Generation of time-dependent ultra-short optical pulse trains in the presence of self-steepening effect

Starting from the extended nonlinear Schrodinger equation in which the self-steepening effect is included, the evolution and the splitting processes of continuous optical wave whose amplitude is perturbed into time related ultra-short optical pulse trains in an optical fibre are numerically simulated by adopting the split-step Fourier algorithm. The results show that the self-steepening effect can cause the characteristic of the pulse trains to vary with time, which is different from the self-steepening-free case where the generated pulse trains consist of single pulses which are identical in width, intensity, and interval, namely when pulses move a certain distance, they turn into the pulse trains within a certain time range. Moreover, each single pulse may split into several sub-pulses. And as time goes on, the number of the sub-pulses will decrease gradually and the pulse width and the pulse intensity will change too. With the increase of the self-steepening parameter, the distance needed to generate time-dependent pulse trains will shorten. In addition, for a large self-steepening parameter and at the distance where more sub-pulses appear, the corresponding frequency spectra of pulse trains are also wider.

Evolution of dark solitons in the presence of Raman gain and self-steepening effect

Based on the equation satisfied by optical pulse that is a slowly varying function, the higher-order nonlinear Schr o¨dinger equation(NLSE) including Raman gain and self-steepening effect is deduced in detail, and a new Raman gain function is defined. By using the split-step Fourier method, the influence of the combined effect between Raman gain and self-steepening on the propagation characteristic of dark solitons is simulated in the isotropic fiber. The results show that gray solitons can be symmetrically formed by high order dark soliton, however self-steepening effect will inhibit the formation mechanism through the phenomenon that gray solitons are produced only in the trailing edge of the central black soliton. Meanwhile, the Raman gain changes the propagation characteristic of optical soliton and inhibits the self-steepening effect, resulting in the broadening of pulse width and the decreasing of pulse offset.

Propagation of Solitary Pulses in Optical Fibers with Both Self-Steepening and Quintic Nonlinear Effects

Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schr¨odinger model are isolated via two invariants of motion. The resulting canonical equation admits exact periodic propagating patterns in terms of the Jacobi elliptic functions, and solitary pulses are recovered in the long wave limit, i.e. degenerate cases of periodic profiles where each pulse is widely separated from the adjacent ones. Two families of such exact wave profiles are identified. The first one has a precise constraint concerning the magnitude of self-steepening and quintic nonlinear effects, while the second one permits more freedom. The reduction to the well established temporal soliton in an optical fiber waveguide in the absence of self-steepening and quintic nonlinearity is demonstrated explicitly. Numerical simulations are performed to identify regimes of parameter values where robust propagation patterns exist.

Propagation of chirped solitons on a cw background in a non-Kerr quintic medium with self-steepening effect

We study the existence and stability of envelope solitons on a continuous-wave background in a non-Kerr quintic optical material exhibiting a self-steepening effect.Light propagation in such a nonlinear medium is governed by the Gerdjikov-Ivanov equation.We find that the system supports a variety of localized waveforms exhibiting an important frequency chirping property which makes them potentially useful in many practical applications to optical communication.This frequency chirp is found to be crucially dependent on the intensity of the wave and its amplitude can be controlled by a suitable choice of self-steepening parameter.The obtained nonlinearly chirped solitons include bright,gray and kink shapes.We also discuss the stability of the chirped solitons numerically under finite initial perturbations.The results show that the main character of chirped localized structures is not influenced by finite initial perturbations such as white noise.

Self—Steepening and Thired—Order Dispersion Induced Optical Solitons in Fiber

Usually,one considers only the group velocity dispersion(GVD)-and self-phase modulation(SPM)-induced solitons in optic soliton communication while other higher order effects such as the third-order dispersion(TOD),self-steepening(SS),and stimulated Raman scattering are considered only perturbatively,In this paper,we study the existence of the TOD-and SS-induced soliton solutions.The existence conditions of the TOD-and SS-induced bright and dark solitons are quite different from those of the GVD-and SPM-induced solitons.

Impact of the self-steepening effect on soliton spectral tunneling in PCF with three zero dispersion wavelengths

This work presents a numerical investigation of the self-steepening（SS） effect on the soliton spectral tunneling（SST） effect in a photonic crystal fiber（PCF） with three zero dispersion wavelengths. Interestingly, the spectral range and flatness can be flexibly tuned by adjusting the SS value. When the SS coefficient increases, the energy between solitons and dispersion waves is redistributed, and the red-shifted soliton forms earlier in the region of long wavelength anomalous dispersion. As a consequence, the SST becomes more obvious. The findings of this work provide interesting insights in regard to the impact of the SST effect on tailored supercontinuum generation.

Spatiotemporal instability in nonlinear dispersive media in the presence of space-time focusing effect

Spatiotemporal instability in nonlinear dispersive media is investigated on the basis of the nonlinear envelope equation. A general expression for instability gain which includes the effects of space-time focusing, arbitrarily higher-order dispersions and self-steepening is obtained. It is found that, for both normal and anomalous group-velocity dispersions, space-time focusing may lead to the appearance of new instability regions and influence the original instability gain spectra mainly by shrinking their regions. The region of the original instability gain spectrum shrinks much more in normal dispersion case than in anomalous one. In the former case, space-time focusing completely suppresses the growing of higher frequency components. In addition, we find that all the oddth-order dispersions contribute none to instability, while all the eventh-order dispersions influence instability region and do not influence the maximum instability gain, therein the fourth-order dispersion plays the same role as space-time focusing in spatiotemporal instability. The main role played by self-steepening in spatiotemporal instability is that it reduces the instability gain and exerts much more significant influence on the new instability regions resulting from space-time focusing.