Fundamental Dark Solitons Research Articles

Bright, dark and breather soliton solutions of the generalized long-wave short-wave resonance interaction system

In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the Hirota bilinear method, the general N-bright and N-dark soliton solutions are deduced and their Gram determinant forms are obtained. A special feature of the fundamental bright soliton solution is that, in general, it behaves like the Korteweg-deVries soliton. However, under a special condition, it also behaves akin to the nonlinear Schrödinger soliton when it loses the amplitude-dependent velocity property. The fundamental dark-soliton solution admits anti-dark, gray, and completely black soliton profiles, in the short-wave component, depending on the choice of wave parameters. On the other hand, a bright soliton-like profile always occurs in the long-wave component. The asymptotic analysis shows that both the bright and dark solitons undergo an elastic collision with a finite phase shift. In addition to these, by tuning the phase shift regime, we point out the existence of resonance interactions among the bright solitons. Furthermore, under a special velocity resonance condition, we bring out the various types of bright and dark soliton bound states. Also, by fixing the phase factor and the system parameter \(\beta \), corresponding to the interaction between long and short wave components, the different types of profiles associated with the obtained breather solution are demonstrated.

Propagation of dark soliton in nonlocal nonlinear coupler

The characteristics of fundamental and mutipole dark solitons in the nonlocal nonlinear couplers are studied through numerical simulation in this work. Firstly, the fundamental dark solitons with different parameters are obtained by the Newton iteration. It is found that the amplitude and beam width of the ground state dark soliton increase with the enhancement of the nonlocality degree. As the nonlinear parameters increase or the propagation constant decreases, the amplitude of the fundamental dark soliton increases and the beam width decreases. The power of the fundamental dark soliton increases with the nonlocality degree and nonlinear parameters increasing, and decreases with the propagation constant increasing. The refractive index induced by the light field decreases with the nonlocality degree increasing and the propagation constant decreasing. The amplitudes of the two components of the fundamental dark soliton can be identical by adjusting the coupling coefficient. These numerical results are also verified in the case of multipole dark solitons. Secondly, the transmission stability of fundamental and mutipole dark solitons are studied. The stability of dark soliton is verified by the linear stability analysis and fractional Fourier evolution. It is found that the fundamental dark solitons are stable in their existing regions, while the stable region of the multipolar dark solitons depends on the nonlocality degree and the propagation constant. Finally, these different types of dark dipole solitons and dark tripole solitons are obtained by changing different parameters, and their structures affect the stability of dark soliton. It is found that the multipole dark soliton with potential well is more stable than that with potential barrier. The refractive-index distribution dependent spacing between the adjacent multipole dark solitons favors their stability.

Dark spatial soliton and quasi-soliton by arbitrary initial beam profiles in negative Kerr local and nonlocal medium

In this paper numerically, generation of dark spatial solitons and quasi-solitons in negative Kerr medium which is described by the (1 + 1)-Dimensional local and nonlocal Nonlinear Schrodinger Equation, using arbitrary initial condition field distributions dissimilar to the analytical solution is demonstrated. In the local and nonlocal case, different initial beam profiles with different initial beam-widths are considered, while different response functions of medium and degrees of nonlocality are governing the nonlocality. For the local case extra (lack of) energy in the center of beam profile is released to (absorbed from) the symmetric transversal area of media respectively, until the beam profile self evolves to the fundamental dark soliton with its appropriate amplitude and beam-width of the analytical dark soliton hyperbolic tangent. In the nonlocal case, the beam profile finds some oscillation on beam-width and evolves to a Reversed-Gaussian function, regardless of the nonlocal response function and the degree of nonlocality. By increasing the degree of nonlocality, the evolved beam profile finds the wider beam-width. Analytical formulas for the propagated intensity profile in nonlocal media are given. All the numerical simulations are done by MATLAB program and Split-Step method.

A harmonically mode-locked dark soliton and bright–dark soliton pair ytterbium fiber laser

We report on an experimental study of a dark soliton and bright–dark soliton pair, harmonically mode-locked, all normal dispersion (ANDi) ytterbium fiber laser with a long cavity length. Mode-locked output up to the fourth harmonic with respect to the fundamental repetition rate has been realized. To the best of our knowledge, this the first such demonstration so far in ANDi mode-locked ytterbium fiber lasers with a birefringence filter as spectral modulation component. The experimentally recorded mode-locked spectrum shows that the generation of a dark soliton is always accompanied by strong continuous-wave emission. Furthermore, by changing the pump power, the fundamental bright–dark soliton pair mode-locked operation can be evolved into the state of the second order bright soliton coexisting with the fundamental dark soliton. Additionally, bright–dark soliton pairs, which are symmetric relative to the vertical coordinate, can be interconverted by rotating waveplates in a fixed maximum pump power condition. The generation of the dark pulse is probably due to the large normal dispersion introduced in the ring cavity except for the nonlinearity.

Study of the gain saturation effect on the propagation of dark soliton in Er + 3 -doped, Ga 5Ge 20Sb 10S 65 chalcogenide fiber amplifier

We study the effect of gain saturation on the propagation of fundamental dark soliton in a nonlinear, dispersive and amplifying medium. The Er + 3 -doped, Ga 5Ge 20Sb 10S 65 chalcogenide glass is used for dark and erbium doped silicon glass for bright solitons. The numerical simulations show that dark soliton doesn't split to subpulses unlike bright soliton and also the dark soliton is more stable in the presence of gain saturation and gain dispersion effects. So the chalcogenide glasses are suitable for designing all optical devices.

Self-tunable chalcogenide Raman laser

We have developed a pervious Raman extracavity laser intensity equation by taking into account the nonlinear Kerr effect and group velocity dispersion and by considering the chalcogenide glass as an active material for its high Raman gain. The propagation of fundamental dark solitons is simulated by the combination of the Crank-Nicolson scheme, FDTD, and the Gause-Seidel iteration scheme. The results show that for a given Kerr nonlinearity there exists a critical minimum input peak power that makes a laser self-tunable such that the different frequency component is achieved by control of the input intensity above the critical intensity.

Three-wave modulational stability and dark solitons in a quadratic nonlinear waveguide with grating

We consider continuous-wave (CW) states and dark solitons (DSs) in a system of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a planar waveguide with the quadratic nonlinearity, the FF components being linearly coupled by resonant reflections on the Bragg grating. We demonstrate that, in contrast with the usual situation in quadratic spatial-domain models, CW states with the phase shift between the FF and SH components are modulationally stable in a broad parameter region in this system, provided that the CW wavenumber does not belong to the system's spectral gap. Stationary fundamental DSs are found numerically, and are also constructed by means of a specially devised analytical approximation. Bound states of two and three DSs are found too. The fundamental DSs and two-solitons bound states are stable in all the cases when the CW background is stable, which is shown by dint of calculation of the corresponding eigenvalues, and verified in direct simulations. Tilted DSs are found too. They attain a maximum contrast at a finite value of the tilt, that does not depend on the phase mismatch. At a maximum value of the tilt, which grows with the mismatch, the DS merges into the CW background. Interactions between the tilted solitons are shown to be completely elastic.

Self-generation of fundamental dark solitons in magnetic films

The self-generation of single, fundamental, stable, spin-wave-envelope black and gray dark solitons has been realized for the first time. These solitons were generated from microwave magnetostatic surface waves (MSSWs) propagated in an in-plane magnetized yttrium iron garnet film MSSW delay line in a resonant ring. These fundamental dark solitons were made possible by a new and general filtering technique for a high gain nonlinear resonant ring. The amplitude and phase profiles together with the power spectra of the self-generated microwave pulses confirm their fundamental dark soliton nature.

(2+1)-dimensional fundamental spatial dark soliton

We give the analytical fundamental dark soliton solutions of the (2+1)-dimensional nonlinear Schrodinger equation [(2+1)-D NSE]. The solutions reduce to (1+1)-D dark soliton solutions when the width of soliton in one transverse direction is much wider than that in the other direction, which is in good agreement with the experimental observation of the dark spatial solitons.

Gordon–Haus effect on dark solitons

The theory of the Gordon-Haus effect with application to dark solitons is presented. It is proved analytically that a random frequency shift of a fundamental dark soliton results in a time jitter radical2 times lower than that for bright solitons.

Picosecond dark soliton over a 1-km fiber at 850 nm

We report the observation of nonlinear propagation of picosecond odd-symmetry dark pulses over 1-km single-mode fiber in the near infrared. The pulses are shown to propagate without distortion at the power corresponding to the fundamental dark soliton of the nonlinear Schrodinger equation. Our measurements are in quantitative agreement with numerical solutions to a modified nonlinear Schrodinger equation—including fiber loss—and constitute the first evidence to our knowledge of dark soliton propagation over fiber lengths compatible with optical telecommunication systems.

Optical dark soliton trains generated by passive spectral filtering technique

A new technique for the generation of fundamental dark soliton trains with uniform intensity background is described. The signal emitted by a multigigahertz repetition rate mode-locked laser source is temporally shaped by high resolution spectral filtering. The proposed shaping device is all-optical shaping is all-optical and passive. The emitted dark pulses are shown to propagate soliton-like over distances compatible with telecommunication applications.

Dark soliton trains formed by visible pulse collisions in optical fibers

It is shown that, through the nonlinear collision of two visible pulses copropagating in an optical fiber, a high-frequency train of dark pulses form, which are well described by the analytic dark soliton solution. Numerical solutions of the nonlinear Schroedinger equation show that the solitons form without secondary pulses and their pulsewidths adiabatically broaden in concert with the slowly decreasing intensity of the background pulse upon which they are situated. For equal input pulse intensities it is shown that the dark pulses asymptotically approach the fundamental dark soliton.

Experimental observation of the fundamental dark soliton in optical fibers.

We present evidence of soliton propagation by 185-fsec dark pulses at a wavelength of 0.62 \ensuremath{\mu}m in a 1.4-m length of single-mode optical fiber. Our experiments utilize specially shaped, antisymmetric input pulses, which closely correspond to the form of the fundamental dark soliton. At appropriate power levels the dark pulses propagate without broadening. Our measurements are in quantitative agreement with numerical solutions to the nonlinear Schr\"odinger equation and constitute the first clear observation of the fundamental dark soliton in optical fibers.