TY - JOUR

T1 - Quasistable two-dimensional solitons with hidden and explicit vorticity in a medium with competing nonlinearities

AU - Leblond, Hervé

AU - Malomed, Boris A.

AU - Mihalache, Dumitru

PY - 2005/3

Y1 - 2005/3

N2 - We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic Χ (2) and self-defocusing cubic Χ - (3) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S 1,2=±1, whereas the SH carries no vorticity, S 3=0. We also consider an ordinary compound vortex, with 2S 1=2S 2=S 3=2. Without the Χ - (3) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z ≃ 15 diffraction lengths, Z diffr, the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with "hidden momentum," i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the Χ - (3) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50 Z diffr. In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S 3 =2S 1,2=2 splits into a set of three or four ZV solitons.

AB - We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic Χ (2) and self-defocusing cubic Χ - (3) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S 1,2=±1, whereas the SH carries no vorticity, S 3=0. We also consider an ordinary compound vortex, with 2S 1=2S 2=S 3=2. Without the Χ - (3) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z ≃ 15 diffraction lengths, Z diffr, the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with "hidden momentum," i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the Χ - (3) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50 Z diffr. In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S 3 =2S 1,2=2 splits into a set of three or four ZV solitons.

UR - http://www.scopus.com/inward/record.url?scp=41349094366&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.036608

DO - 10.1103/PhysRevE.71.036608

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C2 - 15903606

AN - SCOPUS:41349094366

SN - 1539-3755

VL - 71

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 3

M1 - 036608

ER -