Fourth-order Dispersion Effects Research Articles

M-shaped, W-shaped and dark soliton propagation in optical fiber for nonlocal fourth order dispersive nonlinear Schrödinger equation under distinct conditions

The formation of soliton in optical fiber governed by nonlocal nonlinear Schrödinger (NLS) equation with fourth order dispersion is studied. The model of nonlocal NLS equation with fourth order dispersion is solved using the new extended auxiliary method and the solutions are obtained. The solutions are in the form of hyperbolic and trigonometric functions which are based on Jacobi elliptic function m. Shape changing soliton in optical fiber for nonlocal fourth order dispersive NLS equation is discussed by suitably choosing the values of kerr and quintic nonlinearities and by varying fourth order dispersion term. The effect of fourth order dispersion on soliton in fiber for different conditions of kerr and quintic nonlinearity is also discussed. In addition, the phase portraits of the system have been investigated and the stability of wave in optical fiber for nonlocal NLS equation is discussed using fourth order Runge-Kutta algorithm. This paper addresses a significant gap in the current literature by examining the impact of fourth order dispersion on the nonlocal NLS equation in optical fiber.

Propagation of coupled quartic and dipole multi-solitons in optical fibers medium with higher-order dispersions

We present the discovery of two types of multiple-hump soliton modes in a highly dispersive optical fiber with a Kerr nonlinearity. We show that multi-hump optical solitons of quartic or dipole types are possible in the fiber system in the presence of higher-order dispersion. Such nonlinear wave packets are very well described by an extended nonlinear Schrödinger equation involving both cubic and quartic dispersion terms. It is found that the third- and fourth-order dispersion effects in the fiber material may lead to the coupling of quartic or dipole solitons into double-, triple-, and multi-humped solitons. We provide the initial conditions for the formation of coupled multi-hump quartic and dipole solitons in the fiber. Numerical results illustrate that propagating multi-quartic and multi-dipole solitons in highly dispersive optical fibers coincide with a high accuracy to our analytical multi-soliton solutions. It is important for applications that described multiple-hump soliton modes are stable to small noise perturbation that was confirmed by numerical simulations. These numerical results confirm that the newly found multi-soliton pulses can be potentially utilized for transmission in optical fibers medium with higher-order dispersions.

Pure–quartic optical solitons and modulational instability analysis with cubic–quintic nonlinearity

We analyze the propagation dynamics of intense light pulses in an optical medium exhibiting cubic–quintic nonlinearity and pure fourth-order dispersion. We show that this physical system may support a rich variety of periodic wave solutions in the presence of all physical processes. Interestingly, in the long-wave limit, two different types of quartic dark solitons with equal amplitudes and wave numbers but different widths are identified for the first time. The obtained dark soliton solutions are shown to be independent of any free parameters and their characteristics are uniquely determined by system parameters. The numerical examples are presented for illustrating the soliton evolution dynamics in the waveguiding system. The formation of these quartic dark solitons occurs in normal pure fourth-order dispersion when the quintic and cubic nonlinearities are competitive. The modulational instability of a continuous wave is also analyzed under the combined effects of quartic dispersion and cubic–quintic nonlinearities. Additionally, the role of quintic nonlinearity and fourth-order dispersion effects on the modulational instability has been discussed.

Cubic–quartic optical solitons in birefringent fibers with Sasa–Satsuma equation

Objective:The paper recovers cubic–quartic optical solitons with the Sasa–Satsuma equation that includes a combination of third-order dispersion and fourth-order dispersion effects to address cubic–quartic vector solitons for the first time. Methods:Two integration schemes are applied to catch out the solitons to the newly structured model. They are G′/G–expansion scheme and modified Kudryashov’s approach. These pave way for a full spectrum of vector solitons. The recovered vector solitons are enumerated after a revisiting the mathematical strategies. Results:The mathematical approaches retrieve the dark, bright and singular vector solitons to the model. These solitons are presented by virtue of the certain restrictions. Rational and singular periodic solutions are also emerged with the mathematical schemes. Conclusion:Cubic–quartic vector solitons are yielded for such a model in this work for the first time. This would naturally lead to further ventures in this area. The newly structured model would be to address to recover the conservation laws. Other natural extensions to the model would be to consider with DWDM topology that would also lead to soliton solutions and their respective conservation laws.

Impact of higher-order effects on modulation instability in negative index materials

In this article, we present a systematic investigation of modulation instability (MI) in negative index materials (NIMs) with higher-order dispersion and nonlinearity. We adopt the method of linear stability analysis and obtain an expression for the instability gain. Special attention is paid to studying the effect of fourth-order dispersion, quintic nonlinearity, first-order nonlinear dispersion, and second-order nonlinear dispersion on the instability gain. It is found that the fourth-order dispersion forms new instability regions and gives new ways to generate solitons or ultrashort pulse trains. Our study also shows that in the presence of higher-order dispersion a switching of the sign of cubic nonlinearity can generate two distinct MI regions. This result may provide a better way to generate different frequency ultra-short pulses as a result of switching of the sign of cubic nonlinearity by tuning the parameters of constituent elements of the metamaterials. Further, we observed that the cooperating cubic and quintic nonlinearities widen the MI by enhancing maximum gain and bandwidth, on the other hand, the competing cubic and quintic nonlinearities suppress the MI considerably.

Soliton shedding from Airy pulses in a highly dispersive and nonlinear medium

We present a numerical investigation of the propagation dynamics of a truncated Airy pulse in a highly dispersive and nonlinear medium by employing the split-step Fourier transform method and look, in particular, into the effects of fourth-order dispersion (FOD) and cubic-quintic-septic nonlinearity on pulse evolution. Presence of FOD cancels the Airy pulse’s self-acceleration along with eclipsing the oscillatory tail during propagation in the linear regime. Further, we observe soliton shedding at low input pulse power in the presence of cubic and quintic nonlinearity and negative FOD. The emergent soliton exhibits temporal shift, and the direction and the extent of the shift depend upon the strengths of cubic and quintic nonlinearities. In the presence of anomalous group-velocity dispersion (GVD) with negative FOD, soliton shedding is observed at relatively high input pulse power. The strengths of GVD and nonlinearity play a vital role in the temporal shifting of the emergent soliton. Furthermore, we have explored the effects of septic nonlinearity on soliton shedding in different scenarios of nonlinearity and dispersion.

The effects of fourth-order dispersion on modulation instabilities in two-core optical fibers with asymmetric CW state

The effects of fourth-order dispersion (FOD) on modulation instabilities in the twin-core optical fibers with the asymmetric CW state are studied systematically. When the product of the group velocity dispersion and FOD is negative, in the anomalous dispersion regime, two new MI bands in the high frequency are generated with one band either having the equivalent gain with that of original band or dominating the MI depending on the FOD value; in the normal dispersion, a new dominant MI band in the high frequency is always generated, and the original MI bands vanish in the presence of FOD at total power above a critical value. When the product of the group velocity dispersion and FOD is positive, the main effect of FOD is to shift the MI band to the low frequency and reduce the bandwidth simultaneously with minor effects on the instability gain. We also find that the effects of linear coupling coefficient dispersion can be significantly suppressed in the presence of FOD especially for the case of negative product of the group velocity dispersion and FOD. Finally, the effects of FOD on MI are verified numerically by launching continuous waves with the wave propagation method. Our results should provide very benificial information for successfully observing MI in TCFs or MI related applications with TCFs.

Effect of Fourth-Order Dispersion on Solitonic Interactions

Solitons became important in optical communication systems thanks to their robust nature. However, the interaction of solitons is considered as a bad effect. To avoid interactions, the obvious solution is to respect the temporal separation between two adjacent solitons determined as a bit rate. Nevertheless, many better solutions exist to decrease the bit rate error. In this context, the aim of our work is to study the possibility to delete the interaction of adjacent solitons, by using a special dispersion management system, precisely by introducing both of the third- and fourth-order dispersions in the presence of a group velocity dispersion. To study the influence of the fourth- and third-order dispersions, we use the famous non-linear Schr¨odinger equation solved with the Fast Fourier Transform method. The originality of this work is to bring together the dispersion of the fourth, third, and second orders to separate two solitons close enough to create the Kerr-induced interaction and consequently to improve the propagation by decreasing the bit rate error. This study illustrates the influence of the fourth-order dispersion on one single soliton and two co-propagative solitons with different values of the temporal separation. Then the third order dispersion is introduced in the presence of the fourth-order dispersion in the propagation of one and two solitons in order to study its influence on the interaction. Finally, we show the existence of a precise dispersion management system that allows one to avoid the interaction of solitons.

Dark-dark solitons for a coupled variable-coefficient higher-order nonlinear Schrödinger system in an inhomogeneous optical fiber

In this paper, under investigation is a coupled variable-coefficient higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the Lax pair and binary Darboux transformation, we present the nondegenerate N-dark-dark soliton solutions. With the graphical simulation, soliton propagation and interaction are discussed with the group velocity dispersion and fourth-order dispersion effects, which affect the velocity but have no effect on the amplitude. Linear, parabolic and periodic one dark-dark solitons are displayed. Interactions between the two solitons are presented as well, which are all elastic.

Jacobi elliptic solutions, soliton solutions and other solutions to four higher-order nonlinear Schrodinger equations using two mathematical methods

Two mathematical methods, via the (G′/G)-expansion method and extended auxiliary equation method are applied in this article to find many exact solutions with parameters of four higher-order nonlinear Schrodinger equations whose balance numbers are not positive integers, namely, the nonlinear Schrodinger equation with dual power-law nonlinearity, the higher-order dispersive nonlinear Schrodinger equation with both fourth-order dispersion effects and a quintic nonlinearity, the resonant nonlinear Schrodinger equation and the generalized higher-order nonlinear Schrodinger equation. When the parameters take up special values, the solitary and singular solitary wave solutions of these nonlinear Schrodinger equations are given. The used methods in this article present a wider applicability for handling nonlinear wave equations. Comparing our new results and the well-known results are obtained. Comparing the results resulting from the two methods with each others are also given.

Effects of fourth-order dispersion on modulational instability in metamaterials with exponential saturable nonlinearity and self-steepening coefficients

We studied the modulational instability in negative index materials with higher-order effects. An expression for the instability gain is derived through the linear stability analysis. We identify and discuss the salient features of the effect, like fourth-order dispersion, self-steepening and saturable nonlinearity on the modulational instability. The results show that the instability gain depends on the sign of the higher-order dispersion and, for anomalous dispersion, the instability regime is constituted of two parts: the conventional gain spectrum and the secondary gain spectrum induced by the fourth-order dispersion. For large values of the fourth-order dispersion, the secondary instability region spectrum vanishes and merges with the ordinary gain. In the normal dispersion regime, an efficient control of the modulation instability is successfully demonstrated by adjusting the fourth-order dispersion, depending on the presence of the self-steepening parameter or the normalized input power.

Periodic compression of chirped femtosecond pulses in silicon waveguides under fourth-order dispersion

We report the analysis of the compression mechanism for chirped femtosecond pulses in silicon-on-insulator waveguides under the effect of fourth-order dispersion (FOD) using the modified variational approach that involves Rayleighʼs dissipation function (RDF). Our results show that the nonlinear compression in these waveguides is input pulse dependent. Moreover, this study leads to a nearly periodic-like dynamic induced by the interplay between self-phase modulation and FOD in a normal group-velocity dispersion. In addition, when large values of the initial chirp and absorption coefficients present in these waveguides are considered, the compression mechanism is completely destroyed, with the observation of at least one pulse amplification over a short distance of propagation prior to pulse broadening.

Impact of higher-order dispersion in the modulational instability spectrum of a relaxing coupled saturable media

A theoretical analysis of modulational instability (MI) of optical pulses propagating near the zero dispersion wavelength of a lossless fibre with the effect of delayed saturable nonlinear response is presented. We calculate the exact dispersion relation with the effect of higher dispersion for the harmonic perturbation. We analysed the impact of fourth-order dispersion effects in the MI spectrum. We examine the possibility of MI in both dispersion regimes, regardless of the sign of the group velocity dispersion.

Modulation instability induced by cross-phase modulation in dispersion-decreasing fiber with high-order dispersion and high-order nonlinearity

The modulation instability (MI) induced by cross-phase modulation (XPM) in dispersion-decreasing fiber (DDF) is investigated based on extended nonlinear Schrödinger equations with high-order dispersion and high-order nonlinearity considered. The effects of fourth-order dispersion, quintic nonlinearity, dispersion decaying factor and different group velocity dispersion (GVD) on the gain spectra are analyzed. The results show that due to fourth-order dispersion, XPM occurs at two spectral regions in both the normal and the anomalous dispersion regimes of DDF. The positive (negative) quintic nonlinearity will make the width and the peak value of the gain spectra larger (smaller). The spectral width of XPM in DDF increases with increasing dispersion decaying factor. There are still two XPM regions in both the normal and anomalous dispersion regimes in DDF with different GVD.

Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime

We propose a new method for the generation of both triangular-shaped optical pulses and flat-top, coherent supercontinuum spectra using the effect of fourth-order dispersion on parabolic pulses in a passive, normally dispersive highly nonlinear fiber. The pulse reshaping process is described qualitatively and is compared to numerical simulations.

Higher order dispersion effects in the noninstantaneous nonlinear Schrödinger equation

We present a systematic analysis of the effects, of higher-order dispersion, noninstantaneous nonlinear response, as well as stochastic coefficients in optical fiber. This study is motivated by recent experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber. Analytical expression of pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order as well as fourth-order dispersion effects involved. The influence of stochasticity, as well as the delayed Raman response in the nonconventional sidebands obtained due to the fourth-order dispersion, is considered. We note that the shape of the spectrum, and in particular the relative intensities of the higher order harmonics, is highly sensitive to the initial presence of classical noise, and can therefore be taken as a signature that the MI is seeded by vacuum fluctuations. Some direct simulations to see the evolution of different continuous wave states are reported. These show the formation of modulation instability pulses as well as transitions from lower amplitude continuous wave states to higher amplitude continuous wave states. The present results fit well with recent experimental investigations.

A compact split step Padé scheme for higher-order nonlinear Schrödinger equation (HNLS) with power law nonlinearity and fourth order dispersion

In this paper we propose a compact split step Padé scheme (CSSPS) to solve the scalar higher-order nonlinear Schrödinger equation (HNLS) with higher-order linear and nonlinear effects such as the third and fourth order dispersion effects, Kerr dispersion, stimulated Raman scattering and power law nonlinearity. The stability of this method has been proved. It has been shown as well that the CSSPS method gives the same results as classical numerical methods like the split step Fourier method and Crank–Nicholson (CN) method but it presents many advantages over theme. It is more efficient. This proposed scheme is well suited to higher-order dispersion effects and readily generalized for nonlinear and dispersion managed fibers. We tested this scheme for the case of the quintic nonlinearity and confirmed that this effect has no significant role on the propagation of single solitons.

Optimal design of tunable parametric wavelength converters based on degenerate four-wave mixing in optical fibers

We prove that the tuning range of a one-pump fiber parametric wavelength converter based on degenerate four-wave mixing can be maximized by selecting fibers with appropriate zero dispersion wavelength and high-order dispersion coefficients. The maximal tuning range is proportional to the cube root of the product of the pump power and fiber nonlinear coefficient. If the effects of fourth-order dispersion are utilized, the tuning range can increase dramatically.

Solitary wave solutions for high dispersive cubic-quintic nonlinear Schrödinger equation

We consider the higher-order dispersive nonlinear Schrödinger equation including fourth-order dispersion effects and a quintic nonlinearity. This equation describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. By adopting the ansatz solution of Li et al. [Zhonghao Li, Lu Li, Huiping Tian, Guosheng Zhou. New types of solitary wave solutions for the higher-order nonlinear Schrödinger equation. Phys Rev Lett 2000;84:4096], we find two different solitary wave solutions under certain parametric conditions. These solutions are in the form of bright and dark soliton solutions.

Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities

Taking up to fourth-order dispersion effects into account, we show that fiber resonators become stable for a large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for an arbitrary small but nonzero fourth-order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and open the way to experimental implementation.