Dark Similaritons Research Articles

Propagation of M-shaped and W-shaped similaritons in birefringent tapered graded-index nonlinear fiber amplifiers

We study the self-similar transmission of optical beams inside an inhomogeneous birefringent tapered graded-index nonlinear fiber amplifier within the framework of generalized coupled Schrödinger equations with spatially inhomogeneous nonlinearity, group velocity dispersion, tapering and gain or loss. New kinds of similariton solutions for the governing model are constructed by means of the similarity transformation method. Especially, the M-shaped and W-shaped similariton pulses are found successfully for the first time, which do not exist in single-mode waveguide amplifier. In addition, bright–dark similaritons are found in the presence of tapering effect. It is shown that these waveforms exhibit a quadratic phase structure, which leads to chirped self-similar pulses. In addition, we determine the relationships among the tapering profile, gain or loss distribution, nonlinearity, and similariton width, which provide the required conditions for controlling the self-similar wave dynamics. Moreover, we discuss the dynamical evolution of the similariton pulses under the influence of special tapering profiles, which are of physical importance in practical applications. The results show that through selecting the appropriate tapering, dispersion and nonlinearity profiles, we can control the dynamics of similaritons effectively.

Chirped self-similar cnoidal waves and similaritons in an inhomogeneous optical medium with resonant nonlinearity

Abstract Under investigation in this work is the self-similar propagation of light waves inside optical fibers with varying resonant and Kerr law nonlinearities, dispersion, and gain or absorption. A generalized resonant nonlinear Schrodinger equation (NLSE) with distributed parameters that describes the pulse evolution in such inhomogeneous optical system has been studied by the similarity transformation method, and a class of self-similar cnodial wave and similariton solutions is presented. It is found that the obtained bright and dark similaritons have a quadratic phase variation in time implying that the associated frequency chirp is linear. We also discuss the applicability of these linearly chirped optical similaritons in a periodic distributed fiber medium. The results show that a suitable choice of the dispersion and cubic nonlinearity parameters enables one to control the similariton structure and dynamical behavior.

Ultrashort nonautonomous similariton solutions and the cascade tunneling of interacting similaritons

Similarity transformation and Hirota bilinearization are deployed to derive exact bright and dark ultrashort one- and two-similariton solutions of a nonautonomous cubic–quintic nonlinear Schrödinger equation. Such wave packets may emerge when group-velocity dispersion and cubic–quintic self-phase modulations are balanced by Raman self-frequency shift in the presence of an external harmonic trap and linear gain or loss. The solutions presented here can be used to investigate the compression, amplification and interaction phenomena associated with bright and dark similaritons in inhomogeneous fiber systems. Furthermore, the dynamics of the characteristic parameters of the similaritons are studied analytically, and similariton stability in a distributed system is tested through extensive computations. As an example application, the tunneling behavior of bright and dark similaritons through cascade dispersion barriers and dispersion wells on an exponential background is investigated, and some interesting novel features are uncovered which are expected to facilitate the control of bright and dark ultrashort similariton in experimental scenarios.

Compression of optical similaritons induced by cubic-quintic nonlinear media in a graded-index waveguide

We employ the similarity reductions in two steps to obtain a family of bright and dark similaritons for the variable coefficient cubic–quintic nonlinear Schrödinger equation. Also, parameter domains are delineated in which kink and double-kink similaritons exist for this model. This methodology introduces a free parameter through cubic nonlinearity coefficient which gives us freedom to tune the amplitude and the propagation distance of similaritons in a tapered graded-index waveguide. Furthermore, we observe rapid beam compression of these similaritons for varying detuning parameter and the coefficient of cubic nonlinearity.

Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide

We have investigated the ()-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.

Symbiotic multimode spatial similaritons and rogons in inhomogeneously coupled optical fibers

We study the multimode wave propagation in inhomogeneously coupled nonlinear optical fibers modeled by variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE). Under specific conditions on the self- and cross-phase coupling terms, we find that this system supports bright–dark, bright, dark similaritons, self-similar breathers, and rogue waves as possible localized configurations. For each of these solutions, one of the propagating modes can be made prominent by lowering the strength of its self-phase modulation in comparison to the other. We further show that this inhomogeneous system supports semi-rational self-similar rogue waves (rogons) for the equal contribution of self- and cross-phase modulation.

Spatial bright and dark similaritons on cnoidal wave backgrounds in 2D waveguides with different distributed transverse diffractions

We discuss the (2+1)-dimensional nonlinear Schrödinger equation with different distributed transverse diffractions in waveguides via a similarity transformation method and obtain exact solutions including bright and dark similariton solutions on cnoidal wave backgrounds. Moreover, the compression and stretching problems of these similariton solutions in a diffraction decreasing waveguide and constant system are, respectively, investigated. These results are potentially useful for future experiments and application of similaritons and solitons for long-distance optical communications.

Spatiotemporal self-similar nonlinear tunneling effects in the (3 + 1)-dimensional inhomogeneous nonlinear medium with the linear and nonlinear gain

With the help of two kinds of similarity transformations connected with the elliptic equation, at first we analytically derive spatiotemporal self-similar solutions of the (3 + 1)-dimensional inhomogeneous nonlinear Schrödinger equation with the linear and nonlinear gain. Then we give out the mutually exclusive parameter domains for bright and dark similaritons. Finally, we discuss nonlinear tunneling effects for spatiotemporal similaritons passing through the nonlinear barrier or well. Results show that bright and dark similaritons in the normal and anomalous dispersion regions have opposite dynamic behaviors.

Nonautonomous spatiotemporal localized structures in the inhomogeneous optical fibers: Interaction and control

We develop a systematic way to find the similarity transformation and investigate nonautonomous optical similariton dynamics for ( n + 1)-dimensional nonlinear Schrödinger equation in the inhomogeneous optical fibers. A condition between the parameters of the mediums, which hints a exact balance between the dispersion/diffraction, nonlinearity and the gain/loss, has been obtained. Under this condition the optical similariton transmission in the dispersion-decreasing fibers (DDF) can be exactly controlled by proper dispersion management. Moreover, novel propagation dynamics of bright and dark similaritons on the background waves and optical rogue waves (rogons) in DDF are investigated too.

Nonlinear similariton tunneling effect in the birefringent fiber

We derive analytical bright and dark similaritons of the generalized coupled nonlinear Schrodinger equations with distributed coefficients. An exact balance condition between the dispersion, nonlinearity and the gain/loss has been obtained. Under this condition, we discuss the nonlinear similariton tunneling effect.

Envelope self-similar solutions for the nonautonomous and inhomogeneous nonlinear Schrödinger equation

By means of the similarity transformation connecting with the solvable stationary equation, the self-similar combined Jacobian elliptic function solutions and fractional form solutions of the generalized nonlinear Schrödinger equation (NLSE) are obtained when the dispersion, nonlinearity, and gain or absorption are varied. The propagation dynamics in a periodic distributed amplification system is investigated. Self-similar cnoidal waves and corresponding localized waves including bright and dark similaritons (or solitons) for NLSE and arch and kink similaritons (or solitons) for cubic–quintic NLSE are analyzed. The results show that the intensity and the width of chirped cnoidal waves (or similaritons) change more distinctly than that of chirp-free counterparts (or solitons).

Propagation of dark similaritons on the compact parabolic background in dispersion-managed optical fibers

The propagation of optical pulses inside dispersion-managed fibers is considered. It is found that the chirped compact parabolic pulse can propagate inside the dispersion-managed fibers self-similarly. Such a finite-width pulse can be served as the background for the propagation and interaction of dark similaritons. Approximate but highly accurate analytical methods are proposed to describe the interaction dynamics of multiple dark similaritons on the self-similar compact parabolic background.