Group Velocity Dispersion Coefficient Research Articles

Optical soliton solutions of the perturbed fourth-order nonlinear Schrödinger-Hirota equation with parabolic law nonlinearity of self-phase modulation

This article introduces an examination of optical soliton solutions for the perturbed fourth-order nonlinear Schrödinger-Hirota equation, which plays a crucial role in optics. For the first time, it utilizes a novel approach by applying the extended auxiliary equation method. This equation models the propagation of optical pulses through nonlinear media, such as optical fibers, and has been the subject of many studies. Our goal extends beyond merely acquiring a significant number of soliton solutions using the method described in this article; we also aim to investigate the impact of the coefficients of group velocity dispersion, parabolic law, and fourth-order dispersion terms on soliton propagation in the problem examined. The 2D, 3D, and contour plots of the acquired dark and bright solitons, which represent the most fundamental soliton types, are presented. Additionally, all other calculations are performed using symbolic algebraic software. The results provide us with valuable insights, confirming that the introduced model can be analyzed from a physical perspective. It is demonstrated that the proposed technique is not only important but also efficient in analyzing various nonlinear scientific problems.

Analysis of time-fractional Schrödinger equation with group velocity dispersion coefficients and second-order spatiotemporal effects: a new Kudryashov approach

Analysis of time-fractional Schrödinger equation with group velocity dispersion coefficients and second-order spatiotemporal effects: a new Kudryashov approach

Few-cycle two-frequency spatiotemporal solitons in the absence of group velocity dispersion at one of the components

The second harmonic generation by few-cycle pulses is studied when the group velocity dispersion coefficient is equal to zero at the fundamental or doubled frequency. Using numerical simulation, it is shown that in both cases, in the presence of a negative third-order dispersion, the formation of stable two-frequency spatiotemporal solitons is possible.

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

Conservation laws, [formula omitted]-fold Darboux transformation, [formula omitted]-dark-bright solitons and the [formula omitted]th-order breathers of a variable-coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

Optical fiber communication system is one of the core supporting systems of the modern internet age. For the simultaneous propagation of nonlinear waves in an inhomogeneous optical fiber, in this work, a coupled variable-coefficient fourth-order nonlinear Schrödinger system is studied. Infinitely-many conservation laws and N-fold Darboux transformation (DT) based on the existing Lax pair under certain constraints are derived, where N is a positive integer. Via the N-fold DT, the N-dark-bright soliton and Nth-order breather solutions under certain constraints are given. Interactions between the two dark-bright solitons are depicted graphically when the dispersion coefficient in that system, γ1(t), and the group velocity dispersion coefficient in that system, σ(t), are the constants and periodic functions, where t means the normalized retarded time. It is found that the velocities of the two dark-bright solitons increase as γ1(t) and σ(t) increase when γ1(t) and σ(t) are the constants. Interactions between the two breathers are presented graphically.

(3+1)-dimensional Sasa–Satsuma equation under the effect of group velocity dispersion, self-frequency shift and self-steepening

Purpose:The aim of this study is to examine the effects of the coefficients of group velocity dispersion, self-frequency shift and self-steepening terms on the optical solitons of the (3+1)-dimensional Sasa–Satsuma equation which is important for modeling many physical events and it has recently been introduced to the literature. Methodology:To get desired results we have used the solution approach as following. The first step is defining the wave transform and applying it to the nonlinear partial differential equation (NLPDE). Then we have obtained the ordinary differential equation (ODE). Afterwards it is introduced and applied the new Kudryashov method (nKM) and unified Riccati equation expansion method (UREEM) to obtain the algebraic equation system. Finally, by determining the parameters from the solution of algebraic system we have substituted them in the solution function. Findings:By using the solution function we have obtained interesting soliton graphics under different parameter values. In addition to the basic solitons of the (3+1)-dimensional Sasa–Satsuma equation (SSE), V-shaped and periodic singular type solitons have also been obtained. Originality:The findings of the soliton behaviors under the parameter values effect has not been studied before. The results presented in the article are reported for the first time.

Deep neural network for modeling soliton dynamics in the mode-locked laser.

Integrating the information of the first cycle of an optical pulse in a cavity into the input of a neural network, a bidirectional long short-term memory (Bi_LSTM) recurrent neural network (RNN) with an attention mechanism is proposed to predict the dynamics of a soliton from the detuning steady state to the stable mode-locked state. The training and testing are based on two typical nonlinear dynamics: the conventional soliton evolution from various saturation energies and soliton molecule evolution under different group velocity dispersion coefficients of optical fibers. In both cases, the root mean square error (RMSE) for 80% of the test samples is below 15%. In addition, the width of the conventional soliton pulse and the pulse interval of the soliton molecule predicted by the neural network are consistent with the experimental results. These results provide a new insight into the nonlinear dynamics modeling of the ultrafast fiber laser.

Positive and negative exact controllability results for the linear Biharmonic Schrödinger equation

In this paper, we study the exact boundary controllability of the linear Biharmonic Schrödinger equation on a bounded domain with hinged boundary conditions and boundary control acts on the second spatial derivative at the left endpoint. We prove that this system is exactly controllable at any positive time $ T $, if and only if, the group velocity dispersion (GVD) coefficient does not belong to a critical countable set of negative real numbers. The analysis in this work is based on spectral analysis together with the nonharmonic Fourier series method.

Control of the detuning and Rabi frequency on the behavior of soliton fiber laser

This research explore the behavior of soliton in Er +3 fiber laser medium by using a model that use the Quantum optics and three levels system . Starting from the equation of motion of the density operator, the researcher derive the nonlinear Schrödinger equation which include the detuning , Rabi frequency , the group velocity dispersion coefficient of the host fiber and γ the host nonlinearities and use analytic solutions to show that solitary waves can exist and be stable after four loops in ring cavity and the net gain depends on detuning and Rabi frequency

On the study of optical soliton molecules of Manakov model and stability analysis

This paper studies the dynamical behavior of Manakov model which is modeled by two-component nonlinear Schrödinger equation (NLSE). This system models the propagation of soliton flow using group velocity dispersion (GVD) and self-steeping coefficients. By the assistance of two recently developed integration tools, namely, generalized exponential rational function method (GERFM) and new extended direct algebraic method (NEDAM), the different kinds of solutions in the forms of bright, dark, combo and complex solitons are extracted. These types of solutions are quite well-known as optical soliton molecules or pulses in the literature. Moreover, the hyperbolic, exponential and trigonometric function solutions are recovered. In addition, stability analysis of the system is also discussed. A comparison is made between our results and those that are well-known, and the study concludes that the solutions we’ve reached are novel. The significance of the results is illustrated by selecting appropriate parameter values for numerical simulation and physical explanations. For the nonlinear dynamical behavior of a given system, this paper’s results can improve it and demonstrate that the applied methodology is suitable. A wide range of experts in the field of engineering models will benefit from this research, according to our opinion.

Investigation of optical solitons and other solutions in optic fibers modeled by the improved perturbed nonlinear Schrödinger equation

In this manuscript, we discuss the dynamical behavior of improved perturbed nonlinear Schrödinger equation (NLSE) which propagates optical pulses in nonlinear optical fibers. The governing equation is composed of group velocity dispersion (GVD), nonlinearity, self-steeping, higher order and third order dispersion coefficients. The different kinds of solutions in the forms of bright, dark, combo and complex solitons are extracted by the assistance of recently developed integration tools, namely, the extended rational sine-cosine/sinh-cosh techniques, ϕ6-model expansion method and generalized exponential rational function method (GERFM). Moreover, the hyperbolic, Jacobi elliptic function (JEF), exponential, and trigonometric function solutions are recovered. A comparison is made between our results and those that are well-known, and the study concludes that the solutions we’ve reached are novel. The significance of the results is illustrated by selecting appropriate parameter values for numerical simulation and physical explanations. For the nonlinear dynamical behavior of a given system, this paper’s results can improve it and demonstrate that the applied methodology is suitable. A wide range of experts in the field of engineering models will benefit from this research, according to our opinion. The results suggest that the computational methodologies used are direct, efficient, concise, and that they may be applied to more complicated phenomena with the help of symbolic computations.

Dynamics of optical pulses in birefringent fibers without four-wave mixing effect via efficient computational techniques

In this manuscript, we discuss the dynamical behavior of Chen-Lee-Liu (CLL) equation in birefringent fibers which is modeled by two-component nonlinear Schrodinger equation (NLSE) without four-wave mixing effect. In optical fibers and other wave-guide mediums this system models the propagation of soliton flow using group velocity dispersion (GVD) and self-steeping coefficients. In the realms of maritime transport, motion, and energy, the dynamics of deep-sea waves is one of oceanography’s greatest challenges. A mathematical model of the dynamics of solitary waves in the deep ocean under a two-layer stratification yields the NLSE, and resultantly, the interaction between the two can be described by a coupled NLSE. Using two recently developed integration tools, namely the generalized exponential rational function method (GERFM) and the new extended direct algebraic method (NEDAM), the various optical pulses in the forms of bright, dark, combined, and complex solitons are extracted. Moreover, the hyperbolic, exponential, and trigonometric function solutions are recovered. In addition, a comparison is made between our results and those that are well-known, and the study concludes that the solutions we’ve reached are novel. By choosing appropriate parameter values for numerical simulation and physical explanations, the significance of the results is demonstrated. The results of this paper can enhance the nonlinear dynamical behavior of a given system and demonstrate the suitability of the methodology employed. This research, in our opinion, will be beneficial to a wide variety of engineering model specialists.

Investigation of exact soliton solutions to Chen–Lee–Liu equation in birefringent fibers and stability analysis

This study is devoted to uncover the optical solitons and other solutions. The mathematical models used for this purpose is Chen–Lee–Liu equation in birefringent fibers which consist of two components form of vector solitons in optical fiber. This system involves group velocity dispersion (GVD) and self-steeping coefficients that model the propagation of soliton flow through optical fibers and other wave-guide mediums. By the virtue of two innovative norms known as modified exp(−ϕ(ϖ))-expansion function method and Φ6-model expansion method hyperbolic, periodic and plan wave solutions are constructed. The hyperbolic solutions are segregated as dark, bright, singular and their combo forms. Besides, the linear stability mechanism is used to attain modulation instability (MI) gain. By selecting suitable parametric values, numerical simulation and physical interpretations of the achieved outcomes are manifested with interesting figures presenting the meaning of the acquired results. The results reported in this paper can enrich the nonlinear dynamical behaviors of the given system and may be helpful in many fields like telecommunication engineering, mathematical biology, mathematical physics, optical fiber and also exhibit that employed methods are effective and worthy of being tested.

Generation of vector flat-top solitons and hybrid bright–flat-top soliton complexes in optical microresonators via modulated pump

We demonstrate numerically the possibility of generation of vector platicons (or vector flat-top solitons) having orthogonally polarized components by the modulated pump at normal group velocity dispersion (GVD). Dynamics of this process can be controlled by pump polarization and depends on both the spectral interval between pumped modes and the difference of their free spectral ranges. We also show the possibility of the excitation of the hybrid soliton-platicon complexes (or hybrid complexes of bright and flat-top solitons) if pumped modes have alternating signs of the GVD coefficient.

New classifications of nonlinear Schrödinger model with group velocity dispersion via new extended method

This work investigates the nonlinear Schrödinger equation (NLSE) with group velocity dispersion and second order spatiotemporal dispersion coefficients. The governing model is reduced into the classical nonlinear ordinary differential equation. Extended direct algebraic method (EDAM) is implemented to construct many novel mixed dark, and complex optical solutions. As a result, some important analytical solutions such as travelling mixed dark, and complex travelling wave solutions for the model are extracted.

Thermally induced generation of platicons in optical microresonators.

We demonstrate a numerically novel mechanism providing generation of the flat-top solitonic pulses, platicons, in optical microresonators at normal group velocity dispersion (GVD) via negative thermal effects. We found that platicon excitation is possible if the ratio of the photon lifetime to the thermal relaxation time is large enough. We show that there are two regimes of the platicon generation depending on the pump amplitude: the smooth one and the oscillatory one. Parameter ranges providing platicon excitation are found and analyzed for different values of the thermal relaxation time, frequency scan rate, and GVD coefficient. Possibility of the turn-key generation regime is also shown.

On the conformable nonlinear schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients

In this paper, exact traveling wave solutions of the conformable differential equations have been examined. By means of the wave transformation and properties of the conformable derivative (CD), conformable nonlinear Schrödinger equation (CNLSE) has been converted into an integer order differential equation. To extract optical solutions, the wave profile has been divided into amplitude and phase components. A new extension of the Bäcklund method has been offered and applied to the CNLSE which has important applications in quantum mechanics. Some novel exact traveling wave solutions to the CNLSE with group velocity dispersion and second order spatiotemporal dispersion coefficients are successfully obtained by means of this method.

Post-Compression of 9.2-µm Terawatt Laser Pulses to Femtoseconds

Contemporary CO2 laser systems are capable to delivering picosecond pulses of the multi-terawatt peak power. Further pulse compression to a few cycles is possible using a post-compression in bulk materials with negative group velocity dispersion (GVD). We have experimentally demonstrated the post-compression of a long-wave infrared (9.2 μm) 150-GW peak power pulse from 1.85 ps to less than 500 fs using a combination of two optical materials with significantly different ratios of the nonlinear refractive index to the GVD coefficient. Such combination allows for optimization of the compression mechanism and promises a viable path to scaling peak powers to multi-terawatt levels.

Modulation instability analysis and perturbed optical soliton and other solutions to the Gerdjikov-Ivanov equation in nonlinear optics

In this work, we investigate the perturbed optical solitons to the Gerdjikov-Ivanov equation consisting of group velocity dispersion and quintic nonlinearity coefficients, which communicate the propagation of pulses in nonlinear optics. The various kinds of solitons in single and combined forms like dark, singular, dark-singular, bright-dark are derived by Fan-extended sub equation method. Moreover, the singular periodic, triangular type solutions are also obtained. And, we also discuss the stability analysis of the studied nonlinear model with the concept of linear stability, we prove that the governing model is stable. Parametric conditions on physical parameters to ensure the existence criteria of optical solitons are also listed. We also plot 3D profiles for the physical behavior of the obtained solutions by selecting the suitable values of the parameters.

Two-color flat-top solitons in microresonator-based optical parametric oscillators

We studied numerically the generation of the two-color flat-top solitonic pulses, platicons, in the microresonator based doubly resonant optical parametric oscillator. We revealed that if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite, platicon excitation is possible via pump amplitude modulation or controllable mode interaction approach. Upon pump frequency scan generation of platicons was observed at positive pump frequency detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. Interestingly, we found the effect of the transformation of the flat-top platicon profile at half-frequency into the bell-shaped bright soliton profile upon frequency scan. For platicon excitation one needs simultaneous accurate matching of the microresonator free spectral ranges at interacting harmonics and resonant eigenfrequencies. Excitation conditions and platicon generation domains were found for the different generation methods, and properties of the generated platicons were studied for various combinations of the medium parameters.