Light Pulses In Optical Fibers Research Articles

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Derivation of optical solitons of dimensionless Fokas-Lenells equation with perturbation term using Sardar sub-equation method

This paper presents an investigation of soliton solutions for the perturbed Fokas-Lenells (pFL) equation, which has a vital role in optics, using Sardar sub-equation method. The equation models the propagation of ultrashort light pulses in optical fibers. Using appropriate wave transformation, the pFL equation is reduced to a nonlinear ordinary differential equation (NLODE). The solutions of this NLODE equation are assumed to be in the suggested form by the Sardar sub-equation method. Hence, an algebraic equation system is obtained by substituting the trial solution and their necessary derivatives into the NLODE. After finding the unknowns in the system, the soliton solutions of the perturbed Fokas-Lenells equation are extracted. The method produces various kinds of solitons such as dark, periodic, singular periodic, combined bright-dark. To show physical representations of the solitons, 2D, 3D and contour plots of the solutions are demonstrated via computer algebraic systems. It is expected that derived solutions may be useful for future works in various fields of science, especially optics and so, it may contribute to the optic fiber industry.

The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods

The nonlinear Schrödinger hierarchy has a wide range of applications in modeling the propagation of light pulses in optical fibers. In this paper, we focus on the integrable nonlinear Schrödinger (NLS) equation with quintic terms, which play a prominent role when the pulse duration is very short. First, we investigate the spectral signatures of the spatial Lax pair with distinct analytical solutions and their periodized wavetrains by Fourier oscillatory method. Then, we numerically simulate the wave evolution of the quintic NLS equation from different initial conditions through the symmetrical split-step Fourier method. We find many localized high-peak structures whose profiles are very similar to the analytical solutions, and we analyze the formation of rouge waves (RWs) in different cases. These results can be helpful to understand the excitation of nonlinear waves in some nonlinear fields, such as the Heisenberg ferromagnetic spin system in condensed matter physics, ultrashort pulses in nonlinear optical fibers, and so on.

Darboux Transformation for the Hirota Equation

The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and then construct its quasideterminant solutions. The multisoliton and breather solutions of the Hirota equation are given explicitly.

Riemann problem for the light pulses in optical fibers for the generalized Chen-Lee-Liu equation

We provide the classification of possible wave structures evolving from initially discontinuous profiles for the photon fluid propagating in a normal dispersion fiber. The dynamics of light field is described by the generalized Chen-Lee-Liu equation, which belongs to the family of the nonlinear Schr\"odinger equations with a self-steepening type term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. This equation is also used in investigations of the dynamics of modulated waves propagating through a single nonlinear transmission network. We describe its periodic solutions and the corresponding Whitham modulation equations. The wave patterns generated by the initial parameter profiles are composed of different building blocks which are presented in detail. It is shown that evolution dynamics in this case is much richer than that for the nonlinear Schr\"odinger equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity. Our analytic results are confirmed by numerical simulations.

Numerical analysis of the Hirota equation: Modulational instability, breathers, rogue waves, and interactions.

In this paper, we focus on the integrable Hirota equation, which describes the propagation of ultrashort light pulses in optical fibers. First, we numerically study spectral signatures of the spatial Lax pair with distinct potentials [e.g., solitons, Akhmediev-Kuznetsov-Ma (AKM) and Kuznetsov-Ma (KM) breathers, and rogue waves (RWs)] of the Hirota equation. Second, we discuss the RW generation by using the dam-break problem with a decaying initial condition and further analyze spectral signatures of periodized wavetrains. Third, we explore two kinds of noise-derived modulational instabilities: (i) the one case is based on the initial condition (one plus a random noise) such that the KM and AKM breathers, and RWs can be generated, and they agree well with analytical solutions; (ii) another case is to consider another initial condition (one plus a Gaussian wave with a random noise phase) such that some RWs with higher amplitudes can be found. Moreover, we also investigate the spectral signatures of corresponding periodic wavetrains. Finally, we find that the interactions of two waves can also generate the RW phenomena with higher amplitudes. These obtained results will be useful to understand the RW generation in the third-order nonlinear Schrödinger equation and other related models.

Bright and dark solitons in (n + 1)-dimensions with spatio-temporal dispersion

This work is devoted to scrutinize new optical soliton solutions to the spatially temporal (n + 1)-dimensional nonlinear Schrodinger’s equation. The initial ansatz supposed in the form of Jacobi elliptic functions to obtain dark and bright optical solitons in the presence of different non-Kerr media. Kerr law, power law, parabolic law and dual-power law have been utilized as nonlinear medium. The fetched results are new and useful for the propagation of light pulses in optical fibers. For the existence of these solitons constraint conditions are also listed.

Dispersionless limit of the (1+1)-dimensional Fokas-Lenells equation

Nonlinear dispersionless equations can be obtained as dispersionless limits (quasiclassical limits) of integrable hierarchies of equations or by constructing a system of hydrodynamic type. In this paper, the dispersionless limit of the (1+1)-dimensional Fokas-Lenells equation is found. We present Lax pair for this dispersionless equation. As well known, the Fokas-Lenells equation characterizes the propagation of ultrashort nonlinear light pulses in optical fibers. Exact solutions of the dispersionless version of the Fokas-Lenells equation describe nonlinear shock waves in optical fiber systems. By using the obtained results, one can find shock wave solutions of the dispersionless equation, which have different physical applications.

Dynamics of optical solitons incorporating Kerr dispersion and self-frequency shift

This paper deals with the dynamics of optical solitons in nonlinear Schrödinger equation (NLSE) with cubic-quintic law nonlinearity in the presence of self-frequency shift and self-steepening. This type of equation describes the ultralarge capacity transmission and traveling of laser light pulses in optical fibers. Two robust analytical approaches are employed to determine contemporary solutions. Some new explicit rational, periodic and combo periodic soliton solutions are extracted using the extended trial equation method. The Riccati–Bernoulli sub-ODE method provided us with singular and dark soliton solutions. The constraints found are necessary for the existence of solitons.

Performance Analysis of Dispersion Compensation Fiber on NRZ and RZ Modulation with Difference Power Transmission

Optical fiber communication has characteristics that really need attention. The characteristics of fiber optic transmission are very important in designing optical fiber networks, one of which is widening pulses called dispersions. Dispersion is the widening of light pulses in optical fibers which reduces data speed, signal to noise ratio and system quality. In addition to dispersion compensation, which is the most important feature needed in fiber-optic communication systems; transmission power needs to be considered to produce optimal signal output. In this paper, we will simulate the optimization effect of power and fiber dispersion compensation on Non Return to Zero (NRZ) and Return to Zero (RZ) modulation on optical transmission systems, with 5 dBm power parameters, 10 dBm 15 dBm and 0 dBm and DCF 5 km, 10 km, 15 km, 20 km and 25 km. Simulation results show that dispersion compensation is very influential on the transmission system. From these two modulations, there are differences in the results between NRZ and RZ. The results of dispersion compensation also affect the input power and DCF length.

Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity

This work is devoted to scrutinize new optical soliton solutions to the spatially temporal [Formula: see text]-dimensional nonlinear Schrödinger’s equation (NLSE) with anti-cubic nonlinearity. Two different versatile integration architectures are used to extract these solitons. Extended direct algebraic method (EDAM) is utilized to pluck out optical, dark and singular soliton solutions, whereas generalized Kudryashov method (GKM) provides rational solutions. The fetched results are new and useful for the propagation of light pulses in optical fibers in [Formula: see text]-dimensions. For the existence of these solitons, constraint conditions are also listed.

Exact optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity

In this article, the first time, exact optical solitons with (n+1)-dimensional nonlinear Schrödinger equation have been constructed under anti-cubic law of nonlinearity that describes the propagation of light pulses in optical fibers. The integration criteria that is adopted was (G′/G)-scheme. As a result, the dark and singular optical solitons are extracted in (n+1)-dimensions. Additionally, the constraint conditions for the existence of these solutions are also listed. However, this scheme fails to retrieve the bright soliton.

On optical solitons: the nonlinear Schrödinger equation with self-steepening and self-frequency shift

This article studies the dynamics of optical solitons in cubic-quintic nonlinear Schrodinger model that describes the propagation of femtosecond light pulses in optical fibers. The model is considered with self-steepening and self-frequency shift. As a result, the dark and singular optical solitons are extracted using \((G^{\prime }/G)\)-expansion scheme. Additionally, the constraint conditions for the existence of these solutions are also listed.

Optical solitons in (n + 1) dimensions with Kerr and power law nonlinearities

The paper studies the dynamics of optical solitons in [Formula: see text]-dimensional nonlinear Schrödinger equation with Kerr and power law nonlinearities that describe the propagation of light pulses in optical fibers. First time the dark and singular optical solitons are extracted in [Formula: see text] dimensions. The [Formula: see text]-expansion scheme is used to analyze these solutions. Additionally, the constraint conditions for the existence of the solutions are also listed. However, the scheme fails to retrieve the bright soliton.

An extra invariant for the system of four wave packets in one spatial dimension

The system of four wave packets (like light pulses in optical fibers) is shown to have an extra adiabatic-like invariant, in addition to the energy, momentum, and Manley–Rowe relations. A theoretical argument is suggested showing that the 4-wave interaction in one-dimensional systems can restrict spectral broadening.

Exact soliton solutions to a new coupled integrable short light-pulse system

In this paper, we investigate the soliton structure of a two-component vector short-pulse system as part of the new multi-component short-pulse system derived by Dimakis, Muller-Hoissen and Matsuno, separately, and describing the propagation of ultra short vector light-pulses in optical fibers. In the wake of the derivation of the Lax-pairs of the system above, we study deeply its inverse scattering transform within the viewpoint of the Wadati–Konno–Ichikawa approach. As a result, we unwrap some interesting scattering features of elastic interactions. Accordingly, we address some physical implications of the results.

Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with self-steepening and self-frequency shift effects

In this paper, we have obtained the optical solitary wave solutions for the nonlinear Schrödinger equation which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method was used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses were determined. Using the 1-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa-Satsuma cases. We have also constructed some periodic wave solutions of the higher order nonlinear Schrödinger equation by reducing it to quartic anharmonic oscillator equation and by using projective Ricatti equations. Moreover by using He's semi-inverse method, variational formulation was established to obtain exact soliton solutions. The 1-soliton solutions of time dependent form of this equation was also obtained. To visualize the propagation characteristics of dark-bright soliton solutions, few numerical simulations are given.

DARK AND BRIGHT SOLITARY WAVE SOLUTIONS OF THE HIGHER ORDER NONLINEAR SCHRÖDINGER EQUATION WITH SELF-STEEPENING AND SELF-FREQUENCY SHIFT EFFECTS

In this paper, we obtain the exact bright and dark soliton solutions for the nonlinear Schrödinger equation (NLSE) which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method is used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses are determined. Using the one-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa–Satsuma cases and finally, we have constructed some periodic wave solutions by reducing the higher order nonlinear Schrödinger equation (HNLS) to quartic anharmonic oscillator equation. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a HNLS model equation.

Spontaneous Solitons in the Thermal Equilibrium of a Quasi-1D Bose Gas

We show that solitons occur generically in the thermal equilibrium state of a weakly interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state, usually thought of as primarily phase-fluctuating. Thermal solitons are seen in uniform 1D, trapped 1D, and elongated 3D gases, appearing as shallow solitons at low quasicondensate temperatures, becoming widespread and deep as temperature rises. This behavior can be understood via thermal occupation of the type II excitations in the Lieb-Liniger model of a uniform 1D gas. Furthermore, we find that the quasicondensate phase includes very appreciable density fluctuations while leaving phase fluctuations largely unaltered from the standard picture derived from a density-fluctuation-free treatment.

Solitary wave solutions for a higher order nonlinear Schrödinger equation

We consider a higher order nonlinear Schrödinger equation with third- and fourth-order dispersions, cubic–quintic nonlinearities, self steepening, and self-frequency shift effects. This model governs the propagation of femtosecond light pulses in optical fibers. In this paper, we investigate general analytic solitary wave solutions and derive explicit bright and dark solitons for the considered model. The derived analytical dark and bright wave solutions are expressed in terms of the model coefficients. These exact solutions are useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a higher-order nonlinear and dispersive Schrödinger system.