Soliton Management Research Articles

Butterfly-shaped and dromion-like optical similaritons in an asymmetric twin-core fiber amplifier

Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide (GRIN) with an external source are reported for the first time, to our knowledge. More pertinently, we obtain these waves both analytically and numerically in a generalized nonlinear Schrödinger equation (GNLSE), which describes self-similar wave propagation in GRIN with variable group-velocity dispersion (GVD), nonlinearity, gain, and source. The proposed GNLSE appertains to the study of similariton propagation through asymmetric twin-core fiber amplifiers. Dromion-like structures, which have generally been investigated in the (2+1) or higher dimensional systems, are reported in the (1+1) dimensional GNLSE with an external source. Herein, we introduce the concept of soliton management when the variable group-velocity dispersion and Kerr nonlinearity functions are suggested. For example, when the GVD parameter is perturbed, we observe the emergence of vibration of dromion-like structures. Then the dromion-like structure is transformed into oscillation by the modulation instability of the modified coefficient of the Gaussian GVD function, exhibiting interference based on two dromion-like structures. Additionally, the phenomenon of unbreakable PT symmetry of these nonlinear waves has been demonstrated for three explicit examples.

Numerical Methods for Some Nonlinear Schrödinger Equations in Soliton Management

Numerical Methods for Some Nonlinear Schrödinger Equations in Soliton Management

Non-collisional dynamics of nonautonomous three solitons through tailoring of modulated coefficients and modulation instability gain spectra

In this paper, the generalized nonautonomous nonlinear Schrödinger equation with non-isospectral parameter is investigated from the point of view of soliton management through modulation of dispersion and nonlinearity. Based on the obtained analytic soliton solutions, the effect of modulated coefficients such as dispersion and nonlinearity on the control of soliton transmission is studied. Especially, controllable soliton interactions are investigated through suitably tailoring the inhomogeneous profiles. Additionally, modulation instability (MI) has been analyzed graphically through linear stability analysis (LSA) and MI gain spectrum is analyzed for various forms of modulated coefficients. Through this study, we confirm that the modulated coefficients in the theoretical model under investigation affect the amplitudes, widths and trajectories of the nonautonomous solitons. Thus, one can obtain the optical control system by choosing the different form of modulated coefficients for the specific problem. Results obtained in this paper would be worthy in the field of soliton management for improving the capacity of optical fiber communication system.

Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged

We describe how to control the motion – both speed and propagation direction – of a nonlinear traveling wave in real time via soliton management with time-varying dispersion/diffusion and loss/gain terms. When carried out subject to certain parameter constraints we derive, the approach allows for real-time manipulation of wave motion without compromising the structure or stability of the wave, maintaining strict adiabaticity in time. This makes our approach a promising tool for physical systems which admit a degree of control through adjustable dispersion and loss/gain terms, including problems arising in nonlinear optics, atomic physics, Bose-Einstein condensates, and thermally driven chemical reactions, where one is interested in modifying the position or speed of a wave while still maintaining adiabaticity. We illustrate both the utility and simplicity of the method through several canonical examples, demonstrating how the motion of KdV solitons, Fisher-KPP solitary wavefronts, BBM solitons, nonlinear Klein-Gordon equations, and interacting nonlinear waves in a vector NLS system can be controlled in real time.

Impact of external potential and non-isospectral functions on optical solitons and modulation instability in a cubic quintic nonlinear media

We investigate the non-isospectral generalized higher order NLS equation (GHNLS) with external potential which is unswervingly represents the ultrashort optical soliton transmission in inhomogeneous non-Kerr media with combined effects of external potentials. Lax pair is constructed for GHNLS equation and three soliton solutions obtained with the aid of Darboux transformation. For the first time, we include the effects of inhomogeneous non-isospectral parameters on soliton dynamics. Using two soliton solutions, interaction among double hump solitons and using three soliton solutions, interaction characteristics are studied analytically. Furthermore, in order to understand the stability mechanism, linear stability analysis also has been performed. Effects of non-isospectral parameters and variable coefficients on soliton dynamics are investigated graphically. The predicted results may be observed in the future experiments on nonlinear fiber optics and applications to femtosecond soliton management.

Spatially homogeneous few-cycle compression of Yb lasers via all-solid-state free-space soliton management.

The high power and variable repetition-rate of Yb femtosecond lasers makes them very attractive for ultrafast science. However, for capturing sub-200 fs dynamics, efficient, high-fidelity and high-stability pulse compression techniques are essential. Spectral broadening using an all-solid-state free-space geometry is particularly attractive, as it is simple, robust and low-cost. However, spatial and temporal losses caused by spatio-spectral inhomogeneities have been a major challenge to date, due to coupled space-time dynamics associated with unguided nonlinear propagation. In this work, we use all-solid-state free-space compressors to demonstrate compression of 170 fs pulses at a wavelength of 1030nm from a Yb:KGW laser to ∼9.2 fs, with a highly spatially homogeneous mode. This is achieved by ensuring that the nonlinear beam propagation in periodic layered Kerr media occurs in spatial soliton modes, and by confining the nonlinear phase through each material layer to less than 1.0 rad. A remarkable spatio-spectral homogeneity of ∼0.87 can be realized, which yields a high efficiency of >50% for few-cycle compression. The universality of the method is demonstrated by implementing high-quality pulse compression under a wide range of laser conditions. The high spatiotemporal quality and the exceptional stability of the compressed pulses are further verified by high-harmonic generation. Our predictive method offers a compact and cost-effective solution for high-quality few-cycle-pulse generation from Yb femtosecond lasers, and will enable broad applications in ultrafast science and extreme nonlinear optics.

Attosecond soliton switching through the interactions of two and three solitons in an inhomogeneous fiber

We obtain the exact two and three soliton solutions for higher order NLS equation with variable coefficients using Darboux transformation method with some algebraic manipulations based on constructed Lax Pair. For the first time, switching characteristics of two and three solitons in the attosecond regime via inelastic soliton interactions are discussed through some graphical illustrations. Additionally, effects of the inhomogeneous coefficients on propagation features of solitons are analyzed graphically. Our results have certain applications in the construction of optical switching and soliton management in optical communication systems.

Peregrine Soliton Management of Breathers in Two Coupled Gross–Pitaevskii Equations with External Potential

By solving analytically two 1D coupled Gross–Pitaevskii equations with a time-dependent harmonic trap, we find Peregrine solutions that can be effectively controlled by modulating the external potential frequency. Indeed, one observes the onset of instability in the dynamical system as the frequency is varied. This leads to the possibility of stabilizing the Peregrine solitons.

Impact of fifth order dispersion on soliton solution for higher order NLS equation with variable coefficients

In this paper, the variable coefficient nonlinear Schrödinger equation with fifth order dispersion in the inhomogeneous optical fiber is investigated to study the impact of fifth order dispersion on attosecond soliton propagation. Based on the Darboux transformation method, soliton solution is constructed with modulated coefficients though Lax pair. We show that the coefficients of GVD and fifth order term are the main keys to control the amplitude, width and phase shift in the model. With the suitable choices of coefficients for the obtained soliton solution, some new types of soliton management through fifth order are presented for the first time. Especially, the influence of fifth order dispersion of the higher order NLS equations with and without modulated coefficients is discussed in detail. We will also highlight the impact of the studies on application in ocean engineering. Obtained results may be potentially useful in the soliton shaping and management in inhomogeneous fibers.

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

Exactly integrable nonisospectral models for femtosecond colored solitons and their reversible transformations

We present three exactly integrable nonisospectral nonlinear evolution models with varying in time linear potentials: the forced complex modified Korteweg-de Vries (cmKdV), the forced Hirota, and the forced Sasa-Satsuma equations. In all three models we have added the time-varying linear potential to effectively simulate two effects of tremendous significance for soliton management and fiber optics communications: the sliding filter method of the noise separation from a soliton and the Raman soliton self-scattering effect. We find nonlinear gauge transformations between introduced nonisospectral models arranged in such a way that their soliton solutions, accelerating in the linear potential nonautonomous solitons, can be directly obtained without resolving the nonisospectral inverse scattering transform problem.

Combined effects of frequency and higher-order effects on soliton conversion in an erbium fiber with inhomogeneous broadening

In this paper, soliton propagation in an erbium-doped fiber with inhomogeneous broadening is considered which can be described by the inhomogeneous Hirota– Maxwell–Bloch equations. The Darboux transformation method is employed to generate the soliton solution through a linear eigenvalue problem. In particular, our results demonstrate explicitly that a soliton can be converted into various nonlinear waves such as periodic wave, anti-kink soliton and flat-top soliton in the presence of higher-order effects with inhomogeneous broadening. Additionally, we found that higher-order coefficients have strong influence on the soliton transition while frequency is only responsible for phase shift. The results might be of certain value for the study of the soliton management and soliton conversion.

Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities; they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold λcr such that minimizers for this variational problem exist if their power is bigger than λcr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions’ concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of Hundertmark and Lee [J. Nonlinear Sci. 22, 1–38 (2012) and Commun. Math. Phys. 309(1), 1–21 (2012)].

Dispersion managed solitons in the presence of saturated nonlinearity

The averaged dispersion managed nonlinear Schrödinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.

Thresholds for Existence of Dispersion Management Solitons for General Nonlinearities

We prove a threshold phenomenon for the existence of solitary solutions of the dispersion management equation for positive and zero average dispersion for a large class of nonlinearities. These solutions are found as minimizers of nonlinear and nonlocal variational problems which are invariant under a large noncompact group. There exists a threshold such that minimizers exist when the power of the solitons is bigger than the threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions' concentration compactness argument. The existence of dispersion-managed solitons is shown under very mild conditions on the dispersion profile and the nonlinear polarization of an optical active medium, which cover all physically relevant cases for the dispersion profile and a large class of nonlinear polarizations; for example, they are allowed to change sign.

Influence of generalized external potentials on nonlinear tunneling of nonautonomous solitons: Soliton management

Soliton control and management using generalized external potentials in an inhomogeneous fiber to the design of high speed optical devices and ultrahigh capacity transmission systems are investigated based on solving the variable-coefficient generalized nonautonomous nonlinear Schrödinger equation with the help of symbolic computation. We construct Lax pair for GNLS equation by means of AKNS method and two soliton solutions are obtained by virtue of the Darboux transformation. With symbolic computation, we manipulate the control parameters and external potentials to investigate the propagation behaviors of nonautonomous solitons. Moreover, the main evolution features of obtained two soliton solutions are exposed by some interesting figures through computer simulation. Especially, we analyze the influence of external potentials such as periodic, exponential and parabolic potential on soliton propagation. Finally, soliton propagation under the absence (vanishing) of external potential is also discussed. Obtained results confirmed that external potentials has strong influence on the soliton dynamics. Our results might provide a new method to achieve the soliton pulse compression while they passing through the potential barrier or well under the influence of external potentials.

Investigation on nonautonomous soliton management in generalized external potentials via dispersion and nonlinearity

We investigate the controllable behavior of nonautonomous soliton in external potentials with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous fiber system. We derive the Lax pair with a variable spectral parameter and the exact multi-soliton solution is generated via Darboux transformation. Based on these solutions, several novel optical solitons are constructed by selecting appropriate functions and the main evolution features of these waves are shown by some interesting figures with computer simulation. As few examples, breathers in periodic potential, soliton compression in an exponentially dispersion decreasing fiber and interaction of boomerang solitons are discussed. The presented results have applications in the study of nonautonomous soliton birefringence-managed switching architecture. These results are potentially useful in the management of nonautonomous soliton with external potentials in the optical soliton communications and long-haul telecommunication networks.

Study on transmission characteristics of dark solitons in inhomogeneous optical fibers

The terms of gain(or absorption), dispersion, and nonlinearity in the nonlinear Schrödinger equation are usually variables, which can be used to study the propagation of optical pulses in inhomogeneous optical fibers. In this paper, with the aid of the Hirota method, the bilinear forms of the Schrödinger equation are derived. Based on the bilinear form, the analytic dark soliton solutions to the nonlinear Schrödinger equation are obtained. The properties of dark solitons are discussed. Stable dark solitons are observed in the normal dispersion regime. In addition, corresponding parameters for controlling the propagation of dark solitons are analyzed. Results of our reflearch show that the propagation route of solitons can be effectively controlled by the gain(or absorption), dispersion, and nonlinearity, which can improve the quality of signal transmission in optical communications. When the amplitude of the loss coefficient increases, the amplitude of the dark soliton increases suddenly during the transmission process.By means of changing the type of dispersion, the purpose of controlling the dark soliton phase and phase oscillation is achieved. The possibly applicable soliton control techniques, which are used to design dispersion and nonlinearity-managed systems, are proposed. The proposed techniques may find applications in soliton management communication links, like soliton control.In addition, two-soliton solution is obtained. With the dark two-soliton solution, the interaction between two solitons is discussed in the paper. The result may be of potential application in the ultralarge capacity transmission systems.

All-fiber ultralow-energy soliton management at 1.55 µm

A highly nonlinear photonic-crystal fiber (PCF) is shown to enable an efficient coupling of a low-energy picosecond output of an erbium fiber laser into optical solitons. With this fiber, stretched 2.2 ps, 1.2 nJ, 1.55 µm pulses of an erbium fiber laser can be coupled into sub-100 fs optical solitons with an energy slightly below 1 nJ. The peak power and the pulse width of these solitons can be finely tuned by pulse chirp management in a variable-length single-mode fiber, connected to the erbium fiber laser output and cascaded with the PCF.

Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton.