Cross-phase modulation in fiber links with multiple opticalamplifiers and dispersion compensators

We have theoretically and experimentally investigated the cross-phase modulation (XPM) effect in optical fiber links with multiple optical amplifiers and dispersion compensators. Our theory suggests that the XPM effect can be modeled as a phase modulator with inputs from the intensity of copropagating waves. The frequency response of the phase modulator corresponding to each copropagating wave depends on fiber dispersion, wavelength separation, and fiber length. The total XPM-induced phase shift is the integral of the phase shift contributions from all frequency components of copropagating waves. In nondispersive fibers, XPM is frequency-independent; in dispersive fibers, XPM's frequency response is approximately inversely proportional to the product of frequency, fiber dispersion, and wavelength separation. In an N-segment amplified link, the frequency response of XPM is increased N-fold, but only in very narrow frequency bands. In most other frequency bands, the amount of increase is limited and almost independent of N. However, in an N-segment amplified link with dispersion compensators, the frequency response of XPM is increased N-fold at all frequencies if the dispersion is compensated for within each fiber segment. Thus, the XPM-induced phase shift is smaller in systems employing lumped dispersion compensation than in systems employing distributed dispersion compensation     

Cross-phase modulation in multispan WDM optical fiber systems

The spectral characteristics of cross-phase modulation (XPM) in multispan intensity-modulation direct-detection (IM-DD) optical systems are investigated, both experimentally and theoretically. XPM crosstalk levels and its spectral features are found to be strongly dependent on fiber dispersion and optical signal channel spacing. Interference between XPM-induced crosstalk effects created in different amplified fiber spans is also found to be important to determine the overall frequency response of XPM crosstalk effects. XPM crosstalk between channels with different data rates is evaluated. The crosstalk level between higher and lower bit rate channels is found to be similar to that between two lower bit rate channels. The effect of dispersion compensation on XPM crosstalk in multispan optical systems is discussed and per span dispersion compensation was found to be the most effective way to minimize the effect of XPM crosstalk     

Cross-phase modulation in semiconductor optical amplifier

Cross-phase modulation in a semiconductor optical amplifier is demonstrated by using copropagating pump and probe pulse trains of different wavelengths. The relative time delay between the pump and probe pulses was varied and the effect on the spectral distortion is described.<>     

多信道IM—DD密集波分复用光纤传输系统中的交叉相位调制效应

本文研究了交叉相位调制（XPM）对DWDM数字基带主干传输网性的影响,建立了表征XPM效应对任意调制信号在色散信道中传输的指标损伤的等效系统函数模型,并据此推导出了不同系统参数条件下（基带信号速率,波长信道间隔,复用信道数）计算XPM导致和系统光功率代价的计算公式,通过数值模拟计算证明了在基带信号速率高（＞2.5Gbit/s),波长信道间隔窄（－1nm),复用信道数多（＞8）的条件下XPM效应将成为限制系统性能的主要非线性因素。     

Cross-phase modulation in multispan WDM systems with arbitrary modulation formats

Cross-phase modulation (XPM) is a major performance-limiting effect in high bit-rate wavelength-division-multiplexed (WDM) networks with narrow channel spacing. In this paper, we present closed expressions for fast and accurate calculation of both XPM-induced amplitude and phase distortions of WDM channels. This is of particular importance for network optimization and examination of advanced modulation formats. By comparison with simulations, we demonstrate the wide application range of the novel method.     

Cross-phase modulation induced modulation instability in single-mode optical fibers with saturable nonlinearity

Taking into account the saturable nonlinearity of the single-mode optical fibers, condition and gain spectra of scalar modulation instability induced by cross-phase modulation of two optical waves of different frequencies with the same polarizations are investigated. In both of the normal and anomalous dispersion regions, the contour plots of gain spectra of modulation instability with gray levels, the critical perturbation frequency (or instability domain), and the peak perturbation gain versus the input powers of the two waves are analyzed and discussed. The results show that, the critical perturbation frequency (or instability domain) and the peak perturbation gain increase with the input power, reaching a maximum value, and then decrease. This leads to a unique value of peak perturbation gain and critical perturbation frequency for two different input powers.     

Analysis of the cross-phase modulation in dispersion compensatedWDM optical fiber systems

Wavelength-division-multiplexed (WDM) optical systems are affected by cross-phase modulation (XPM) due to Kerr effect. In this letter, dispersion compensated optical WDM systems affected by XPM are investigated by an analytical model. The theoretical results fit rather well with previous simulations performed in the case of fully compensated and under compensated optical fiber links     

40-Gb/s RZ transmission over a transoceanic distance in a dispersion managed standard fiber using a modified inline synchronous modulation method

This paper analyzes in detail numerically a 40-Gb/s return-to-zero (RZ) transmission system over a transoceanic distance in a strongly dispersion managed line composed of standard single-mode fiber (SMF) and dispersion compensation fiber (DCF). We derived a periodically steady-state pulse (a DM soliton) in a DM line. Since the pulse width of a steady-state pulse is too broad for a 40 Gb/s system, the conventional in-line synchronous modulation technique cannot greatly improve the transmission quality. However, we found that the modified inline synchronous modulation technique, which is reported as the black-box optical regenerator, can effectively extend the transmission distance even in such a strongly DM line. We discuss the mechanism of the modified synchronous modulation technique with respect to a steady-state pulse in a transmission line, and show that a 40-Gb/s RZ signal can be transmitted over 20 000 km.     

Role of intra and interchannel cross-phase modulation in higherorder fiber dispersion management

Nonlinear effects are a major source of impairment in higher order dispersion managed fiber optics links, where both second- and third-order dispersion are compensated over a wide spectral band. We analyze the impact of intrachannel pulse coalescence and interchannel collisions and optimize the span-averaged dispersion in order to reduce cross-phase modulation effects     

Cross-phase modulation in a semiconductor laser amplifierdetermined by a dispersive technique

Cross-phase modulation in a semiconductor laser diode amplifier is reported. A simple expression for the chirp imparted on a weak signal pulse by the action of a strong pump pulse is derived. A novel dispersive technique for characterizing the resulting nonlinear chirp is introduced and used in the present experiment. A maximum frequency excursion of 16 GHz, due to the cross-phase modulation, was measured. A value of 6 was found for α_xpm, which is a factor for characterizing the cross-phase modulation in a similar manner to the conventional linewidth enhancement factor α     

Cross-phase modulation in dispersive fibers: theoretical andexperimental investigation of the impact of modulation frequency

We investigated, theoretically and experimentally, the impact of modulation frequency on cross-phase modulation (XPM) in dispersive fibers. A simple expression for the XPM index has been derived and verified by experiment. The XPM index is found to depend on fiber length, fiber chromatic dispersion, wavelength separation between the signal and the pump, and the intensity modulation frequency. At high modulation frequencies, the XPM index is inversely proportional to the product of the modulation frequency and wavelength separation     

Cross-phase modulation in intensity modulation-direct detection WDMsystems with multiple optical amplifiers and dispersioncompensators

The cross-phase modulation (XPM) effect in intensity modulation-direct-detection (IM)-(DD) optical fiber links with multiple fiber segments with different characteristics and optical amplifiers is investigated theoretically and numerically. A generalized model of the IM induced by an arbitrary number of channels through XPM is derived, compared to simulation results and its validity range is presented. Results show that the XPM-induced IM can be modeled as an intensity modulator driven by the intensity of copropagating waves. The frequency response of the intensity modulator corresponding to each copropagating wave is mainly affected by the walk-off parameter and fiber dispersion. When the walk-off effect is weak the XPM-induced IM is approximately proportional to the square frequency. In single-segment fiber links when the walk-off effect is strong the XPM-induced IM is approximately linearly proportional to the frequency and inversely proportional to the wavelength separation. Both theory and simulation show that the XPM-induced IM in fiber links with multiple optical amplifiers can be enhanced or reduced by properly arranging the dispersion characteristics in each fiber segment. In a nondispersion compensated amplified link and for weak walk-off effect, the total XPM-induced IM increases approximately with the square of the number of fiber segments and of modulation frequency. However, if the dispersion is compensated for within each fiber segment the total XPM-induced IM increases proportionally to the number of fiber segments and to the square frequency. Furthermore, it is shown that in fiber links with a large number of segments placing a single dispersion compensator in the last segment of the link leads to almost the same performance as for non dispersion compensated fiber link and is significantly worse than placing one dispersion compensator in each fiber segment as far as the XPM-induced IM reduction is concerned     

CO-OFDM系统中基于Pilot位置的XPM补偿及优化

研究了相干光正交频分复用(CO-OFDM)系统中基于射频导频(RF-Pilot)的交叉相位调制(XPM)补偿的关键技术,提出了基于Pilot位置的补偿优化方案,通过理论分析得到了最优Pilot位置的选取原则和Q因子分布规律,仿真结果证明了理论分析的正确性.针对7信道CO-OFDM系统,最优和最差Pilot位置处的系统性能相差1.6dB,在实际设计中应根据具体信道配置和该信道上XPM损伤的分布情况来选取最优的Pilot位置,以提升补偿效果和系统性能.     

Simultaneous all-optical demultiplexing and regeneration based onself-phase and cross-phase modulation in a dispersion shifted fiber

Simultaneous demultiplexing and regeneration of 40-Gb/s optical time division multiplexed (OTDM) signal based on self-phase and cross-phase modulation in a dispersion shifted fiber is numerically and experimentally investigated. The optimal walkoff time between the control pulse and OTDM signal is obtained by numerical simulation. Our experiment also shows that it is an effective method for realizing simultaneous demultiplexing and regeneration when used in the middle of a system or in the receiver with a proper walkoff time     

色散管理孤子色散周期长度的极值特性

在色散管理系统中建立了周期扰动模型,研究了它们对孤子传输的影响.数值模拟发现,在脉冲传输距离与扰动周期长度的关系中存在着一种多极值结构.     

Intrachannel four-wave mixing in dispersion managed RZ systems

We model the interaction of three consecutive pulses in a dispersion managed transmission system, and obtain an analytical expression for the energy exchange. The results show that interaction can be suppressed using unequally spaced pulses, which has been verified by the computer simulations. The central pulse pumps energy to the adjacent pulses if the phase shift is zero, and the energy exchange process is reversed if the central pulse has a phase shift of π/2     

Effects of self-phase modulation on sub-500 fs pulse transmissionover dispersion compensated fiber links

The effects of nonlinearity on sub-500 fs pulse transmission over dispersion compensated fiber links using dispersion compensating fiber technique are investigated numerically and experimentally. The pulse broadening and recompression ratio of the 2.5-km transmission link is over 300. The postcompensated and precompensated links are compared when the input pulse energy ranges from 15 to 159 pJ. At high powers, self-phase modulation (SPM) degrades the pulse recompression process and provides an upper bound on the transmitted pulse energy. The SPM effect is stronger in the postcompensated link than in the precompensated link. A dramatic spectral narrowing effect was observed in the postcompensated link. Pulse energies up to tens of pJ, consistent with high quality communication, should be possible for a sub-500 fs pulse in such dispersion compensated links     

Interactions between dispersion managed solitons inoptical-time-division-multiplexed system

Nonlinear interactions between neighboring pulses in optical-time-division-multiplexed (OTDM) systems may cause a timing jitter of the signal pulse, which results in a limitation of the transmission distance and bit-rate. We show that alternating the phases or amplitudes of pulses in the time sequence is effective for reducing the interactions between dispersion managed solitons as in the case of ideal solitons, but only for a relatively weak dispersion management     

Anomalous dispersion in photonic crystal fiber

We describe the measured group-velocity dispersion characteristics of several air-silica photonic crystal fibers with anomalous group-velocity dispersion at visible and near-infrared wavelengths. The values measured over a broad spectral range are compared to those predicted for an isolated strand of silica surrounded by air. We demonstrate a strictly single-mode fiber which has zero dispersion at a wavelength of 700 mm. These fibers are significant for the generation of solitons and supercontinua using ultrashort pulse sources     

Evolution behavior of chirped tan-hyperbolic pulse through single mode fiber in the simultaneous presence of fiber loss,dispersion and self-phase modulation

We present the results of tan-h pulse propagation through single mode fiber in dispersion dominant regime as well as in the simultaneous presence of fiber loss, group velocity dispersion and self-phase modulation. Both un-chirped/chirped cases have been considered. The pulse was propagated using split-step Fourier method based nonlinear Schrödinger equation. Results clearly show that in the absence of fiber nonlinearity, the pulse goes on broadening with the propagated distance. However, in the presence of the fiber nonlinearity, the pulse initially experiences compression and then undergoes broadening at a faster rate. As the value of sharpness parameter increases, the compression also increases. The results of compensation of group velocity dispersion using dispersion compensating fiber considering the setups of pre-, post- and the combination of pre- and post-compensations are also presented. These investigations provide a detailed study and deeper insight about how fiber responses to such type of optical pulses.