping potential. / Sakaguchi, Hidetsugu; Malomed, Boris A.

    In: Journal of the Optical Society of America B: Optical Physics, Vol. 29, No. 10, 01.10.2012, p. 2741-2748.

    Research output: Contribution to journalArticle

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    abstract = "We consider two-dimensional (2D) localized modes in the second-harmonic-generating (X(2)) system with the harmonic-oscillator (HO) trapping potential. In addition to its realization in optics, the system describes the mean-field dynamics of mixed atomic-molecular Bose-Einstein condensates (BECs). The existence and stability of various modes is determined by their total power, N, topological charge, m/2 [m is the intrinsic vorticity of the second-harmonic (SH) field], and X(2) mismatch, q. The analysis is carried out in a numerical form and, in parallel, by means of the variational approximation (VA), which produces results that agree well with numerical findings. Below a certain power threshold, N ≤ Nm (q), all trappedmodes are of the single-color type, represented by the SH component only, while the fundamental frequency (FF) one is absent. In contrast with the usual situation, where such modes are always unstable, we demonstrate that they are stable, for m = 0, 1, 2 (the mode with m = 1 may be formally considered as a semivortex with topological charge m/2 = 1 /2), at N ≤ Ncm(q), and unstable above this threshold. On the other hand, Ncm(q) = 0 at q = qmax (in our notation, qmax = 1); hence the single-color modes are unstable in the latter case. At N = Nc(m), the modes with m = 0 and m = 2 undergo a pitchfork bifurcation, which gives rise to two-color states, which remain completely stable for m = 0. The two-color vortices with m = 2 (topological charge 1) have an upper stability border, N = Nc2(q). Above the border, they exhibit periodic splittings and recombinations, while keeping their vorticity. The semivortex does not bifurcate; at N = Nc(m=1), it exhibits quasi-chaotic oscillations and a rotating {"}groove{"} resembling a screw-edge dislocation induced by the semi-integer vorticity.",
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