Matter-wave vortices and solitons in anisotropic optical lattices

Mayteevarunyoo, Thawatchai; Malomed, Boris A.; Baizakov, B. B.; Salerno, Mario

doi:10.1016/j.physd.2008.07.024

Cited by 42 publications

(27 citation statements)

References 58 publications

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“…were also investigated [19][20][21][22][23][24]. Vortex dipoles, i.e., composite states with two embedded vortices of opposite topological charges (vortex-antivortex pairs), do exist as stationary soliton solutions to the effectively two-dimensional Gross-Pitaevskii equation for both symmetric and asymmetric traps.…”

Section: Introductionmentioning

confidence: 99%

Elliptic vortices in composite Mathieu lattices

Mihalache

2009

Phys. Rev. A

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Section: Introductionmentioning

confidence: 99%

Elliptic vortices in composite Mathieu lattices

Mihalache

2009

Phys. Rev. A

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“…In our experiment with the 1-cm-long crystal, the donut-shaped DMs excited with an optical vortex remain robust during linear propagation. We mention that such linear vortex DMs are quite different from the nonlinear vortex modes found in anisotropic lattices [15][16][17], where the vortex covers four lattice sites and is localized by the nonlinearity-induced defect. Our singlesite vortex tends to break up during nonlinear propagation due to the anisotropic nonlinearity and modulation instability.…”

mentioning

confidence: 62%

Observation of bandgap guidance of optical vortices in a tunable negative defect

et al. 2010

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We experimentally demonstrate linear bandgap guidance of optical vortices as high-gap defect modes (DMs) in twodimensional induced photonic lattices. We show that donut-shaped vortex beams can be guided in a tunable negative (lower-index) defect, provided that the defect strength is set at an appropriate level. Such vortex DMs have fine features in the "tails" associated with the lattice anisotropy and can be considered as a superposition of dipole DMs. Our numerical results find good agreement with experimental observations.

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“…Adding more beams with phase shifts between them, one can construct composite vortices. For an example, a composite vortex with the total phase circulation of 2π may appear as a four-beam complex with the off-site vortex core in the center and the phase shifts π/2 between adjacent beams [49,50]. We have found that the composite vortices can exist in the system of the uniform setting.…”

Section: (A)mentioning

confidence: 85%

Bulk vortices and half-vortex surface modes in parity-time-symmetric media

Zhu

Shi

et al. 2014

Phys. Rev. A

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We demonstrate that in-bulk vortex localized modes, and their surface half-vortex ("horseshoe") counterparts self-trap in two-dimensional (2D) nonlinear optical systems with PT -symmetric photonic lattices (PLs). The respective stability regions are identified in the underlying parameter space. The in-bulk states are related to truncated nonlinear Bloch waves in gaps of the PL-induced spectrum. The basic vortex and horseshoe modes are built, severally, of four and three beams with appropriate phase shifts between them. Their stable complex counterparts, built of up to 12 beams, are reported too.PACS numbers: 03.65. Ge, 11.30.Er, 42.65.Sf, 42.65.Tg Nonlinear spatially periodic systems support diverse types of self-trapped in-gap states. In particular, spatial gap solitons [1,2] originate from the interplay between the periodicity and nonlinearity. Further, surface gap solitons [4][5][6][7][8] appear at the interface between a uniform medium and a photonic lattice (PL) built into a nonlinear material. Extended self-trapped waves with steep edges also exist in these settings, being related to truncated nonlinear Bloch waves [9,10]. Modes of the latter type provide a link between extended nonlinear Bloch waves [11,12] and tightly localized gap solitons [1][2][3].Recently, a great deal of interest has been drawn to the realization of parity-time (PT ) symmetry in optics. Originally, this concept was developed in quantum mechanics, where it was demonstrated that, beyond the conventional Hermitian Hamiltonians, their PTsymmetric non-Hermitian counterparts may also give rise to purely real (hence physically relevant) spectra [13][14][15][16]. Following the similarity between quantum mechanics and paraxial optics [17,18], PT -symmetric optical systems with complex refractive indices [19,20] have been extensively studied theoretically [21][22][23][24][25][26][27][28][29][30][31][32][33] and experimentally [34][35][36][37][38][39][40][41]. In this context, PT -symmetric PLs play an important role. Taking into account the non-orthogonality of the respective eigenmodes, their coupled-mode description had to be reformulated via the variational principle [21]. The light propagation in PTsymmetric PLs embedded into linear media were analyzed preliminarily [24,42]. Further, it has been found that 1D and 2D spatial gap solitons exist in PLs built into a nonlinear material [23,[43][44][45][46][47].Although PT -symmetric systems combining lattices and nonlinearity was not reported yet. In particular, such self-trapped nonlinear states may serve as a necessary link between spatially localized gap solitons and extended nonlinear Bloch waves under the PT symmetry.Self-trapped vortices and surface modes are of great interest in the context of the PT -symmetric settings. Indeed, the study of nonlinear surface modes pinned on the interface of a PT -symmetric system opens a way to explore the interplay between surface effects, the nonlinearity, and the PT -symmetry. On the other hand, the analysis of localized vortices supported by PT ...

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Matter-wave vortices and solitons in anisotropic optical lattices

Cited by 42 publications

References 58 publications

Elliptic vortices in composite Mathieu lattices

Elliptic vortices in composite Mathieu lattices

Observation of bandgap guidance of optical vortices in a tunable negative defect

Bulk vortices and half-vortex surface modes in parity-time-symmetric media

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