Generation of pulse trains in the normal dispersion regime of a dielectric medium using a relaxing nonlinearity

We show that modulation-type instability can occur in the normal dispersion regime of a dielectric medium for the case of a relaxing self-focusing nonlinearity. This instability leads to the generation of pulse trains with almost no pedestal when periodic boundary conditions are applied. © 1991 American Institute of PhysicsThis work was supported by the Joint Services Optical Program of the Air Force Office of Scientific Research and the Army Research Office, the Army Research Office (DAAL03-88-KOO66), and J. M. Soto-Crespo acknowl- edges a grant from the Ministerio de Education y Ciencia, Spain.Peer Reviewe

Electromagnetic scattering from very rough random surfaces and deep reflection gratings

A theoretical study of electromagnetic wave scattering from deep perfectly conducting one-dimensional random rough surfaces and reflection gratings is performed by means of the extinction theorem. The scattering equations are solved numerically (instead of being solved by the usual analytical procedures, which are valid only for slight corrugations). This permits us to obtain an exhaustive collection of results for the mean scattered intensity as a function of polarization and surface parameters. In particular, Lambertian scattering and enhanced backscattering are predicted for random surfaces. Also, the range of validity of the Kirchhoff approximation is established for random surfaces whose correlation length is comparable with or smaller than the wavelength. Concerning gratings, random surfaces whose correlation length is comparable with or smaller than the wavelength. Concerning gratings, is shown that the blaze of the antispecular order for gratings is at the root of the enhanced backscattering for random surfaces. © 1989 Optical Society of AmericaThis research was supported by the Comisión Interministerial de Ciencia y Tecnología under grant PB0278.Peer Reviewe

Stability of three-dimensional self-trapped beams with a dark spot surrounded by bright rings of varying intensity

We analytically and numerically examine the stability of three-dimensional self-trapped beams with a dark spot surrounded by bright rings of varying intensity in a uniform saturable self-focusing medium. It is shown that the fundamental bound state of the family is stable to a symmetric perturbation but unstable to an asymmetric perturbation (that breaks the azimuthal symmetry of the beam, i.e., transverse instabilities). The higher-order states are also found to display transverse (modulation) instabilities. The development of the instabilities is shown to lead to the emission of filaments which spiral away from the center of the dark spot as stable entities. © 1994 The American Physical Society.Peer Reviewe

Dissipative vortex solitons in 2D-lattices

We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a topological charge S = 1. Surprisingly, the dynamical evolution of unstable solutions of this family does not alter significantly their profile, instead their phase distribution completely changes. They transform into two-charges swirl-vortex solitons. We dynamically excite this novel structure showing its experimental feasibility.Comment: 4 pages, 20 figure

Solitary-wave vortices in quadratic nonlinear media

We find families of vortex solitary waves in bulk quadratic nonlinear media under conditions for second-harmonic generation. We show that the vortex solitary waves are azimuthally unstable and that they decay into sets of stable spatial solitons. We calculate the growth rates of the azimuthal perturbations and show how those affect the pattern of output light. © 1998 Optical Society of AmericaPeer ReviewedPostprint (published version

Extreme wave dynamics in ultrashort fiber lasers

Conferencia invitada; IS-PALD 2015, Metz, France, November 4- 6, 2015; http://ispald.web2.ncku.edu.tw/We review recent experiments that demonstrate the existence of optical wave transients of unusually high amplitude in fiber lasers operated in the vicinity of mode locking. These transients are analyzed in the context of optical rogue wave formation, with an important role played by the constraints of ultrafast measurements. From these investigations, a universal rogue wave mechanism is highlighted, which results from the evolution of a chaotic bunch of pulses or sub-pulses, subjected to numerous inelastic collisions, while traveling round the laser cavity.Peer Reviewe

Breather turbulence versus soliton turbulence: Rogue waves, probability density functions, and spectral features

10 págs.; 12 figs.Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states >breather turbulence> or >soliton turbulence.> The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics. ©2016 American Physical SocietyThe authors acknowledge the support from the Volkswagen Stiftung. The work of JMSC was also supported by MINECO under Contract No. TEC2015-71127-C2-1-R, and by C.A.M. under Contract No. S2013/MIT-2790. N.D. and N.A. acknowledge support of the Australian Research Council (Discovery Project No. DP140100265).Peer Reviewe

Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes

Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation.N.A. acknowledges support from the Australian Research Council. The work of J.M.S.-C. was supported by the M.E.y C. under Contract No. FIS2006-03376 and P.G. acknowledges support from Agence Nationale de la Recherche

Variational approach for walking solitons in birefringent fibres

We use the variational method to obtain approximate analytical expressions for the stationary pulselike solutions in birefringent fibers when differences in both phase velocities and group velocities between the two components and rapidly oscillating terms are taken into account. After checking the validity of the approximation we study how the soliton pulse shape depends on its velocity and nonlinear propagation constant. By numerically solving the propagation equation we have found that most of these stationary solutions are stable.Comment: LaTeX2e, uses graphicx package, 23 pages with 8 figure

Extreme soliton pulsations in dissipative systems

8 págs.; 18 figs.; PACS number(s): 42.65.Sf, 42.60.Mi, 42.65.Tg© 2015 American Physical Society. We have found a strongly pulsating regime of dissipative solitons in the laser model described by the complex cubic-quintic Ginzburg-Landau equation. The pulse energy within each period of pulsations may change more than two orders of magnitude. The soliton spectra in this regime also experience large variations. Period doubling phenomena and chaotic behaviors are observed in the boundaries of existence of these pulsating solutions.The authors acknowledge the support of the Australian Research Council (Grants No. DE130101432, No. DP140100265, and No. DP150102057). The work of J.M.S.-C. was supported by MINECO under Contract No. TEC2012-37958-C02-02, and by Comunidad Autonoma de Madrid under Contract No. S2013/MIT-2790. J.M.S.-C. and N.A. acknowledge the support of the Volkswagen Foundation.Peer Reviewe