1
|
Chowdury A, Tan DTH. Resonant Akhmediev breathers. Sci Rep 2024; 14:10686. [PMID: 38724621 PMCID: PMC11081960 DOI: 10.1038/s41598-024-61533-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Accepted: 05/07/2024] [Indexed: 05/12/2024] Open
Abstract
Modulation instability is a phenomenon in which a minor disturbance within a carrier wave gradually amplifies over time, leading to the formation of a series of compressed waves with higher amplitudes. In terms of frequency analysis, this process results in the generation of new frequencies on both sides of the original carrier wave frequency. We study the impact of fourth-order dispersion on this modulation instability in the context of nonlinear optics that lead to the formation of a series of pulses in the form of Akhmediev breather. The Akhmediev breather, a solution to the nonlinear Schrödinger equation, precisely elucidates how modulation instability produces a sequence of periodic pulses. We observe that when weak fourth-order dispersion is present, significant resonant radiation occurs, characterized by two modulation frequencies originating from different spectral bands. As an Akhmediev breather evolves, these modulation frequencies interact, resulting in a resonant amplification of spectral sidebands on either side of the breather. When fourth-order dispersion is of intermediate strength, the spectral bandwidth of the Akhmediev breather diminishes due to less pronounced resonant interactions, while stronger dispersion causes the merging of the two modulation frequency bands into a single band. Throughout these interactions, we witness a complex energy exchange process among the phase-matched frequency components. Moreover, we provide a precise explanation for the disappearance of the Akhmediev breather under weak fourth-order dispersion and its resurgence with stronger values. Our study demonstrates that Akhmediev breathers, under the influence of fourth-order dispersion, possess the capability to generate infinitely many intricate yet coherent patterns in the temporal domain.
Collapse
Affiliation(s)
- Amdad Chowdury
- Photonics Devices and Systems Group, Singapore University of Technology and Design, 8 Somapah Rd., Singapore, 487372, Singapore.
| | - Dawn T H Tan
- Photonics Devices and Systems Group, Singapore University of Technology and Design, 8 Somapah Rd., Singapore, 487372, Singapore.
- Institute of Microelectronics (IME), Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-02, Singapore, 138634, Singapore.
| |
Collapse
|
2
|
Sun Z, Li J, Bian R, Deng D, Yang Z. Transmission mode transformation of rotating controllable beams induced by the cross phase. OPTICS EXPRESS 2024; 32:9201-9212. [PMID: 38571158 DOI: 10.1364/oe.520342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 02/23/2024] [Indexed: 04/05/2024]
Abstract
In this paper, complex-variable sine-Gaussian cross-phase (CVSGCP) beams are proposed, and the transmission dynamics properties of the CVSGCP beams in strongly nonlocal nonlinear media are investigated. CVSGCP beams can produce a variety of mode transformation characteristics during transmission. The roles of parameters in the sine and cross-phase terms of the initial light field expression in the evolution of light intensity modes, phase, and beam width are analyzed in detail, and it is proved that the effect of cross phase is to cause the beams to rotate. The control of different modes can be achieved by selecting suitable parameters, which have certain advantages in the practical application of CVSGCP beams. CVSGCP beams can be regarded as generalized high-order breathers because light intensity modes and beam width show periodic oscillation distribution during transmission. The typical evolution characteristics of the CVSGCP beams are verified by numerical simulation. Strongly nonlocal nonlinear optical media can be mathematically equivalent to a variety of optical systems, such as gradient index potential wells and resonant potential wells, so the conclusions in this paper can also be extended to these equivalent optical systems.
Collapse
|
3
|
Steinberg AB, Maucher F, Gurevich SV, Thiele U. Exploring bifurcations in Bose-Einstein condensates via phase field crystal models. CHAOS (WOODBURY, N.Y.) 2022; 32:113112. [PMID: 36456347 DOI: 10.1063/5.0101401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 10/03/2022] [Indexed: 06/17/2023]
Abstract
To facilitate the analysis of pattern formation and the related phase transitions in Bose-Einstein condensates, we present an explicit approximate mapping from the nonlocal Gross-Pitaevskii equation with cubic nonlinearity to a phase field crystal (PFC) model. This approximation is valid close to the superfluid-supersolid phase transition boundary. The simplified PFC model permits the exploration of bifurcations and phase transitions via numerical path continuation employing standard software. While revealing the detailed structure of the bifurcations present in the system, we demonstrate the existence of localized states in the PFC approximation. Finally, we discuss how higher-order nonlinearities change the structure of the bifurcation diagram representing the transitions found in the system.
Collapse
Affiliation(s)
- A B Steinberg
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
| | - F Maucher
- Departament de Física, Universitat de les Illes Balears and IAC-3, Campus UIB, E-07122 Palma de Mallorca, Spain
| | - S V Gurevich
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
| | - U Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
| |
Collapse
|
4
|
Bland T, Poli E, Politi C, Klaus L, Norcia MA, Ferlaino F, Santos L, Bisset RN. Two-Dimensional Supersolid Formation in Dipolar Condensates. PHYSICAL REVIEW LETTERS 2022; 128:195302. [PMID: 35622047 DOI: 10.1103/physrevlett.128.195302] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Revised: 01/19/2022] [Accepted: 04/11/2022] [Indexed: 06/15/2023]
Abstract
Dipolar condensates have recently been coaxed to form the long-sought supersolid phase. While one-dimensional supersolids may be prepared by triggering a roton instability, we find that such a procedure in two dimensions (2D) leads to a loss of both global phase coherence and crystalline order. Unlike in 1D, the 2D roton modes have little in common with the supersolid configuration. We develop a finite-temperature stochastic Gross-Pitaevskii theory that includes beyond-mean-field effects to explore the formation process in 2D and find that evaporative cooling directly into the supersolid phase-hence bypassing the first-order roton instability-can produce a robust supersolid in a circular trap. Importantly, the resulting supersolid is stable at the final nonzero temperature. We then experimentally produce a 2D supersolid in a near-circular trap through such an evaporative procedure. Our work provides insight into the process of supersolid formation in 2D and defines a realistic path to the formation of large two-dimensional supersolid arrays.
Collapse
Affiliation(s)
- T Bland
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Innsbruck 6020, Austria
| | - E Poli
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck 6020, Austria
| | - C Politi
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Innsbruck 6020, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck 6020, Austria
| | - L Klaus
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Innsbruck 6020, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck 6020, Austria
| | - M A Norcia
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Innsbruck 6020, Austria
| | - F Ferlaino
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Innsbruck 6020, Austria
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck 6020, Austria
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Hannover 30167, Germany
| | - R N Bisset
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck 6020, Austria
| |
Collapse
|
5
|
Ramaniuk A, Trippenbach M, Jung PS, Christodoulides DN, Krolikowski W, Assanto G. Scalar and vector supermode solitons owing to competing nonlocal nonlinearities. OPTICS EXPRESS 2021; 29:8015-8023. [PMID: 33820256 DOI: 10.1364/oe.417352] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
We investigate scalar and vector multi-hump spatial solitons resulting from competing Kerr-like nonlinear responses excited in a nonlocal medium by either one or two (mutually incoherent) light beams. Two-color vector supermode solitons are more amenable to control but exhibit an intriguing form of spontaneous symmetry breaking in propagation.
Collapse
|
6
|
Musso D, Naegels D. Independent Goldstone modes for translations and shift symmetry from a real modulated scalar. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.101.045016] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
7
|
Paredes A, Blanco-Labrador J, Olivieri DN, Salgueiro JR, Michinel H. Vortex revivals and Fermi-Pasta-Ulam-Tsingou recurrence. Phys Rev E 2019; 99:062211. [PMID: 31330596 DOI: 10.1103/physreve.99.062211] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Indexed: 11/07/2022]
Abstract
We study the self-trapped vortex-ring eigenstates of the two-dimensional Schrödinger equation with focusing Poisson and cubic nonlinearities. For each value of the topological charge l, there is a family of solutions depending on a parameter that can be understood as the relative importance of the cubic term. We analyze the perturbative stability of the solutions and simulate the fate of the unstable ones. For l=1 and l=2, there is an interval of the family of eigenstates for which the initial profile breaks apart but subsequently reconstructs itself, a process that can be interpreted as a nontrivial nonlinear oscillation between the vortex and an azimuthon. This revival provides a compelling realization of a recurrence of the Fermi-Pasta-Ulam-Tsingou type. Outside this interval, the vortices can be stable (for small cubic terms) or unstable and nonrecurrent (for large cubic terms). We argue that there is a crossover between these regimes that resembles a strong stochasticity threshold. For l≥3, all solutions are unstable and nonrecurrent. Finally, we comment on the possible experimental implementation of this phenomenon in the context of nonlinear laser beam propagation in thermo-optical media.
Collapse
Affiliation(s)
- Angel Paredes
- Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense, ES-32004 Spain
| | - José Blanco-Labrador
- Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense, ES-32004 Spain
| | - David N Olivieri
- Departamento de Linguaxes e Sistemas Informáticos, Universidade de Vigo, As Lagoas s/n, Ourense, ES-32004 Spain
| | - José R Salgueiro
- Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense, ES-32004 Spain
| | - Humberto Michinel
- Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense, ES-32004 Spain
| |
Collapse
|
8
|
Zhang YC, Maucher F, Pohl T. Supersolidity around a Critical Point in Dipolar Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2019; 123:015301. [PMID: 31386402 DOI: 10.1103/physrevlett.123.015301] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Indexed: 06/10/2023]
Abstract
We explore spatial symmetry breaking of a dipolar Bose-Einstein condensate in the thermodynamic limit and reveal a critical point in the phase diagram at which crystallization occurs via a second-order phase transition. This behavior is traced back to the significant effects of quantum fluctuations in dipolar condensates, which moreover stabilize a new supersolid phase, namely a regular honeycomb pattern with high modulational contrast and near-perfect superfluidity.
Collapse
Affiliation(s)
- Yong-Chang Zhang
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK 8000 Aarhus, Denmark
| | - Fabian Maucher
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK 8000 Aarhus, Denmark
| | - Thomas Pohl
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK 8000 Aarhus, Denmark
| |
Collapse
|
9
|
Maucher F, Skupin S, Gardiner SA, Hughes IG. Creating Complex Optical Longitudinal Polarization Structures. PHYSICAL REVIEW LETTERS 2018; 120:163903. [PMID: 29756941 DOI: 10.1103/physrevlett.120.163903] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Indexed: 06/08/2023]
Abstract
In this Letter, we show that it is possible to structure the longitudinal polarization component of light. We illustrate our approach by demonstrating linked and knotted longitudinal vortex lines acquired upon nonparaxially propagating a tightly focused subwavelength beam. The remaining degrees of freedom in the transverse polarization components can be exploited to generate customized topological vector beams.
Collapse
Affiliation(s)
- F Maucher
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
- Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom
| | - S Skupin
- Univ. Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications, UMR 5107, F-33405 Talence, France
- Institut Lumière Matière, UMR5306 Université Lyon 1 - CNRS, Université de Lyon, F-69622, Villeurbanne, France
| | - S A Gardiner
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - I G Hughes
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| |
Collapse
|
10
|
Alberucci A, Laudyn UA, Piccardi A, Kwasny M, Klus B, Karpierz MA, Assanto G. Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects. Phys Rev E 2018; 96:012703. [PMID: 29347250 DOI: 10.1103/physreve.96.012703] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Indexed: 11/07/2022]
Abstract
We investigate nonlinear optical propagation of continuous-wave (CW) beams in bulk nematic liquid crystals. We thoroughly analyze the competing roles of reorientational and thermal nonlinearity with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells excited by a single CW beam in the highly nonlocal limit. To adjust the relative weight between the two nonlinear responses, we employ two distinct wavelengths, inside and outside the absorption band of the dye, respectively. Different concentrations of the dye are considered in order to enhance the thermal effect. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation based on a semi-analytic approach. Theoretical results are finally compared to experimental results in the Nematic Liquid Crystals (NLC) 4-trans-4'-n-hexylcyclohexylisothiocyanatobenzene (6CHBT) doped with Sudan Blue dye.
Collapse
Affiliation(s)
- Alessandro Alberucci
- Photonics Laboratory, Tampere University of Technology, FI-33101 Tampere, Finland
| | - Urszula A Laudyn
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Armando Piccardi
- NooEL-Nonlinear Optics and OptoElectronics Lab, University "Roma Tre," I-00146 Rome, Italy
| | - Michał Kwasny
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Bartlomiej Klus
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Mirosław A Karpierz
- Faculty of Physics, Warsaw University of Technology, PL-00662 Warsaw, Poland
| | - Gaetano Assanto
- Photonics Laboratory, Tampere University of Technology, FI-33101 Tampere, Finland.,NooEL-Nonlinear Optics and OptoElectronics Lab, University "Roma Tre," I-00146 Rome, Italy
| |
Collapse
|
11
|
Brée C, Babushkin I, Morgner U, Demircan A. Regularizing Aperiodic Cycles of Resonant Radiation in Filament Light Bullets. PHYSICAL REVIEW LETTERS 2017; 118:163901. [PMID: 28474936 DOI: 10.1103/physrevlett.118.163901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Indexed: 06/07/2023]
Abstract
We demonstrate an up to now unrecognized and very effective mechanism which prevents filament collapse and allows persistent self-guiding propagation retaining a large portion of the optical energy on axis over unexpected long distances. The key ingredient is the possibility of continuously leaking energy into the normal dispersion regime via the emission of resonant radiation. The frequency of the radiation is determined by the dispersion dynamically modified by photogenerated plasma, thus allowing us to excite new frequencies in spectral ranges which are otherwise difficult to access.
Collapse
Affiliation(s)
- Carsten Brée
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany
| | - Ihar Babushkin
- Institute for Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
| | - Uwe Morgner
- Institute for Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
| | - Ayhan Demircan
- Institute for Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
| |
Collapse
|
12
|
Feijoo D, Paredes A, Michinel H. Dynamics of vortex-antivortex pairs and rarefaction pulses in liquid light. Phys Rev E 2017; 95:032208. [PMID: 28415211 DOI: 10.1103/physreve.95.032208] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Indexed: 11/07/2022]
Abstract
We present a numerical study of the cubic-quintic nonlinear Schrödinger equation in two transverse dimensions, relevant for the propagation of light in certain exotic media. A well-known feature of the model is the existence of flat-top bright solitons of fixed intensity, whose dynamics resembles the physics of a liquid. They support traveling wave solutions, consisting of rarefaction pulses and vortex-antivortex pairs. In this work, we demonstrate how the vortex-antivortex pairs can be generated in bright soliton collisions displaying destructive interference followed by a snake instability. We then discuss the collisional dynamics of the dark excitations for different initial conditions. We describe a number of distinct phenomena including vortex exchange modes, quasielastic flyby scattering, solitonlike crossing, fully inelastic collisions, and rarefaction pulse merging.
Collapse
Affiliation(s)
- David Feijoo
- Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Angel Paredes
- Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Humberto Michinel
- Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| |
Collapse
|
13
|
Small-Amplitude Nonlinear Modes under the Combined Effect of the Parabolic Potential, Nonlocality and PT Symmetry. Symmetry (Basel) 2016. [DOI: 10.3390/sym8080072] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
|