Influence Of Third-order Dispersion Research Articles

Tunable modulation instability spectra in negative index materials

This paper investigates the formation of tunable modulation instability windows in metamaterials. We consider the influence of third-order dispersion, fourth-order dispersion, cubic nonlinearity, quintic nonlinearity, detuning parameter, self-steepening and higher-order nonlinear dispersions on the gain spectrum in addition to the basic requirement to observe modulation instability such as group velocity dispersion and self-phase modulation. As the metamaterials provide engineering freedom, all the material parameters are tunable, which leads to tunable modulation instability gain spectrum formation. This tunable gain spectrum provides additional ways to form solitons and ultrashort pulses with desired parameters.

Bright solitons under the influence of third-order dispersion and self-steepening effect

Bright solitons under the influence of third-order dispersion and self-steepening effect

Periodic and solitary waves in an inhomogeneous optical waveguide with third-order dispersion and self-steepening nonlinearity

We demonstrate the formation of periodic waves and envelope solitons in dispersive optical media having a Kerr nonlinear response under the influence of third-order dispersion and self-steepening effect. The stability properties of the bright- and dark-soliton solutions are proved using the stability criterion based on the theory of nonlinear dispersive waves. Regimes for the modulation instability of a continuous wave signal propagating inside the dispersive optical medium are also investigated. The results show that the gain spectrum depends crucially on the self-steepening parameter, while the third-order dispersion has no effect on the modulation instability condition. A similarity transformation is presented to reduce the generalized extended nonlinear Schr\"odinger equation with distributed coefficients which models the pulse evolution in the presence of the inhomogeneities of media to the related constant-coefficient one. The propagation behaviors of self-similar bright and dark solitons are discussed in a periodic distributed fiber system and an exponential dispersion decreasing fiber.

Third Order Dispersion in Time-Delayed Systems.

Time-delayed dynamical systems materialize in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. However, they are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. We show how dispersion may appear naturally in delayed systems and we exemplify our result by studying theoretically and experimentally the influence of third order dispersion in a system composed of coupled optical microcavities. Dispersion-induced pulse satellites emerge asymmetrically and destabilize the mode-locking regime.

Analytical and numerical demonstration of phase characteristics on two solitons under the influence of third-order dispersion

In the present work, influence of third-order dispersion (TOD) on phase change properties of two-soliton model is numerically and analytically investigated. Using perturbation theory approach and split-step Fourier transform, phase characteristics of two solitons pulse are evolved and solved by nonlinear Schrodinger’s equation. Each phase variation in the form of temporal shift under the base of third-order dispersion is also numerically devoted using the moments equation. As a result, it was found that the shift of soliton pulse mainly depends on third-order dispersion parameter β3. With the good agreement between analytical and numerical analysis, the impact of TOD has realized in a single channel telecommunication system.

Combined influence of third order dispersion (TOD) and intra-pulse Raman scattering (IRS) on initially phase imparted solitons

The temporal shifts caused by the combined influence of Third Order Dispersion (TOD) and Intra-pulse Raman scattering (IRS) on initially phase imparted soliton pulses is demonstrated analytically and numerically. Further the effects are realized in a 160 Gbps, single channel telecommunication system. The phase (ψ) characteristics of soliton with respect to initial relative spacing (qo) is governed by Perturbative equation while the temporal shift under the influence of Third Order Dispersion and Intra-pulse Raman scattering is noted by Moment equation. By combining the Perturbative and Moment equations, the temporal shift under the combined effects is noted analytically. Also the similar effect is noted numerically by using the Split-Step Fourier transform (SSFT) to support analytics. The temporal shift at the interaction point (where two in-phase soliton interacts) using analytical and numerical method is characterized by the ‘Spacing between the solitons’ in terms of picoseconds. It could be realized by both analytical and numerical methods that the Intra-pulse Raman scattering is more dominant over third order dispersion in shifting the soliton pulses temporally with respect to distance. Apart from analytical and numerical approached, the shift of soliton pulses under the combined effect is realized in telecommunication system and the performance is noted using the Q-value and Time domain analyzer view.

Combined influence of third-order dispersion, intra-pulse Raman scattering, and self-steepening effect on soliton temporal shifts in telecommunications

Here, we discuss the influence of higher-order nonlinear effects like third-order dispersion, intra-pulse Raman scattering, and self-steepening effects on 1-ps soliton pulse shift or displacement from its initial position. The temporal shifts of soliton due to these higher-order nonlinear effects were studied numerically by "Method of Moments" to realize the contribution of these HOE on shifts. Further, we note the influence of positive and negative TOD on the shift produced by the combined HOE. The soliton shift is then analyzed in 160-Gbps telecommunication system implemented with conventional single-mode fiber (C-SMF) for the length 10 and 20 km. The disturbances between the adjacent soliton pulses in noted with different 16-bit data sequences, and the deterioration of system is characterized in terms of quality factor. It could be seen for an unchirped soliton of pulsewidth $$T_{\mathrm{o}}\sim 1\hbox {ps}$$To~1ps, the shift is highly influenced due to intra-pulse Raman scattering, while the shifting due to third-order dispersion can be treated negligibly small. Moreover, negative TOD was expected to inhibit the soliton temporal shift such that it would reduce collision with adjacent pulses; it results in more resonant radiation resulting in pulse decaying. Although negative TOD helps in good reception of pulses for 10 km, it fails to perform in system with 20 km C-SMF, where the dispersive components break more and more while traveling along the length of fiber.

Quantitative analysis of the mode-pulling effect in microcomb generation based on the modal expansion method

We present a quantitative analysis of the mode-pulling effect in microresonator-based comb (microcomb) generation. It is found that the initial dispersion of the microresonator can be ideally compensated or quasi-compensated by the Kerr effect. The ideal dispersion compensation leads to a stable comb, while the comb remains unstable in the quasi-compensation case. Four-wave mixing (FWM) is found to play a critical role in the mode-pulling effect. The influence of third-order dispersion is also analyzed and found to be insignificant. Additionally, the mode-pulling effect can also result in blue-shift of the cavity resonance due to the strong contribution from the phase-dependent FWM process.

Modulation instability, Cherenkov radiation, and Fermi–Pasta–Ulam recurrence

We study, numerically, the influence of third-order dispersion (TOD) on modulation instability (MI) in optical fibers described by the extended nonlinear Schrödinger equation. We consider two MI scenarios. One starts with a continuous wave (CW) with a small amount of white noise, while the second one starts with a CW with a small harmonic perturbation at the highest value of the growth rate. In each case, the MI spectra show an additional spectral feature that is caused by Cherenkov radiation. We give an analytic expression for its frequency. Taking a single frequency of modulation instead of a noisy CW leads to the Fermi–Pasta–Ulam (FPU) recurrence dynamics. In this case, the radiation spectral feature multiplies due to the four-wave mixing process. FPU recurrence dynamics is quite pronounced at small values of TOD, disappears at intermediate values, and is restored again at high TOD when the Cherenkov frequency enters the MI band. Our results may lead to a better understanding of the role of TOD in optical fibers.

Influences of third-order dispersion on linear birefringent optical soliton transmission systems

This article presents the propagation of solitons in linear birefringent single-mode fibers under the influence of third-order dispersion. The behaviour of two partial pulses evolved due to polarization mode dispersion is investigated under the presence of third-order dispersion (TOD). The analytical solutions to coupled nonlinear Schrodinger equations (CNLSE) with TOD are derived using multiple scale perturbation expansion and the results are compared with the solutions obtained using split-step Fourier method to find the effects of TOD on soliton propagation. It is found that the resultant soliton deviates from its initial position with third-order dispersion and this deviation is considerably small when the pulse propagates relatively far from the zero-dispersion wavelength. It is observed that the behaviour of two partial pulses and their subsequent properties depend not only on the fiber parameters, but also on the amplitude of the launched soliton pulses.

Influence of third-order dispersion on delay performance in broadband Brillouin slow light: erratum

We investigate theoretically the delay performance of Brillouin slow light employing a broadband pump with a rectangular spectrum. Analytical expression of delayed Gaussian pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order dispersion effects involved. Calculated results show that the Gaussian pulse with full-width at half maximum of 200 ps is delayed by 80 ps with little pulse broadening in a single-stage Brillouin slow-light medium, and the time delay is extended to multi-hundred ps with low distortion in a cascaded Brillouin slow-light system. Comparing the analytical results with the numerical ones, we confirm that the pulse distortion is mainly attributed to the large third-order dispersion introduced by stimulated-Brillouin scattering.

Influence of third-order dispersion on delay performance in broadband Brillouin slow light

We investigate theoretically the delay performance of Brillouin slow light employing a broadband pump with a rectangular spectrum. Analytical expression of delayed Gaussian pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order dispersion effects involved. Calculated results show that the Gaussian pulse with full-width at half maximum of 200 ps is delayed by 80 ps with little pulse broadening in a single-stage Brillouin slow-light medium, and the time delay is extended to multi-hundred ps with low distortion in a cascaded Brillouin slow-light system. Comparing the analytical results with the numerical ones, we confirm that the pulse distortion is mainly attributed to the large third-order dispersion introduced by stimulated-Brillouin scattering.

Bulletlike light pulses in photonic crystals

We report the bulletlike propagation of light pulse in a particularly designed two-dimensional (2D) photonic crystal. Unlike traditional light bullet supported by nonlinear materials, this bulletlike propagation is achieved only by 2D photonic crystal, where the diffraction and the group velocity dispersion of a light pulse are eliminated naturally by combining two distinct properties of photonic crystal, i.e., self-collimation and zero group velocity dispersion. Moreover, we studied the influence of third order dispersion on the propagation of light bullet and found that it can be greatly suppressed by an improved structure of photonic crystal.

Soliton coupling in birefringent optical fiber with third-order dispersion

Nonlinear coupling of polarized solitons in birefringent optical fiber in the presence of third-order dispersion is considered in the framework of the coupled nonlinear Schrödinger equations. The influence of third-order dispersion on the interaction between solitons is investigated. For sufficiently strong third-order dispersion the interaction may even become repulsive. The stable conditions for solitons of partial pulses are analyzed and amplitude threshold, which decreases with third-order dispersion coefficient decreasing, for the capture of solitons of partial pulses into a coupled two-component pulse is obtained.

Bi-Soliton under the Influence of Third Order Dispersion in Dispersion-Managed Optical Transmission System

In this paper, firstly, effects of third order dispersion (TOD) on coupled pulses are analyzed. Then, averaging method is modified and proved to be an effective way for obtaining non-radiative bi-soliton solution of the TOD perturbed nonlinear Schrodinger equation (NLSE), which models a dispersion managed (DM) optical transmission system. Finally, the obtained bi-soliton evolution behavior is studied, and compared with that of uni-soliton. With the increase of average TOD, pulse velocity of bi-soliton largely deviates from that of uni-soliton. Thus, even though TOD cannot be exactly vanished in fabrication, it is suggested to compensate average TOD as low as possible.

Bright solitary waves in high dispersive media with parabolic nonlinearity law: The influence of third order dispersion

Bright solitary waves in high dispersive media with parabolic nonlinearity law: The influence of third order dispersion

Bright solitary waves in high dispersive media with parabolic nonlinearity law: The influence of third order dispersion

Bright solitary waves in high dispersive media with parabolic nonlinearity law: The influence of third order dispersion

Bright solitary waves in high dispersive media with parabolic nonlinearity law: The influence of third order dispersion

We find exact bright solitary wave solutions of a cubic-quintic nonlinear Schrödinger equation describing the propagation of extremely short pulses. Particular cases are discussed. The influence of third order dispersion is numerically investigated, showing the pulse stability for relative low values of the third order dispersion coefficient. When propagation at the zero dispersion point is considered the pulses are always unstable.

Nonlinear pulse distortion at the zero dispersion wavelength of an optical fibre

Pulse propagation at the zero dispersion wavelength of a standard optical fibre is investigated experimentally and theoretically. The respective results are in remarkably good agreement and demonstrate that the combined influence of third order dispersion and fibre nonlinearity leads to severe distortions of the pulse temporal and spectral profiles. Using a straightforward physical model an analytical expression is derived which allows to calculate the critical experimental parameters for which significant nonlinear pulse distortion occurs.