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Marchiano R, Thomas JL. Doing arithmetic with nonlinear acoustic vortices. PHYSICAL REVIEW LETTERS 2008; 101:064301. [PMID: 18764457 DOI: 10.1103/physrevlett.101.064301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2008] [Revised: 05/20/2008] [Indexed: 05/26/2023]
Abstract
Phase singularities of wave-front-like screw dislocations or vortices possess a well-defined quantity that can only take integer value: the topological charge. In the nonlinear regime, it has been demonstrated that optical or acoustical vortices interact and the topological charge follows a conservation law. Here this facility is used in nonlinear parametric interaction of two vortices shifted in frequency to perform sums and subtractions of the topological charge. Thus, we experimentally demonstrate a new technique to perform wave computation in the group of integer Z. When the two vortices have commensurable frequencies, different combinations give the same frequencies but different tolopological charges may occur. We show that an energy criterion can be used to predict the outcome. A corollary is that a modulation of amplitude of the vortices switches from one result to the other.
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Affiliation(s)
- Régis Marchiano
- Université Pierre et Marie Curie-Paris6, CNRS, UMR 7190, Institut Jean le Rond d'Alembert, 4 place Jussieu, Paris, F-75005 France.
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Passier R, Devaux F, Chauvet M. Impact of tensorial nature of the electro-optic effect on vortex beam propagation in photorefractive media. OPTICS EXPRESS 2008; 16:7134-7141. [PMID: 18545416 DOI: 10.1364/oe.16.007134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Influence of the anisotropic tensorial electro-optic effect of LiNbO(3):Fe photorefractive defocusing medium on propagation of a vortex beam is numerically and experimentally investigated. Characteristic behaviors are depicted by varying light polarization, sign of vortex angular momentum and propagation directions.
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Affiliation(s)
- Rémy Passier
- Département d'Optique, Institut Femto-ST, Université de Franche-Comté16, route de Gray, 25030 Besançon Cédex, France.
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Aleshkevich VA, Egorov AA, Kartashov YV, Vysloukh VA, Zelenina AS. Stability analysis of spatiotemporal cnoidal waves in cubic nonlinear media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 67:066605. [PMID: 16241366 DOI: 10.1103/physreve.67.066605] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2003] [Indexed: 11/07/2022]
Abstract
We analyze numerically the modulational instability of spatiotemporal cnoidal waves of cn, dn, and sn types that are periodic along a single space coordinate and are uniform in time. The band of possible increments is calculated for all three types of cnoidal waves as a function of parameter describing the degree of localization of the wave field energy. It is shown that this band transforms into a set of discrete values for waves of cn and dn types in the limit of strong spatial localization. Simulation of perturbed cnoidal-wave propagation revealed suppression of collapse and multiple-wave filamentation on the developed stage of instability. Different instability scenarios are considered in detail.
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Affiliation(s)
- Victor A Aleshkevich
- Physics Department, M. V. Lomonosov Moscow State University, 119899 Vorobiovy Gory, Moscow, Russia
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Kartashov YV, Vysloukh VA, Torner L. Stable ring-profile vortex solitons in bessel optical lattices. PHYSICAL REVIEW LETTERS 2005; 94:043902. [PMID: 15783560 DOI: 10.1103/physrevlett.94.043902] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2004] [Indexed: 05/24/2023]
Abstract
Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034, Barcelona, Spain
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Xu Z, Kartashov YV, Crasovan LC, Mihalache D, Torner L. Multicolor vortex solitons in two-dimensional photonic lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016616. [PMID: 15697756 DOI: 10.1103/physreve.71.016616] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2004] [Indexed: 05/24/2023]
Abstract
We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable almost in the entire domain of their existence, and that the instability domain decreases with the increase of the lattice depth. We also show the generation of the solitons, and the feasibility of the concept of lattice soliton algebra.
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Affiliation(s)
- Zhiyong Xu
- ICFO-Institut de Ciencies Fotoniques, Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
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Bigelow MS, Zerom P, Boyd RW. Breakup of ring beams carrying orbital angular momentum in sodium vapor. PHYSICAL REVIEW LETTERS 2004; 92:083902. [PMID: 14995774 DOI: 10.1103/physrevlett.92.083902] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2003] [Indexed: 05/24/2023]
Abstract
We have observed filamentation due to azimuthal modulational instabilities in spinning ring solitons with orbital angular momentum m variant Planck's over 2pi in sodium vapor. We show experimentally that vortex beams with m values of 1, 2, and 3 tend to break into two, four, and six filaments, respectively. Treating the sodium vapor as a Doppler broadened two-level atomic system, we find that we can accurately model the propagation and breakup of these beams with numerical simulations.
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Affiliation(s)
- Matthew S Bigelow
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
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Mihalache D, Mazilu D, Crasovan LC, Malomed BA, Lederer F, Torner L. Robust soliton clusters in media with competing cubic and quintic nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:046612. [PMID: 14683070 DOI: 10.1103/physreve.68.046612] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2003] [Indexed: 05/24/2023]
Abstract
Systematic results are reported for dynamics of circular patterns ("necklaces"), composed of fundamental solitons and carrying orbital angular momentum, in the two-dimensional model, which describes the propagation of light beams in bulk media combining self-focusing cubic and self-defocusing quintic nonlinearities. Semianalytical predictions for the existence of quasistable necklace structures are obtained on the basis of an effective interaction potential. Then, direct simulations are run. In the case when the initial pattern is far from an equilibrium size predicted by the potential, it cannot maintain its shape. However, a necklace with the initial shape close to the predicted equilibrium survives very long evolution, featuring persistent oscillations. The quasistable evolution is not essentially disturbed by a large noise component added to the initial configuration. Basic conclusions concerning the necklace dynamics in this model are qualitatively the same as in a recently studied one which combines quadratic and self-defocusing cubic nonlinearities. Thus, we infer that a combination of competing self-focusing and self-defocusing nonlinearities enhances the robustness not only of vortex solitons but also of vorticity-carrying necklace patterns.
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Affiliation(s)
- D Mihalache
- ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 8034 Barcelona, Spain
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Petrov DV, Carrasco S, Molina-Terriza G, Torner L. Deflection of quadratic solitons at edge dislocations. OPTICS LETTERS 2003; 28:1439-1441. [PMID: 12943084 DOI: 10.1364/ol.28.001439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We report the observation of deflection of optical solitons generated in the frequency doubling of light beams containing edgelike topological amplitude and phase dislocations. The angular deflection of the solitons was found to be controllable through the position of the dislocation. The experiments were conducted near phase matching in a bulk potassium titanyl phosphate crystal pumped with picosecond light pulses at 1064 nm.
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Affiliation(s)
- Dmitri V Petrov
- ICFO-Institut de Ciencies Fotoniques, Universitat Politecnica de Catalunya, Barcelona, ES 08034, Spain.
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Crasovan LC, Kartashov YV, Mihalache D, Torner L, Kivshar YS, Pérez-García VM. Soliton "molecules": robust clusters of spatiotemporal optical solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046610. [PMID: 12786512 DOI: 10.1103/physreve.67.046610] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2002] [Indexed: 05/24/2023]
Abstract
We show how to generate robust self-sustained clusters of soliton bullets-spatiotemporal (optical or matter-wave) solitons. The clusters carry an orbital angular momentum being supported by competing nonlinearities. The "atoms" forming the "molecule" are fully three-dimensional solitons linked via a staircaselike macroscopic phase. Recent progress in generating atomic-molecular coherent mixing in the Bose-Einstein condensates might open potential scenarios for the experimental generation of these soliton molecules with matter waves.
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Affiliation(s)
- Lucian-Cornel Crasovan
- Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 08034 Barcelona, Spain
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Mamaev AV, Lodahl P, Saffman M. Observation of spatial modulation instability in intracavity second-harmonic generation. OPTICS LETTERS 2003; 28:31-33. [PMID: 12656526 DOI: 10.1364/ol.28.000031] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We report the observation of spatial instabilities in singly resonant intracavity second-harmonic generation. Self-focusing as well as spatially ordered near- and far-field structures are observed. Experimental results are compared with mean-field analysis as well as three-dimensional numerical simulations.
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Affiliation(s)
- A V Mamaev
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
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Kartashov YV, Crasovan LC, Mihalache D, Torner L. Robust propagation of two-color soliton clusters supported by competing nonlinearities. PHYSICAL REVIEW LETTERS 2002; 89:273902. [PMID: 12513208 DOI: 10.1103/physrevlett.89.273902] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2002] [Indexed: 05/24/2023]
Abstract
We reveal numerically the remarkably robust propagation of quasistationary two-color soliton clusters in media with competing quadratic and cubic nonlinearities. We predict that such clusters carrying nonzero angular momentum can propagate over any practically feasible crystal length before they decay, even in the presence of input random perturbations.
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Affiliation(s)
- Yaroslav V Kartashov
- Institute of Photonic Sciences and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
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Minardi S, Arrighi G, Di Trapani P, Varanaviius A, Piskarskas A. Solitonic all-optical switch based on the fractional Talbot effect. OPTICS LETTERS 2002; 27:2097-2099. [PMID: 18033453 DOI: 10.1364/ol.27.002097] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
A periodic pattern of hundreds of beams is shifted by half its transverse period as the result of excitation of parametric spatial solitons and the fractional Talbot effect. The all-optical switch that is obtained operates with 1-ps pulses.
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