Robust self-trapping of vortex beams in a saturable optical medium

Reyna, Albert S.; Boudebs, Georges; Malomed, Boris A.; Araújo, Cid B. de

doi:10.1103/physreva.93.013840

Cited by 49 publications

(34 citation statements)

References 63 publications

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“…29. Spatial 2D solitons with embedded vorticity, which were effectively stabilized, as transient states, by nonlinear (cubic) losses in the medium with the CQ nonlinearity (liquid carbon disulfide), were reported too [303], as shown in Fig. 30.…”

Section: A Brief Outline Of Experimental Resultsmentioning

confidence: 99%

“…Transverse intensity distributions in vortex light beams (with S = 1), launched into the CQ medium, with essential cubic losses, as per Ref. [303]. (a) expansion of the quasi-linear beam, created with a low total power (1 GW/cm 2 ); (b) transient stability of the nonlinear vortex beam, with initial total power 9 GW/cm 2 , up to propagation distance z = 3 mm.…”

Section: Conclusion: a Summary Of The Reviewmentioning

confidence: 99%

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(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

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A comparative review is given of some well-known and some recent results obtained in studies of two-and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to instabilities induced by the occurrence of the critical and supercritical collapse, respectively, in the 2D and 3D models with the cubic self-focusing nonlinearity. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses in detail two well-established topics, viz., the stabilization of vortex solitons by means of competing nonlinearities, or by trapping potentials (harmonic-oscillator and spatially-periodic ones). The former topic includes a new addition, closely related to the recent breakthrough, viz., the prediction and creation of robust quantum droplets. Two other topics included in the review outline new schemes which were recently elaborated for the creation of stable vortical solitons in BEC. One scheme relies on the use of the spin-orbit coupling (SOC) in binary condensates with cubic intrinsic attraction, making it possible to predict stable 2D and 3D solitons, which couple or mix components with vorticities S = 0 and ±1 (semi-vortices (SVs) or mixed modes (MMs), respectively). In this system, the situation is drastically different in the 2D and 3D geometries. In 2D, the SOC helps to create a ground state (GS, which does not exist otherwise), represented by stable SV or MM solitons, whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow one to create a GS, but metastable solitons of the SV and MM types can be constructed. Another new scheme makes it possible to create stable 2D vortex-ring solitons with arbitrarily high S in a binary BEC with components coupled by microwave radiation. Some other topics are addressed briefly, such as vortex solitons in dissipative media, and attempts to create vortex solitons in experiments.List of acronyms: 1D -one-dimensional; 2D -two dimensional; 3D -three-dimensional; BEC -Bose-Einstein condensate; CGLE -complex Ginzburg-Landau equation; CQ -cubic-quintic (nonlinearity), FF -fundamental frequency; GPE -Gross-Pitaevskii equation; GS -ground state; GVD -group-velocity dispersion; HO -harmonic oscillator (potential); HV -hidden vorticity; LHY -Lee-Huang-Yang (correction to the mean-field dynamics of BEC); MF -mean field; MM -mixed mode; NLSE -nonlinear Schrödinger equation; OL -optical lattice; PT -parity-time (symmetry); QD -quantum droplet; SH -second harmonic; SOC -spin-orbit coupling; SV -semi-vortex; TF -Thomas-Fermi (approximation); TS -Townes' soliton; VA -variational approximation; VAV -vortex-antivortex (composit...

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Section: A Brief Outline Of Experimental Resultsmentioning

confidence: 99%

Section: Conclusion: a Summary Of The Reviewmentioning

confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

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168

115

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“…Indeed, the splitting of the flat-top vortical QD in two or several fundamental solitons, which also feature the flat-top shape, in the first approximation does not alter the bulk energy, which is proportional to the conserved total norm of the solitons, as per Eq. (12). Then, the stability against the splitting is determined by the balance of three other terms: the surface energy, E surf , the vortical (phase-gradient) energy of the unsplit vortex, E vort , and the kinetic energy of the splinters, E kin , which is determined by the conservation of the angular momentum.…”

Section: Dynamical Stability: Numerical Results and Analytical Estimatesmentioning

confidence: 99%

Two-dimensional vortex quantum droplets

et al. 2018

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It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian of binary atomic boson condensates suppresses the collapse and creates stable localized modes (twocomponent "quantum droplets", QDs) in two and three dimensions (2D and 3D). In particular, the LHY effect modifies the effective Gross-Pitaevskii equation (GPE) in 2D by adding a logarithmic factor to the usual cubic term. In the framework of the accordingly modified two-component GPE system, we construct 2D self-trapped modes in the form of QDs with vorticity S embedded into each component. Due to the effect of the logarithmic factor, the QDs feature a flat-top shape, which expands with the increase of S and norm N . An essential finding, produced by a systematic numerical investigation and analytical estimates, is that the vortical QDs are stable (which is a critical issue for vortex solitons in nonlinear models) up to S = 5, for N exceeding a certain threshold value, which is predicted to scale as N th ∼ S 4 for large S (for three-dimensional QDs, the scaling is N th ∼ S 6 ). The prediction is corroborated by numerical findings. Pivots of QDs with S ≥ 2 are subject to structural instability, as specially selected perturbations can split the single pivot in a set of S or S + 2 pivots corresponding to unitary vortices; however, the structural instability remains virtually invisible, as it occurs in a broad central "hole" of the vortex soliton, where values of fields are very small, and it does not cause any dynamical instability. In the condensate of 39 K atoms, in which QDs with S = 0 and a quasi-2D shape were created recently, the vortical droplets may have radial size 30 µm, with the number of atoms in the range of 10 4 − 10 5 . The role of three-body losses is considered too, demonstrating that they do not prevent the creation of the vortex droplets, but may produce a noteworthy effect, leading to sudden splitting of "light" droplets. In addition, hidden-vorticity states in QDs, with topological charges S+ = −S− = 1 in their components, which are prone to strong instability in other settings, have their stability region too. Unstable HV states tend to spontaneously merge into zero-vorticity solitons. Collisions of QDs, which may lead to their merger, and dynamics of elliptically deformed QDs (which form rotating elongated patterns or ones with oscillations of the eccentricity) are briefly considered too.

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“…nonlinearities was experimentally reported in 2 CS [54,55] and in suspensions of metallic nanoparticles [56], albeit in the presence of significant linear and nonlinear absorption, which severely limits the applicability of such materials in their present form.…”

Section: Uniform Mediamentioning

confidence: 97%

Frontiers in multidimensional self-trapping of nonlinear fields and matter

et al. 2019

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We review the state of the art and recently obtained theoretical and experimental results for two-and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates (BECs), and other fields -in particular, liquid crystals. The central challenge is avoiding the trend of 2D and 3D solitary states supported by the ubiquitous cubic nonlinearity to be strongly unstable -a property far less present in one-dimensional systems. Many possibilities for the stabilization of multi-dimensional states have been theoretically proposed over the years. Most strategies involve non-cubic nonlinearities or using different sorts of potentials, including periodic ones. New important avenues have arisen recently in systems based on two-component BEC with spin-orbit coupling, which have been predicted to support stable 2D and metastable 3D solitons. An important recent breakthrough is the creation of 3D quantum droplets. These are self-sustained states existing in two-component BECs, which are stabilized by the presence of Lee-Hung-Yang quantum fluctuations around the underlying mean-field states. By and large, multi-dimensional geometries afford unique opportunities to explore the existence of complex self-sustained states, including topologically rich ones, which by their very nature are not possible in one-dimensional geometries. In addition to vortex solitons, these are hopfions, skyrmions, and hybrid vortex-antivortex complexes, which have been predicted in different models. Here we review recent landmark findings in this field and outline outstanding open challenges. List of acronyms:1D one-dimensional 2D two dimensional 3D three dimensional BEC Bose-Einstein condensate FF fundamental frequency GPE Gross-Pitaevskii equation GVD group-velocity dispersion LHY Lee-Huang-Yang (correction to the mean-field dynamics of BEC) MF mean field MM mixed mode NLSE nonlinear Schrödinger equation SH second harmonic SOC spin-orbit coupling SV semi-vortex TS Townes' soliton VK Vakhitov-Kolokolov (stability criterion)

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Robust self-trapping of vortex beams in a saturable optical medium

Abstract: We report the first observation of robust self-trapping of vortex beams propagating in a uniform condensed medium featuring local saturable self-focusing nonlinearity. Optical

Cited by 49 publications

References 63 publications

(INVITED) Vortex solitons: Old results and new perspectives

(INVITED) Vortex solitons: Old results and new perspectives

Two-dimensional vortex quantum droplets

Frontiers in multidimensional self-trapping of nonlinear fields and matter

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