1
|
Melchert O, Willms S, Bose S, Yulin A, Roth B, Mitschke F, Morgner U, Babushkin I, Demircan A. Soliton Molecules with Two Frequencies. PHYSICAL REVIEW LETTERS 2019; 123:243905. [PMID: 31922846 DOI: 10.1103/physrevlett.123.243905] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2019] [Revised: 09/23/2019] [Indexed: 06/10/2023]
Abstract
We demonstrate a peculiar mechanism for the formation of bound states of light pulses of substantially different optical frequencies, in which pulses are strongly bound across a vast frequency gap. This is enabled by a propagation constant with two separate regions of anomalous dispersion. The resulting soliton compound exhibits moleculelike binding energy, vibration, and radiation and can be understood as a mutual trapping providing a striking analogy to quantum mechanics. The phenomenon constitutes an intriguing case of two light waves mutually affecting and controlling each other.
Collapse
Affiliation(s)
- Oliver Melchert
- Cluster of Excellence PhoenixD, Welfengarten 1, 30167, Hannover, Germany
- Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
- Hannover Centre for Optical Technologies, Nienburger Strasse 17, 30167, Hannover, Germany
| | - Stephanie Willms
- Cluster of Excellence PhoenixD, Welfengarten 1, 30167, Hannover, Germany
- Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Surajit Bose
- Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Alexey Yulin
- Department of Nanophotonics and Metamaterials, ITMO University, 197101 Saint Petersburg, Russia
- Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavik, Iceland
| | - Bernhard Roth
- Cluster of Excellence PhoenixD, Welfengarten 1, 30167, Hannover, Germany
- Hannover Centre for Optical Technologies, Nienburger Strasse 17, 30167, Hannover, Germany
| | - Fedor Mitschke
- Institute for Physics, University of Rostock, 18059 Rostock, Germany
| | - Uwe Morgner
- Cluster of Excellence PhoenixD, Welfengarten 1, 30167, Hannover, Germany
- Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
- Hannover Centre for Optical Technologies, Nienburger Strasse 17, 30167, Hannover, Germany
| | - Ihar Babushkin
- Cluster of Excellence PhoenixD, Welfengarten 1, 30167, Hannover, Germany
- Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Ayhan Demircan
- Cluster of Excellence PhoenixD, Welfengarten 1, 30167, Hannover, Germany
- Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
- Hannover Centre for Optical Technologies, Nienburger Strasse 17, 30167, Hannover, Germany
| |
Collapse
|
2
|
Cai X, Liu J, Wang S. Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit. OPTICS EXPRESS 2009; 17:2287-2297. [PMID: 19219132 DOI: 10.1364/oe.17.002287] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.
Collapse
Affiliation(s)
- Xin Cai
- Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
| | | | | |
Collapse
|
4
|
Zhu Y, Yang J. Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036605. [PMID: 17500807 DOI: 10.1103/physreve.75.036605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2006] [Indexed: 05/15/2023]
Abstract
Weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions, and phases of interacting solitary waves. These dynamical equations contain a single parameter, which accounts for the different forms of nonlinearity. When this parameter is zero, these dynamical equations are integrable, and the exact analytical solutions are derived. When this parameter is nonzero, the dynamical equations exhibit fractal structures which match those in the original wave equations both qualitatively and quantitatively. Thus the universal nature of fractal structures in the weak interaction of solitary waves is analytically established. The origin of these fractal structures is also explored. It is shown that these structures bifurcate from the initial conditions where the solutions of the integrable dynamical equations develop finite-time singularities. Based on this observation, an analytical criterion for the existence and locations of fractal structures is obtained. Lastly, these analytical results are applied to the generalized nonlinear Schrödinger equations with various nonlinearities such as the saturable nonlinearity, and predictions on their weak interactions of solitary waves are made.
Collapse
Affiliation(s)
- Yi Zhu
- Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, People's Republic of China.
| | | |
Collapse
|
5
|
Friedler I, Kurizki G, Cohen O, Segev M. Spatial Thirring-type solitons via electromagnetically induced transparency. OPTICS LETTERS 2005; 30:3374-6. [PMID: 16389836 DOI: 10.1364/ol.30.003374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
We show that the giant Kerr nonlinearity in the regime of electromagnetically induced transparency in vapor can give rise to the formation of Thirring-type spatial solitons, which are supported solely by cross-phase modulation that couples the two copropagating light beams.
Collapse
Affiliation(s)
- Inbal Friedler
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | | | | | | |
Collapse
|
6
|
Liu J, Hao Z. Evolution of separate screening soliton pairs in a biased series photorefractive crystal circuit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:066601. [PMID: 12188845 DOI: 10.1103/physreve.65.066601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2001] [Indexed: 05/23/2023]
Abstract
This paper presents calculations for an idea in photorefractive spatial soliton, namely, screening solitons form in a biased series photorefractive crystal circuit consisting of two photorefractive crystals connected electronically by electrode leads in a chain with a voltage source. A system of two coupled equations is derived under appropriate conditions for two-beam propagation in the crystal circuit. The possibility of obtaining steady-state bright and dark screening soliton solutions is investigated in one dimension and, the existence of dark-dark, bright-dark, and bright-bright separate screening soliton pairs in such a circuit is proved. The numerical results show that the two solitons in a soliton pair can affect each other by the light-induced current and their coupling can affect their spatial profiles, dynamical evolutions, stabilities, and self-deflection. Under the limit in which the optical wave has a spatial extent much less than the width of the crystal, only the dark soliton can affect the other soliton by the light-induced current, but the bright soliton cannot. For a bright-dark or dark-dark soliton pair, the dark soliton in a weak input intensity can be obtained for a larger nonlinearity than for a stronger input intensity. For a bright-dark soliton pair, increasing the input intensity of the dark soliton can increase the bending angle of the bright soliton. Some potential applications are discussed.
Collapse
Affiliation(s)
- Jinsong Liu
- State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People's Republic of China.
| | | |
Collapse
|
7
|
Yang J. Interactions of vector solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:026607. [PMID: 11497730 DOI: 10.1103/physreve.64.026607] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2001] [Indexed: 05/23/2023]
Abstract
In this paper, we study the interaction of two widely separated vector solitons in the nonintegrable coupled nonlinear Schrödinger (NLS) equations. Using a modification of Karpman-Solov'ev perturbation method, we derive dynamical equations for the evolution of both solitons' internal parameters. We show that these dynamical equations allow fixed points that correspond to stationary two-vector-soliton bound states if these solitons have the same phase in one component (same sign) and pi-phase difference in the other component (opposite sign). However, linear stability analysis indicates that these bound states are always unstable due to a phase-related unstable eigenvalue. We also investigate vector-soliton interactions and show that, in contrast to soliton interactions in the single NLS equation, vector solitons repel or attract each other depending not only on their relative phases but also on their initial position separation. Lastly, interaction of an arbitrary number of vector solitons is also studied in brief. All our analytical results are supported by direct numerical simulations.
Collapse
Affiliation(s)
- J Yang
- Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington 05401, USA.
| |
Collapse
|