Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions

A new exactly solvable ($1+1$)-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space–time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.     

Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation

We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi–Pasta–Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.     

Approximate rogue wave solutions of the forced and damped nonlinear Schrödinger equation for water waves

We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped nonlinear Schrödinger (NLS) equation into the standard NLS with constant coefficients. The transformation is valid as long as |Γt|?1$|\Gamma t|?1$, with Γ the growth/damping rate of the waves due to the wind/dissipation. Approximate rogue wave solutions of the equation are presented and discussed. The results shed some lights on the effects of wind and dissipation on the formation of rogue waves.     

Emergence of rogue waves from optical turbulence

We provide some general physical insights into the emergence of rogue wave events from optical turbulence by analyzing the long term evolution of the field. Depending on the amount of incoherence in the system (i.e., Hamiltonian), we identify three turbulent regimes that lead to the emergence of specific rogue wave events: (i) persistent and coherent rogue quasi-solitons, (ii) intermittent-like rogue quasi-solitons that appear and disappear erratically, and (iii) sporadic rogue waves events that emerge from turbulent fluctuations as bursts of light or intense flashes.     

Evaluating the robustness of rogue waves under perturbations

Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this work, we develop a novel numerical perspective towards identifying such states as localized solutions in space-time. Importantly, we illustrate this methodology for different perturbations of nonlinear Schrödinger models. In particular, in addition to benchmarking known solutions (and confirming their numerical propagation under controllable error) this enables the continuation of such solutions over parametric variations to non-integrable models. As a result, we can answer in the positive the question about the parametric robustness of Peregrine-like waveforms and even of generalizations thereof on a cnoidal wave background.     

Interesting effect of optical Kerr nonlinearity in expanding single-mode regime of optical fibers using dispersion-flattened profiles

An interesting effect of optical Kerr nonlinearity is reported from theoretical investigation on the fundamental and first higher mode cutoff frequencies in single-mode fibers doped with highly nonlinear materials like CdS_xSe_1−x with W-type dispersion-flattened profiles. It is observed that whereas the single-mode regime decreases absolutely for dispersion-shifted profiles due to reduction of the first higher order mode cutoff frequency as is evident from earlier studies, it increases for W-type profiles for such nonlinearity taking its effect on the nonzero fundamental mode cutoff frequency into consideration. Thus, one can go further down below the fundamental mode cutoff frequency while using W-fibers in single mode nonlinear fiber devices involving evanescent field coupling in the low V region.     

Early detection of rogue waves in a chaotic wave field

The ability to unveil growing rogue waves in the ocean is essential for safe marine travel in stormy conditions. This vital problem has not been adequately addressed so far. We show that the specific triangular spectra of rogue waves can be detected at early stages of their development in a chaotic wave field. Continuously measuring the spectra of various parts of the wave field allows us to find a rogue wave before the dangerous peak appears. This possibility of early detection is a necessary part of a rogue wave early-warning system.     

Optical characterization of quantum dots entrained in microstructured optical fibers

We present a study of the basic optical properties of colloidal CdSe/ZnS core/shell quantum dots entrained in a microstructured optical fiber. Quantum dots suspended in heptane were pulled into the holes surrounding the solid core of a microstructured optical fiber of the holey fiber class via capillary action and are found to remain in the fiber. In this experiment, a laser coupled into the fiber photoexcited quantum dots along the length of the fiber. Quantum dot emission was observed to couple into the fiber core and propagate along the fiber. To investigate the use of such a system in fiber-based light generation or amplification, a second laser overlapping the low-energy portion of the quantum dot emission was simultaneously coupled into the fiber. We observed apparent amplification of this light when photoexciting the quantum dots well above their bandedge.     

Photophysical and nonlinear optical properties of zincphthalocyanines with peripheral substitutions

Photophysical and nonlinear optical properties of zinc phthalocyanines (ZnPc) bearing peripheral phenoxy substituents containing different functionalized groups were studied. Fluorescence spectra corresponding to the optical transition S₁ → S₀ are found to be appeared at 684 or 686.4 nm. Z-scan technique reveals large nonlinearities, where the absorptive and refractive effects are separately evaluated. Saturation absorption of ZnPc-1 was observed at 632.8 nm, with a very large nonlinear absorption coefficient β = −1.36 × 10⁻² cm/W. However a strong nonlinear refractive effect was found in all ZnPcs (1-4). Transmitted versus incident irradiance measurements carried out on ZnPc-1 and ZnPc-2, showed a very clear optical limiting behavior with irradiance thresholds around be 44 W/cm² and 90 W/cm² respectively.     

Sum-frequency mixing of optical vortices in nonlinear crystals

Results of theoretical and experimental investigation of the influence of walk-off on sum-frequency mixing of optical vortices in nonlinear crystals are presented. Various phenomena of vortex interaction such as decay of higher order vortices into singly charged vortices, formation of aligned arrays of vortices perpendicular to walk-off direction, particle-like pulling and pushing of vortices, and appearance of pairs of vortices having opposite charges were observed.     

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.     

On Nth-order rogue wave solution to nonlinear coupled dispersionless evolution equations

The generalized Darboux transformation is applied to obtain Nth-order rogue wave solution of nonlinear coupled dispersionless evolution equations (NLCDEE). In particular, the interesting structures for these solutions from first to third order rogue wave are shown.     

All optical self signal processing using chalcogenide nonlinear fiber Bragg grating

In this study, we simulate numerically quasi pulse propagation in a uniform nonlinear fiber Bragg grating (FBG) made of chalcogenide glasses. Because of bistability and nonlinearity behavior of FBG, the shapes of output pulse vary abruptly and strongly according to the input peak intensity. We take Gaussian pulse as input and produce saw-tooth wave and square wave in the output by suitable input amplitude and FBG length also we could reach pulse chopping and pulse compression. These all optical signal processing achieved for a few length, i.e. 6.6 mm and few intensity, i.e. 35 W/m² because of high nonlinearity of chalcogenide glasses.     

Stimulated Brillouin scattering phase conjugating properties of long multimode optical fibers

This paper describes and characterizes a detailed experiment that proves the phase conjugating properties of stimulated Brillouin scattering in multimode fibers (km of length), a problem still in debate in the literature, by studying the random aberrations correction abilities of this nonlinear interaction. Detailed qualitative and quantitative evaluation of aberration correction, by using the M² beam propagation ratio as a criterion to assess beam quality of the beams, proves the phase conjugation via SBS in long MM fibers. A new parameter to characterize the efficiency of the SBS phase conjugation process is proposed and conditions to obtain a complete healing of distortions (complete phase conjugation) are discussed.     

Modulational instability,rogue waves,and envelope solitons in opposite polarity dusty plasmas

Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust grains as well as inertialess non-extensive $q?$distributed electrons and non-thermal ions. A nonlinear Schrödinger equation (NLSE) is derived by using the reductive perturbation method. It has been observed from the analysis of NLSE that the modulationally stable solitary DAWs give rise to the existence of dark envelope solitons, and that the modulationally unstable solitary DAWs give rise to the existence of bright envelope solitons or rogue structures. It is also observed for the fast mode of DAWs that the basic features (viz. stability of the DAWs, MI, growth rate, amplitude, and width of the DA rogue waves, etc.) are significantly modified by the related plasma parameters (viz. dust masses, dust charge state, non-extensive parameter q, and non-thermal parameter α). The results of our present investigation might be useful for understanding different nonlinear electrostatic phenomena in both space (viz. ionosphere and mesosphere) and laboratory plasmas (viz. high intensity laser irradiation and hot cathode discharge).     

Optical fibers with low nonlinearity and low polarization-mode dispersion for terabit communications

Refractive-index nonlinearities have negligible effect on the performance of short-haul fiber-optic communication links utilizing electronic repeaters. However, in long links, nonlinearities can cause severe signal degradations. To mitigate nonlinear effects, a new generation of fibers, referred to as large effective-area fibers, have been introduced in recent years. This paper reviews the latest research and development work on these fibers conducted by several research groups around the world. Attention is focused on a class of large effective-area fibers that are based on a depressed-core multiple-cladding design. Another important issue in long-haul and high capacity fiber optic systems is the polarization-mode dispersion (PMD) which has been recognized as a serious limiting factor. In this paper, an improved fiber design is proposed which, in addition to providing large effective-area and low bending loss, eliminates PMD due to elliptical deformation in the single-mode wavelength region. Furthermore, this design is allowed to provide a small chromatic dispersion about few ps/nmkm, in order to overcome four-wave mixing effects.     

Dark and composite rogue waves in the coupled Hirota equations

The intriguing dark and composite rogue wave dynamics in a coupled Hirota system are unveiled, based on the exact explicit rational solutions obtained under the assumption of equal background height. It is found that a dark rogue wave state would occur as a result of the strong coupling between two field components with large wavenumber difference, and there would appear plenty of composite structures that are attributed to the specific wavenumber difference and the free choice of three independent structural parameters. The coexistence of different fundamental rogue waves in such a coupled system is also demonstrated.     

Numerical simulations of the nonlinear propagation of femtosecond optical pulses in gases

A two-dimensional axisymmetric model of the propagation of intense femtosecond laser pulses through dispersion-free transparent media is described. The effects of diffraction, nonlinear Kerr effect (instantaneous and retarded) and multiphoton ionisation are included. Numerical results concerning air and other gases are discussed. In particular, time self-compression of femtosecond pulses is predicted. Stable self-guided pulses are simulated, in agreement with recent experimental observations. Received: 19 June 1998 / Received in final form: 14 January 1999     

On the transmission by liquid crystal tapered optical fibers

A three-layer liquid crystal tapered optical fiber (LCTF) is investigated with the emphasis on the power confinements by the low order TE and TM modes sustained in the different sections of LCTF. The outermost clad section is considered to be made of liquid crystal with radial anisotropy whereas the core and the inner clad are dielectric regions. Rigorous field expressions in the different LCTF sections are deduced, and the plots of power confinement factors (or the relative distributions) are ultimately made considering different fiber dimensions. The results reveal that the TE modes confine maximum amount of power in the outermost liquid crystal region, which is attributed to the radial anisotropy of the section. Such features of LCTFs attract their usefulness in the area of field coupling devices and optical sensing where evanescent field technique is primarily implemented.