Comparison of soliton robustness with respect to polarization-mode dispersion with first-order polarization-mode dispersion compensated linear systems

Soliton robustness to polarization-mode dispersion (PMD) is compared, both analytically and numerically, with that of linear pulses that use first-order PMD compensation. It is found that soliton robustness to PMD is comparable with first-order PMD compensation and in some cases is even better. The effects of soliton control methods on soliton robustness to PMD were also investigated, and it was found that soliton control methods can significantly improve the soliton's robustness to PMD, particularly for long-distance systems.     

Soliton interaction in birefringent optical fibers: Effects of nonlinear gain devices

This paper presents the influences of polarization mode dispersion (PMD) on the performance of soliton transmission system in birefringent fibers. Dispersive waves generated in single mode fibers due to PMD degrade the soliton transmission system in two aspects. First, solitons continuously lose their energy, thus cause enhancement in pulse width. Second, the dispersive waves interact with neighboring pulses and cause distortion in a sequence of pulses. Both these effects reduce the effective bit-rate and degrade the performance of high-speed optical transmission systems. Optical fibers with large group velocity dispersion (GVD) have less dispersive waves and are relatively robust to pulse broadening, but it enhances the interaction between the adjacent pulses. In this paper, we analyzed these effects of PMD on soliton propagation in birefringent fibers and introduced nonlinear gain devices with perturbation terms proportional to second and fourth power of amplitudes to reduce these effects. We proposed Symmetric Split-Step Fourier Method to solve the coupled nonlinear Schrödinger equations (CNLSE); which yields better results over the existing Split-Step Fourier Method.     

Soliton Propagation in Birefringent Fibers

In this article, the propagation of solitons in a single mode fiber with polarization mode dispersion (PMD) is analyzed. In optical fibers, the randomly varying birefringence degrades soliton transmission system in two aspects. First, the dispersive waves cause pulse broadening. Second, the dispersive waves interact with other soliton pulses. Here we studied the effects of PMD on a single pulse and the variation of pulse broadening, energy decay, and degree of polarization on a single soliton pulse propagating over a very long distance.     

Asymmetrically Apodized Linearly Chirped Fiber Bragg Gratings for Efficient Pulse Compression

Abstract

A simple and stable technique of optical short pulse generation for soliton transmission based on external modulation is reviewe.By using nonlinearity of absorption characteristics of an electroabsorption modulator, ultra-short optical pulse trains having a shape close to sech² shape can be generated just with sinusoidal modulation, without ultra-short driving pulses and ultra-broad bandwidth of the modulator. The pulse width and the repetition rate can be varied by changing the electrical driving conditions. Quasi-transform-limited optical pulseswith time-bandwidth product of 0.32 were successfully generated by the sinusoidally driven InGaAsP electroabsorption modulator with up to 20 GHz repetition rate. An application of a λ/4-shifted DFB laser-electroabsorption modulator integrated light source to a single-chip soliton source is also described. The high quality of the modulator-generator pulses has been proven by long-distance soliton transmission over 6400 km at 2.5 Gb/s using a recirculating fiber loop.     

偏振模色散影响色散控制孤子传输的理论研究

采用变分法分析高速色散控制孤子在双折射光纤中的传输规律。首先建立了色散控制孤子在双折射光纤中的扰动传输模型 ,然后解析了偏振模色散影响下色散控制孤子各参量的传输演化规律 ,最后对解析结果进行了计算。研究结果表明 ,偏振模色散参量对色散控制孤子能量、脉宽的演化影响很大 ,当偏振模色散很大时 ,如Dp>0 .3ps/km1/ 2 时 ,必须考虑采用某些在线控制手段来有效抑制偏振模色散对传输系统的影响 ,然而 ,当Dp≤ 0 .1ps/km1/ 2 时 ,系统几乎不受影响 ,同时本文还证明了色散控制孤子抗偏振模色散扰动的能力强的这一特点。为研究偏振模色散对高速非线性传输系统、特别是色散控制孤子传输系统的影响提供了理论依据和研究方法。     

偏振模色散影响下飞秒孤子的传输特性研究

以Maxwell电磁场理论为基础，在综合考虑了高阶色散、高阶非线性、自相位调制、交叉相位调制、自变陡、脉冲内喇曼散射及偏振模色散等因素的基础上，推导了飞秒孤子脉冲在双折射光纤中传输的耦合非线性薛定谔方程，并利用分步傅里叶方法对该方程进行了数值计算，研究分析了偏振模色散对飞秒孤子传输的影响。结果发现：当Dp≤0.1ps/km1/2时，偏振模色散对系统的影响很小，随着偏振模色散值的增大，系统的传输性能迅速恶化，当偏振模色散值达到0.3ps/km1/2时，系统的传输距离已经不到无偏振模色散时的1/3；若同时考虑光纤的高阶效应，以飞秒孤子作为载体的系统已经不能实现高速长距离的传输。     

Performance improvement by positioning DCF non-symmetrically in a periodic amplified re-circulating loop for long-haul optical soliton transmission link

In this paper, we have carried out simulative performance analysis by positioning the DCF non-symmetrically in a periodic amplified re-circulating loop for optical soliton transmission link over a long haul. The investigations indicate that relatively stable pulses can propagate in a mid-compensated optical soliton transmission over a long-haul dispersion-managed soliton regime in a fiber link with loss and periodic amplification by keeping the average dispersion small but non-zero. Here non-zero anomalous fiber dispersion equal to 6 ps/nm is maintained by inserting DCF in the beginning, middle and end of the fiber loop. Here it is demonstrated that solitons can propagate even when β₂ varies along the fiber length up to transmission distance of 18,000 km.     

Significance of prechirping on long-haul path-averaged soliton impulse in re-circulating loop at 10 and 20 Gb/s with TOD

In this paper, we have investigated the performance of first- and second-order path-averaged soliton long-haul transmission link including the impact of third-order dispersion (TOD) at varied chirp. Here, the varied chirp is considered keeping in view the inadvertent frequency chirp imposed on all practical sources of short optical pulses. The propagation of strongly chirped pulses in loss-managed long-haul path-averaged soliton transmission network has been shown. The investigations reveal that in first-order (N=1) path-averaged soliton transmission link at 10 and 20 Gb/s, SPM effect on the rising and falling edges of a pulse results in spectral broadening for all values of induced chirp. On the contrary, spectral narrowing of the pulses is observed in second-order negatively chirped path-averaged soliton pulses. The effect of the nonlinearity changes from narrowing to broadening of pulses if the sign of the initial chirp is changed to positive. The results ascertain that the system is capable of transmitting a pulse up to the distance of 24,500 km at bit rates of 10 and 20 Gb/s. Investigations have been carried out by varying the chirp factor in the range −1 to 1 and −1 to 0.4] for 10 and 20 Gb/s, respectively, to demonstrate the robustness of the long-haul soliton link. The observations establish that the pulse width (full-width at half-maximum (FWHM)) remains within the optimal range even at the transmission distance of 24,500 km without and at discrete values of the chirp factor.     

Breathing solitons in optical fiber links

We introduce the concept of “breathing” solitons to describe the dynamics of optical pulses in transmission lines with passive compensation of fiber chromatic dispersion. The “breathing” pulse can be used as the information carrier. The theory presented is complimentary to the concept of the guiding-center soliton. It is shown that an average bright soliton can propagate in a system with large variations of the dispersion, including segments with high normal dispersion. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 814–819 (25 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Filter control polarization mode dispersion in dispersion managed soliton systems

In this paper, the dispersion managed soliton (DMS) transmission equation is built on considering the effects of polarization mode dispersion (PMD) and filter control. The DMS transmission of filtering control in constant birefringence fibers is firstly analyzed by varitional method, from which the evolving rules of characteristical DMS parameters are obtained. Secondly, the stability of DMS transmission and its timing jitter are investigated in the random varying birefringence fibers with the conventional model of PMD. The results reveal that filter control DMS system has powerful robustness to PMD effects and DMS's timing jitter can be decreased considerably with the help of filters.     

Polarization Mode Dispersion in High-Speed Optical Communication Systems

Abstract

We review the research progress concerning some fundamental issues related to polarization-mode dispersion (PMD) in high-speed fiber-optic transmission systems. We pay particular attention to issues such as the PMD-induced pulse broadening, PMD measurement and emulation, as well as PMD compensation. An electrical equalization technique based on a transversal filter and an optical technique based on a nonlinear chirped fiber Bragg gratings for PMD compensation will be discussed.     

GHz frequency band soliton generation using integrated ring resonator for WiMAX optical communication

New system of optical soliton signal generation with a high frequency band is presented. Microring resonator can be used to generate soliton signals with high frequency of GHz. These signals can be transmitted via a wireless network system known as WiMAX, which is providing broadband wireless access up to 50 km. The soliton pulses are more stable with less loss during propagation which is good candidate compare to other current optical waves used in optical communication. In this study, soliton pulses with full width at half maximum of 3 MHz and FSR of 85 MHz could be generated using an add/drop filter system which is used to generate high frequency signals, required for wireless network systems. These pulses can be used as carrier signals in order to transmit information codes without significant changes, thus improving transmission quality and delivery of the right information.     

Periodic and Chaotic Exploding Dissipative Solitons

Abstract

This article shows for the first time the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order non-linear and dispersive effects are added to the complex cubic–quintic Ginzburg–Landau equation modeling soliton transmission lines. This counter-intuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations leading to chaos (chaotic explosions). This periodic behavior is persistent even when small amounts of noise are added to the system. Since for ultrashort optical pulses it is necessary to include these higher-order effects, it is conjectured that the predictions can be tested in mode-locked lasers.     

The Statistical Analysis of Polarziation Mode Dispersion and Filter Control on Dispersion Managed Soliton Links

In this paper, the statistical distributing and magnitude of the first and the second-order PMD (polarization mode dispersion) vectors are evaluated and the filters control PMD effects also are analyzed on DMS (dispersion-managed soliton) links. Firstly, the so-called coarse-step approach is applied to the DMS links. The PMD statistical characteristics of the first and the second-order are simulated and the evolutions of energy and mean square of time displacement of DMS two polarization modes are gotten. Secondly, The DMS transmission of filter control with the conventional model of PMD is analyzed by Varitional method, from which the evolving rules of characteristically DMS parameters are obtained and the stability of filter control the DMS transmission are investigated. The results are not only very useful to simplify the measurement of the second-order PMD and instructively reveal degree of PMD effects in DMS systems, but also give that condition of stability of filter control PMD in DMS systems.     

Simulative demonstration of soliton pulse stability over the nonlinear regime in a birefringent optical fiber

In this paper, the results of numerical analysis are demonstrated for sech pulse (soliton) propagation in a birefringent optical fiber using computer modeling and simulation. Here, the initial pulse is polarized linearly and guided into the fiber at an angle of 45° to its polarization axes. The birefringence-induced time delay of 200 and 440 ps between X and Y polarization components has been reported at a fiber length of 631.72 km (10 soliton periods) by considering linear and nonlinear regimes, respectively. The Kerr nonlinearity, which stabilizes solitons against spreading due to GVD, also stabilizes them against splitting due to birefringence. A similar fact is true for the birefringent walk-off. Above a certain soliton order (N_th), the evolution scenario is qualitatively different and two orthogonally polarized components of the soliton move with a common group velocity despite their different modal indices or polarization mode dispersion (PMD) at a fiber length of 631.72 km (10 soliton periods) and 1264.344 km (20 soliton periods) over a nonlinear regime at θ≠45°. The physical effect responsible for this type of behavior is the cross-phase modulation (XPM) between the two polarization components.     

超高偏振模色散光纤中光脉冲传输行为的研究

利用耦合非线性薛定谔方程分析了光脉冲在超高偏振模色散光纤中传输时，偏振模色散引起脉冲分裂。并用基模的两正交偏振分量耦合走离解释了脉冲分裂的成因。利用偏振模色散为237．95ps／km^1/2的光纤进行了实验验证。     

Two-stage optical pulse compression for a mode-locking SOAFL driven by an asymmetric-duty-cycle square wave

We demonstrate ultra-short optical pulses by using a two-stage compression of pulses from a mode-locking SOAFL driven by the injection of a periodic square wave with an asymmetric duty cycle. Through cascading a linear compressor of 110-m dispersion compensation fiber and a soliton compressor of 12-m single-mode fiber, the optical pulses can be shortened to 55 fs with a timing jitter of 0.45 ps. In the ninth-order soliton compression, the spectral linewidth of the mode-locking SOAFL pulses can be broadened by the self-phase-modulation effect. Also, the compression performance includes a time-bandwidth product up to 0.437 and a pulse-compressing ratio of 54.     

Optical Solitons in Fibers for Communication Systems

Abstract

A brief history of attempts to use solitons for optical fiber communications and of the technical developments toward making soliton transmission practical is reviewed. The main problems affecting long-distance soliton transmission, as well as techniques to solve them, are described. Recent developments concerning the use of dispersion management and some of the remarkable properties of dispersion managed solitons are also discussed.     

Nonlinear responses of the periodic structure composed of single negative materials

We investigate the nonlinear responses of the one-dimensional periodic structure containing alternate single negative materials. The transmission property of this nonlinear periodic structure is studied and the bistable behavior is found. Similar as in the linear periodic structure, the transmission property of this nonlinear structure in the zero phase (zero-?) gap region is found to be relatively insensitive to the incident angle from 0° to 30°, in comparison with that in the Bragg gap. Especially, the transmissions associated with the zero-? gap reach the peaks at almost the same input intensity for different incident angles. Another merit of the transmission property in the zero-? gap is that a lower threshold is needed to achieve the bistability than in the Bragg gap. The electric field distribution in the system is further studied. We observe the zero-? gap soliton and compare it with the usual Bragg gap soliton. The differences between these two kinds of solitons are analyzed, and the zero-? gap soliton is shown to be insensitive to the incident angle. In the end, we find that the transmission and the soliton in the zero-? gap are also weakly dependent on the loss and the scaling in contrast to that in the Bragg gap.     

Bit-error rate evaluation for non-linear propagation in optical fibres

The influence of soliton time jitter on the bit-error rate in long-distance single-mode optical fibre transmission lines was studied. It was assumed that mutual interactions between two adjacent solitons were prevented by periodic amplification. It was found that the upper bit rate bound of practically acceptable non-linear transmission is about 50 Gbit s^–1. Above a bit rate of 50 Gbit s^–1 the advantage of non-linear (soliton) transmission, related to dispersion-free linear transmission, disappears.