Wiener solution of electrical equalizer coefficients in lightwave systems

Electrical dispersion compensation equalizer is a key and cost-effective element in optical communication on-off-keying systems in the presence of chromatic dispersion. Here, for the first time, to the best of the authors? knowledge, an analytical solution is established for the electrical equalizer coefficients in an optical communication system. The solution is based on minimum mean-square error criterion. The analytical results show a perfect match with computer simulation. In addition BER performance comparison with the adaptive least mean square (LMS) method reveals that the analytical solution performs better due to LMS excess mean-square error.     

Jitter in fibre- based soliton transmission systems

High bit rate long-haul transmission systems on optical fibres are mainly limited by the Kerr effect. Solitons, that balance exactly the Kerr effect by the chromatic dispersion are thus the optimal pulses for fibre transmission. However, the chromatic dispersion associated to the amplifier noise is responsible for a large jitter at receiver end. A calculation of the jitter variance and statistics is presented in this paper. Soliton control techniques can reduce efficiently the jitter variance but they are shown to strongly affect the statistics. It is finally demonstrated that the whole jitter statistics is needed to correctly characterize the soliton transmission system performance.     

First-order PMD compensation in nonlinearly dispersive opticalcommunication systems via transmission over the principal states ofpolarization

Soliton propagation in the presence of polarization mode dispersion (PMD) is studied with an analytical approach. It is shown that there exist two peculiar initial states of polarization that may prevent the soliton to undergo shape distortions. These states coincide with the states that, in the absence of chromatic dispersion and nonlinearity, are usually referred to as principal states of polarization. This fact is used to show that it is possible to improve the performance of an optical transmission system operating in the presence of chromatic dispersion, PMD and Kerr nonlinearity by coupling the input pulses to one of the principal states of polarization     

Determination of Achievable Information Rates (AIRs) of IM/DD Systems and AIR Loss Due to Chromatic Dispersion and Quantization

The achievable information rates (AIRs) of a nonreturn-to-zero optical transmission system operating at 10Gb/s are determined based on experimentally obtained conditional probability density functions for an amplified spontaneous emission noise-dominated system in the presence of chromatic dispersion (with and without optical dispersion compensation). Specifically, we concentrate on the AIR loss due to the accumulation of chromatic dispersion, as well as the practical constraint of the analog-to-digital conversion and quantization of log-likelihood ratios     

光纤OFDM系统中的色散补偿技术研究

为了减小光纤的色度色散对光纤正交频分复用（OFDM）系统性能的影响,提出了将无线通信中的信道估计器引入光纤OFDM系统进行信道估计的色散补偿方法。在理论上分析了光纤的色度色散对于传输OFDM信号的影响,并在实验中采用梳状导频的形式,在每个OFDM码元的特定的子载波上插入导频,在接收端通过基于最小平方（LS）原则的LS估计器进行信道估计,得到了OFDM光纤传输的信道幅度响应和相位响应,通过使用LS估计器,直接调制的光OFDM信号在单模光纤中传输200km,误比特率低于10-6 ,功率代价小于2dB。结果表明,高频子载波较低频子载波更容易受到色散的影响,在光纤OFDM系统中引入信道估计器进行信道估计能够有效补偿由色度色散带来的相位偏移和幅度衰减。     

888nm半导体抽运的60W皮秒激光振荡器模型

为了建立一个基于888nm半导体抽运的高平均功率和高效率皮秒激光振荡器的理论模型,采用模拟计算方法和谐振腔理论、ABCD定律、自洽条件以及连续被动锁模条件,利用激光晶体Nd:YVO4对波长888nm半导体抽运源的吸收特性和元件的相关参量、合适的腔模参量、实现稳定锁模的参量进行了理论分析和计算,并通过以上研究和模拟计算得到了皮秒振荡器模型的相关数据。结果表明,在120W的抽运功率下,激光器可以输出约61.5W的皮秒激光,光光转换效率51.3%。这一理论模型的建立对高平均功率和高效率皮秒激光振荡器的实验研究起着指导作用。     

On the Decision-Feedback Equalizer in Optically Amplified Direct-Detection Systems

This paper investigates the combined feed-forward and decision-feedback equalizer (DFE) in a lightwave system with optical amplifiers and a direct-detection receiver. Based on a nonlinear channel model, the paper provides a modification of the classical minimum mean square error theory of the DFE. Furthermore, an analytical method that is capable of accurate bit error rate (BER) evaluation is used to optimize the DFE for minimum BER. The paper evaluates the DFE performance for both optical ON-OFF keying and duobinary modulation formats in the presence of chromatic dispersion as well as the DFE performance for the mitigation of higher order polarization mode dispersion in first-order compensated systems. The paper shows that the DFE can compensate for the BER degradation due to narrow-band receiver-side optical filtering and can significantly improve the spectral efficiency of dense wavelength-division multiplexed systems.     

High-Resolution Optical Sampling of 640-Gb/s Data Using Four-Wave Mixing in Dispersion-Engineered Highly Nonlinear As$_2$S $_3$ Planar Waveguides

We present the first demonstration of an optical sampling system, using the optical Kerr effect in a chip-scale device, enabling combined capability for femtosecond resolution and broadband signal wavelength tunability. A temporal resolution ${ ≪ }500$ fs is achieved using four-wave mixing in a 7-cm-short chalcogenide planar waveguide. The use of a short length, dispersion-shifted waveguide with ultrahigh nonlinearity ($10^4;{rm W}^{-1}{cdot}{rm{km}}^{-1}$) enables high-resolution optical sampling without the detrimental effect of chromatic dispersion on the temporal distortion of the signal and sampling pulses, as well as their phase mismatch. Using the device, we successfully monitor a 640-Gb/s optical time-division multiplexing (OTDM) datastream, showcasing its potential for integrated chip-based monitoring of signals at bitrates approaching and beyond Tb/s. We discuss fundamental limitations and potential improvements.      

Comparison of the performance of optically amplified transmissionsystems

In this paper, we show a comparison among the performance of single- and multichannel optical systems considering NRZ and soliton signals. The results have been obtained by means of numerical simulations, taking into consideration the chromatic dispersion, the Kerr nonlinearity, the fiber loss, and the ASE noise of the optical amplifiers. The performance of IM-DD and coherent asynchronous ASK systems have been evaluated in terms of the Q factor. We have considered the propagation in links encompassing conventional step-index fibers, DS fibers and in links with two different dispersion management techniques in which the chromatic dispersion is varied along the propagation distance both in randomly and in deterministically way. The effects of the in-line filtering process are mainly investigated in soliton propagation     

Performance evaluation of very long span direct detection intensityand polarization modulated systems

In this paper long distances very high capacity NRZ optical transmission systems adopting direct detection are considered in links with a low average chromatic dispersion. Particular attention is devoted to polarization modulated (PM-DD) systems. Polarization modulated systems results to he more degraded with respect to intensity modulated (IM-DD) systems by the light depolarization induced by the interplay among the Kerr effect, the ASE noise of the optical amplifiers and the polarization mode dispersion. The light depolarization is particularly strong in conditions of large spectral broadening that are met when the chromatic dispersion value is maintained very low along the link. On the other hand the use of a fluctuating chromatic dispersion with a mean value equal to zero, whereas the local dispersion is different from zero, shows the double advantage to reduce the chromatic dispersion impairments and to limit the spectral broadening. The advantages offered by this dispersion management technique have been already shown in several experiments for IM-DD systems: in this work we show that this technique is very important also for PM-DD systems since the limitation in the spectral broadening reduces the light depolarization. We show that adopting a suitable dispersion management and an opportune preamplifier optical filter transmissions at 5 Gb/s can be attained in transoceanic links by means of FM-DD systems     

Change of field spectrum of signal light due to fibre nonlinearities and chromatic dispersion in long-haul coherent systems using in-line optical amplifiers

The change of a field spectrum of signal light in long-haul coherent optical fibre communication systems using in-line amplifiers is measured in the normal and anomalous dispersion regions of a fibre. Results show that the interplay of nonlinear Kerr effect and fibre chromatic dispersion cause a fatal change in the field spectrum in the anomalous dispersion region.<>     

色散管理传输系统中克尔效应对偏振模色散的补偿研究

光纤的随机双折射效应可导致脉冲无规展宽即偏振模色散(PMD)。在零路径色散管理孤子传输系统中，二阶色散和三阶色散效应均被完全补偿，克尔效应成为一种有害因素会使脉冲变窄，但是当光纤的随机双折射被考虑时，克尔效应正好与PMD相互抵消，使光脉冲准稳定传输，不同的光纤偏振模色散参数分别对应不同的最佳系统功率。此外，如果考虑不同偏振方向的损耗差异，则即使在最佳匹配条件下，微小的偏振损耗差异也可产生很大的脉宽波动。因此，偏振相关损耗是影响脉冲传输质量的相当重要的因素，不论在理论计算还是在工程设计中都应当认真考虑。     

Performance characterization of a closed-loop chaotic communication system including fiber transmission in dispersion shifted fibers

The transmission performance of an all-optical closed-loop chaotic communication system is numerically studied, assuming various span lengths of dispersion shifted fiber between transmitter and receiver. Calculation of the mean synchronization error and Q-factor values obtained from the corresponding eye diagrams has been carried out for two encoding methods (chaotic modulation and chaos shift keying) and two repetition rates (2.4 and 5 Gbps). It is shown that transmission impairments including chromatic dispersion, fiber nonlinearity, fiber losses, and amplified spontaneous emission noise of the inline amplifiers degrade significantly the synchronization quality especially when high-bit-rate message encoding is applied. The influence of key system parameters such as launched optical power, amplifier spacing, positive or negative dispersion, etc., to the transmission performance has been investigated. Acceptable system performance can be achieved for approximately 200 km at 2.4 Gbps.     

Estimated performance of 2.488 Gb/s CPFSK optical non-repeateredtransmission system employing high-output power EDFA boosters

The configuration of a practical nonrepeatered coherent optical transmission system and its performance are reported. The practicability of combining continuous-phase frequency-shift keying (CPFSK) with erbium-doped fiber amplifier (EDFA) boosters is verified by laboratory and field experiments. A system gain of 60.8 dB is achieved at a BER at 10^-11; the EDFA's optical output power is +18 dBm and the receiver sensitivity is -42.8 dBm. The stimulated Brillouin scattering (SBS) effect is examined to estimate the dependence of error rate characteristics on the bit sequence length. No power penalty is observed for a pseudorandom bit sequence (PRBS) of more than 2⁵-1 or STM-16 patterns containing a 30-byte block of consecutive identical digits. The power penalty of 1.3 dB caused by the 310-km non-dispersion-shifted transmission fiber is successfully compensated by installing a chromatic dispersion compensator in each orthogonal polarization branch. During a four month field experiment, error-free operation was observed over a 30 day period, and the long-term error rate is under 6×10^-16     

12300 ps/nm, 2.4 Gb/s nonregenerative optical fiber transmissionexperiment and effect of transmitter phase noise

A nonregenerative optical transmission experiment with a chromatic dispersion of more than 10000 ps/nm is reported. Externally intensity-modulated 2.4 Gb/s optical signals were transmitted over 710 km of nondispersion-shifted optical fiber using ten Er-doped fiber amplifiers with a total net optical gain of 125 dB. Although the total chromatic dispersion amounted to 12300 ps/nm, the power penalty observed was as small as 0.5 dB, and an error floor was not observed. The effect of transmitter phase noise associated with fiber chromatic dispersion was experimentally investigated     

Electrical Dispersion Compensation Equalizers in Optical Direct- and Coherent-Detection Systems

We study the performances of several electrical dispersion compensation (EDC) equalizers in the presence of chromatic dispersion (CD) and polarization mode dispersion (PMD) for optical coherent and direct detection on-off keying systems. The EDCs that are analyzed include the decision-feedback equalizer, linear equalizer, and maximum-likelihood sequence estimator (MLSE). We present an inclusive quantitative analysis of the performance difference between the various techniques. The MLSE gives a good indication of the best possible performance     

Generation of optical phase-conjugate waves and compensation forpulse shape distortion in a single-mode fiber

The generation of optical phase-conjugate waves and the application of optical phase conjugation (OPC) to optical communication systems is described. The method of pulse shape distortion compensation by OPC is outlined including distortion due to both fiber dispersion and the optical Kerr effect. The generation of a forward-going phase-conjugate wave in a third-order nonlinear medium is discussed and that by a nondegenerate forward four-wave mixing in a zero-dispersion single-mode fiber (SMF) is investigated. Suppressing the stimulated Brillouin scattering (SBS) of a pump wave in the fiber prevents saturation of the generation efficiency of the phase-conjugate wave even when the pump power exceeds the SBS threshold. In transmission experiments through a 200-km standard SMF with a 16-Gb/s intensity-modulated signal and a 5-Gb/s continuous-phase FSK (CPFSK) modulated signal, it is shown the applicability of OPC is modulation independent and that OPC effectively compensates for both chromatic dispersion and the optical Kerr effect     

Network cost impact of solutions for mitigating optical impairments: comparison of methods, techniques, and practical deployments constraints

Based on the simulations of realistic network conditions, this paper analyzes the network-cost dependence of the following parameters: the reach, the presence of optical add-drop multiplexers (OADMs) and branching nodes, and the chromatic dispersion. Trends and guidelines for the determination of the best match between system specifications and optimum network cost are proposed. The performance and cost impact of electrical and optical methods are critically analyzed.     

Ultrafast all-optical switching utilizing the optical Kerr effectin polarization-maintaining single-mode fibers

An ultrafast all-optical switching scheme utilizing the optical Kerr effect in two birefringent fibers concatenated with each fast axis crossed is proposed. Stable optical Kerr modulation and all-optical demultiplexing of an ultrashort (30 p.s.) optical pulse train at 1.97 GHz from a gain-switched distributed-feedback laser diode (DFB LD) have been sufficiently demonstrated using CW mode-locking Nd:YAG laser pulses as a pump. Switching speed and required pump powers are studied in terms of fiber bandwidth due to fiber birefringence, and combined effects of chromatic and polarization dispersions on Kerr modulation profiles. By utilizing the optical Kerr modulation properties in the presence of dispersions, the nondiagonal yx component of the nonlinear refractive index is also determined to be 0.34 relative to the diagonal component xx. The intrinsic stability and ultimate switching capabilities are discussed     

Effect of the cross-phase modulation on WDM optical systems:analysis of fiber propagation

In wavelength-division-multiplexed (WDM) optical systems, cross-phase modulation induced by Kerr effect gives rise to nonlinear phase modulation of each channel, which depends on the overall power in all the other channels. In this letter, the fiber propagation of WDM optical signals affected by cross-phase modulation is analyzed. In particular, the effect due to fiber chromatic dispersion is evaluated after that cross-phase modulation has arisen and stabilized