Interaction Of Optical Solitons Research Articles

High-order effect on the transmission of two optical solitons

For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers, a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed. In this paper, in order to study the dynamic mechanism of femtosecond solitons in different media, we take the nonlinear Schrödinger equation considering higher-order effects as the theoretical model, discuss the propagation of solitons in single-mode fibers, and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons. The exact solution of the theoretical model is obtained through the bilinear method, and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied. The influence of various conditions on the transmission and interaction of optical solitons is explored. Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested. The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.

Influence of the initial parameters on soliton interaction in nonlinear optical systems

In nonlinear optical systems, optical solitons have the transmission properties of reducing error rate, improving system security and stability, and have important research significance in future research on all optical communication. This paper uses the bilinear method to obtain the two-soliton solutions of the nonlinear Schrödinger equation. By analyzing the relevant physical parameters in the obtained solutions, the interaction between optical solitons is optimized. The influence of the initial conditions on the interactions of the optical solitons is analyzed in detail, the reason why the interaction of the optical solitons is sensitive to the initial condition is discussed, and the interactions of the optical solitons are effectively weakened. The relevant results are beneficial for reducing the error rate and promoting the communication quality of the system.

Dynamic Behavior of Optical Soliton Interactions in Optical Communication Systems

In optical systems, it is necessary to investigate the propagation of optical solitons in optical fiber systems for fiber-optic communications. By means of the bilinear method, we obtain the two-soliton solution of the variable coefficient higher-order coupled nonlinear Schrödinger equation. According to the obtained two-soliton solution, a novel two-soliton interaction structure of the system is constructed, and their interactions are studied. Two optical solitons occur with elastic interaction under certain conditions, and their amplitudes, shapes and velocities remain unchanged before and after the action. In addition to the elastic interaction, splitting action and polymerization also occur. The present study on the dynamic behavior of interaction of optical solitons may be valuable for research and applications in optical communication and other fields.

Study on weakening optical soliton interaction in nonlinear optics

Study on weakening optical soliton interaction in nonlinear optics

Coherent control of optical solitons interaction via external potential in electromagnetically induced transparency system

A scheme is proposed to realize coherent control of optical solitons propagation and interaction in a three level Λ type electromagnetically induced transparency (EIT) system with external potential. For single soliton propagation, we realize the transmission and trapping of optical soliton via external potential. For double solitons interaction, we realize the coherent control of attractive and repulsion interaction of two optical solitons, and design a XNOR logical operation. At last, for triple solitons incident case, we study the interaction properties of the three solitons depending on the initial phase difference, based on the coherent control of interaction between three solitons via external potential, we design a beam selector. The results obtained here are useful not only for the deep understanding of optical soliton interaction, but also for applications in all optical quantum information processing, etc.

Coherent control of optical soliton interaction via electromagnetically induced transparency with spatial modulation

We propose a scheme to realize the coherent control of optical soliton propagation and interaction in a three level Λ type electromagnetically induced transparency system with the control field being spatially modulated. We show that the spatial perturbation of the control field has no influence on the linear propagation properties and self-phase modulation of the probe field but can produce an equivalent external potential to affect the nonlinear propagation of the probe field. For single soliton propagation, we realize the transmission and trapping of optical solitons via external potential. For double soliton interaction, we realize the coherent control of attractive and repulsion interactions of two optical solitons and design an XNOR logical operation. Finally, for the triple soliton incident case, based on the coherent control of interaction between three solitons via external potential, we design a beam selector. The results obtained here are useful not only for the deep understanding of optical soliton interaction but also for applications in all optical quantum information processing.

A conservative numerical scheme for capturing interactions of optical solitons in a 2D coupled nonlinear Schrödinger system

In this study, an efficient fourth-order conservative explicit numerical scheme using method of lines is developed to simulate different scenarios of soliton interactions and reflections for a (2 + 1)-dimensional coupled nonlinear Schrodinger (CNLS) system. The fourth-order Runge–Kutta technique is applied as a time integrator to the resulting ordinary differential system. Both integrable and nonintegrable cases of the CNLS system are considered. A condition for the scheme to be stable is deduced with the aid of von Neumann stability analysis. Several numerical experiments have been carried out to exhibit the reliability of the scheme in capturing and understanding the interesting phenomenon of elastic and inelastic soliton collisions/reflections related to many nonlinear evolution equations. The ability of the scheme to preserve the conserved invariants in long terms confirms its accuracy and stability. New results associated with interactions and reflections of soliton waves are obtained.

Attosecond timing jitter within a temporal soliton molecule

The interactions of optical solitons in passively mode-locked lasers result in abundant bound states that reflect intriguing nonlinear attractor behaviors in complex dissipative systems. In this study, we tested the strength limits of the fixed-point attractors that govern bound soliton molecule formation in passively mode-locked lasers. To this end, we probed the relative timing jitter in a closely separated stationary doublet soliton molecule produced by a Kerr-lens mode-locked Ti:sapphire laser. By adopting a balanced optical cross-correlation method with a 5 z s / 0 H z temporal resolution, we derive an upper estimate of 60 as intramolecular timing jitter, which is integrated from 100 Hz to the Nyquist frequency (60 MHz). To the best of our knowledge, this is the first evidence for attosecond timing jitter within robust bound solitons in dissipative systems.

Analytic study on triple-S, triple-triangle structure interactions for solitons in inhomogeneous multi-mode fiber

The analytic multi-soliton solutions for nonlinear Schrödinger (NLS) equations are complex to obtain. Based on those solutions, interactions among multiple solitons show more abundant characteristics than two soliton interactions. With the Hirota method, bilinear forms and analytic soliton solutions of the coupled NLS equation are derived, and the influences of the dispersion parameter β(x) and constant parameters p1, p2 and p3 on soliton interactions are discussed in detail. The novel triple-S structures are presented via choosing suitable values. The phase, intensity and incidence angles of dark solitons are controlled with appropriate constant parameters. Besides, bound states of dark solitons are observed with different periods. In addition, the peculiar triple-triangle structures are presented when one sets β(x) as the hyperbolic tangent function. Results in this paper are useful for the generation and interaction of optical solitons in nonlinear optics and ultrafast optics.

Controllable soliton interaction in three mode nonlinear optical fiber

In this paper, the analytical bright soliton solutions are obtained for the 3-coupled nonlinear Schrödinger equations with variable coefficients in a three-mode fiber. Lax pair is constructed for 3-coupled NLS system by employing AKNS procedure. With the help of symbolic computation, the multi-soliton solutions are obtained by means of Darboux transformation technique. Based on two-soliton solutions, we demonstrate the various interaction scenarios of solitons in three mode fiber through the choice of control parameters. Furthermore, we investigate the dynamical behaviors of solitons for both constant and variable coefficients. Our result reveals that interactions of optical solitons have some specific applications such as the construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Inverse Cherenkov effect and control of optical solitons by resonant dispersive waves

The interactions of optical solitons with dispersive waves of low intensity in optical fibers with high-order dispersion are considered numerically and analytically. It is shown that Cherenkov phase matching between the solitons and the dispersive waves makes it possible to achieve an efficient interaction between the solitary and the incident dispersive waves. The inverse Cherenkov effect (resonant absorption of dispersive wave by the soliton) and the effect of phase locking of the solitons to the dispersive waves are demonstrated numerically. To explain the phenomena observed in numerical simulations, a simple analytical theory is developed and compared against the numerical data.

Dynamics of the optical solitons for a ([formula omitted])-dimensional nonlinear Schrödinger equation

In this paper, a nonlinear Schrödinger equation (NLS) has been studied, which can describe the propagation and interaction of optical solitons in a material with x-directional localized and y-directional nonlocal non-linearities. By the aid of variable separation and transformation, bilinear forms and multi-soliton solutions of the NLS equation are attained. Propagation and interaction of the solitons are discussed. As a special case of the optical solitons, Hermite-Gaussian vortex solitons are studied: the numbers of wave crests are increase with the order of the Hermite polynomial.

Impact of phase on collision between vortex solitons in three-dimensional cubic-quintic complex Ginzburg-Landau equation.

We present a systematic analysis for three generic collisional outcomes between stable dissipative vortices with intrinsic vorticity S = 0, 1, or 2 upon variation of relative phase in the three-dimensional (3D) cubic-quintic complex Ginzburg-Landau equation. The first type outcome is merger of the vortices into a single one, of which velocity can be effectively controlled by relative phase. With the increase of the collision momentum, the following is creation of an extra vortex, and its velocity also increases with growth of relative phase. However, at largest collision momentum, the variety of relative phase cannot change the third type collisional outcomes, quasielastic interaction. In addition, the dynamic range of the outcome of creating an extra vortex decreases with the reduction of cubic-gain. The above features have potential applications in optical switching and logic gates based on interaction of optical solitons.

Collisions between Solitons Modulated by Gain/Loss and Phase in the Complex Ginzburg—Landau Equation

We present a systematic analysis for influence of phase φ on collisions of dissipative solitons, using the cubic-quintic complex Ginzburg—Landau equation in the absence of viscosity. Four generic outcomes are revealed upon the variation of gain/loss: merger of the two solitons into a single one; quasi-elastic interactions; creation of an extra soliton; and dissipation of the two solitons for in-phase. The velocities of the merger-soliton and the extra soliton can be effectively controlled by relative phase. The above features have potential applications in optical switching and logic gates based on interaction of optical solitons.

REFRACTION OF NONLINEAR LIGHT BEAMS IN NEMATIC LIQUID CRYSTALS

We use modulation theory to analyze the interaction of optical solitons and vortices with a dielectric interface between two regions of nematic liquid crystals. In the analysis we consider the role of nonlocality, anisotropy and nonlinear reorientation and compare modulation theory results with numerical results. Upon interacting with the interface, nematicons undergo transverse distortion but remain stable and eventually return to a steady state, whereas vortices experience an enhanced instability and can break up into bright beams or solitary waves.

Phase controlling of collisions between solitons in the two-dimensional complex Ginzburg-Landau equation without viscosity

We present a systematic analysis of the outcome of soliton collisions upon variation of the relative phase φ of the solitons, in the two-dimensional cubic-quintic complex Ginzburg-Landau equation in the absence of viscosity. Three generic outcomes are identified: merger of the solitons into a single one, creation of an extra soliton, and quasielastic interaction. The velocities of the merger soliton and the extra soliton can be effectively controlled by φ. In addition, the range of the outcome of creating an extra soliton decreases to zero with the reduction of gain or the increasing of loss. The above features have potential applications in optical switching and logic gates based on interaction of optical solitons.

Radiation-induced interaction of optical solitons in fibers with randomly varying birefringence.

We study propagation of solitons in optical fibers with randomly varying birefringence which results in polarization mode dispersion. Due to the disorder, solitons emit radiation, i.e., the energy of the solitons is partly transferred into the delocalized modes. The radiation serves as a mediator of the intersoliton interaction leading to fluctuations of the soliton separations. We establish statistics of the fluctuations which is found to be sensitive to the phase mismatches and mutual polarizations of the solitons, and independent of the soliton separation. The theoretical results are justified by direct numerical simulations.

Interchannel interaction of optical solitons.

We study interaction between two solitons from different frequency channels propagating in an optical fiber. The interaction may be viewed as an inelastic collision, in which energy is lost to continuous radiation due to small but finite third order dispersion. We develop a perturbation theory with two small parameters: the third order dispersion coefficient d(3), and the reciprocal of the interchannel frequency difference, 1/beta. We find that amplitude of the leading contribution to radiation emitted during the collision is proportional to d(3)/beta(2). The source term for this radiation is of the form that would be generated by a variation in the second order dispersion coefficient. In addition, the only other effects up to the combined third order of the perturbation theory are phase changes and position shifts of the solitons. Solitons propagating in a given frequency channel interact via radiation emitted due to collisions with many solitons from other frequency channels. We show that this intrachannel interaction effect, induced by many interchannel collisions, is identical to the radiation mediated intrachannel interaction effect observed for solitons propagating under the influence of disorder in the second order dispersion coefficient.

Propagation and interaction of optical solitons in random media

The propagation of an optical soliton is studied in a fiber with randomly varying core diameter or random amplification along the fiber. The adiabatic dynamics of the soliton and radiative processes are investigated by a perturbation method based on the inverse scattering transform. The mean emitted power and the damping rate of the soliton are calculated. The interaction of solitons in random media is investigated by the Karpman–Solov’ev perturbation theory. Numerical simulations of the full nonlinear Schrodinger equation with multiplicative white- and colored-noise perturbations are performed for initial conditions corresponding to a single soliton and to two interacting solitons. The results obtained are in good agreement with the analytical estimates for white noise in the initial stage of the propagation. The numerical simulations reveal a new phenomenon in which single solitons disintegrate or split under white-noise perturbation but stabilize under colored-noise action. Finally, the existence of a bound state of two interacting solitons is observed in numerical simulations in media with colored-noise perturbation.

Coupled-soliton photonic logic gates: practical design procedures

The feasibility of and, or, and ex-or functions based on the interaction of optical solitons is proved by use of a five-layer dielectric structure with a nonlinear core. With the exception of the or logic gate, the design of these devices is rather flexible, offering a wide variety of choices with respect to both the geometrical parameters and the input power levels.