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Temgoua DDE, Tchokonte MBT, Kofane TC. Combined effects of nonparaxiality, optical activity, and walk-off on rogue wave propagation in optical fibers filled with chiral materials. Phys Rev E 2018; 97:042205. [PMID: 29758712 DOI: 10.1103/physreve.97.042205] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2017] [Indexed: 11/07/2022]
Abstract
The generalized nonparaxial nonlinear Schrödinger (NLS) equation in optical fibers filled with chiral materials is reduced to the higher-order integrable Hirota equation. Based on the modified Darboux transformation method, the nonparaxial chiral optical rogue waves are constructed from the scalar model with modulated coefficients. We show that the parameters of nonparaxiality, third-order dispersion, and differential gain or loss term are the main keys to control the amplitude, linear, and nonlinear effects in the model. Moreover, the influence of nonparaxiality, optical activity, and walk-off effect are also evidenced under the defocusing and focusing regimes of the vector nonparaxial NLS equations with constant and modulated coefficients. Through an algorithm scheme of wider applicability on nonparaxial beam propagation methods, the most influential effect and the simultaneous controllability of combined effects are underlined, showing their properties and their potential applications in optical fibers and in a variety of complex dynamical systems.
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Affiliation(s)
- D D Estelle Temgoua
- Laboratory of Mechanics, Materials and Structures, Post Graduate School in Sciences, Technology and Geosciences, Doctoral Research, Unit in Physics and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Organization for Women in Science for the Developing World, ICTP Campus, Strada Costiera 11, 34151 Trieste, Italy.,Department of Physics and Astronomy, University of the Western Cape, Private Bag X17, Bellville, 7535 South Africa
| | - M B Tchoula Tchokonte
- Department of Physics and Astronomy, University of the Western Cape, Private Bag X17, Bellville, 7535 South Africa
| | - T C Kofane
- Laboratory of Mechanics, Materials and Structures, Post Graduate School in Sciences, Technology and Geosciences, Doctoral Research, Unit in Physics and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
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Liu TY, Chiu TL, Clarkson PA, Chow KW. A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane. CHAOS (WOODBURY, N.Y.) 2017; 27:091103. [PMID: 28964137 DOI: 10.1063/1.5001007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.
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Affiliation(s)
- T Y Liu
- Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong
| | - T L Chiu
- Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong
| | - P A Clarkson
- School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7FS, United Kingdom
| | - K W Chow
- Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong
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