Equalization in coherent lightwave systems using a fractionallyspaced equalizer

The performance of a fractionally spaced analog tapped delay line equalizer that has the advantages of being adaptive, being capable of equalizing other linear distortions such as polarization dispersion and nonideal receiver response, and eliminating chromatic dispersion over any distance if a sufficient number of taps are used is discussed. It is shown how this equalizer can be implemented at intermediate frequency and at baseband (for homodyne detection). Results show that an N-tap equalizer increases the maximum bit rate distance approximately (N-1)/twofold (e.g. a threefold increase in distance with a seven-tap equalizer)     

Simultaneous compensation of laser chirp, Kerr effect, anddispersion in 10-Gb/s long-haul transmission systems

The effects of chirp and fiber nonlinearity in a directly modulated 10-Gb/s intensity-modulated direct-detection (IM-DD) fiber transmission system are investigated by simulation, and a simple and flexible technique for compensating these effects is discussed. Self-phase-modulation (SPM) in optical fiber can be equalized by an anomalous dispersion fiber, whereas pulse broadening caused by laser transient chirp can be compensated by normal dispersion. Using these characteristics, laser transient chirp, SPM, and fiber dispersion can be simultaneously compensated by equalizing fibers inserted within certain intervals. Optimum compensation is always realizable for such fixed equalizing fibers, since the magnitude of SPM can be controlled by changing the optical power in the fiber. Simulation suggests that this technique enables 10-Gb/s, 100-km fiber transmission by direct modulation     

Optimal Equalization of Distortions due to Group Delay Ripples of Chirped Fiber Bragg Gratings (CFBG)

We present a closed solution for an optimal equalizer which compensates for signal distortions caused by group delay ripples in chirped fiber Bragg gratings (CFBG) employed for dispersion compensation in optical communication systems. The theory is verified with the help of group delay measurement results of a dispersion compensating CFBG and the improvements achieved by the equalizer are presented on the basis of simulation results.     

Acoustically scanned low-coherence interrogated simultaneousmeasurement of absolute strain and temperature using highly birefringentfibers

We have utilized a traveling acoustic pulse in a two-mode optical fiber to create a moving beam splitter coupling light from LP₀₁ to LP₁₁ mode. As these optical modes have different group velocities, a variable intermodal delay is generated as a function of acoustic pulse position in the fiber. The device can be used as a receiving interferometer in low-coherence interferometry to scan time delay for carrying out fast extended range absolute measurement using simple analog electronic circuits. With this scanning technique we demonstrate measurement of absolute strain over 1600 με in the temperature range from 20 to 60°C with resolutions of the order of 40 με and 0.7°C, respectively, employing highly birefringent fibers as sensing elements     

强双折射光纤中三阶色散对DGD的影响

依据强双折射光纤中两垂直偏振分量所满足的非线性耦合模方程,研究了三阶色散对偏振分量间的时延差的影响。结果表明,当二阶色散、三阶色散同时存在时,三阶色散可以减小时延差;当只有三阶色散时,除了产生较大时延差外,还会在两个偏振脉冲的前后沿产生较大的色散波。     

Theoretical basis of polarization mode dispersion equalization upto the second order

We introduce a theoretical basis of polarization mode dispersion (PMD) equalizers based on the operator representation of PMD using Taylor's expansion. The two types of configuration of PMD equalizers are derived as the inverse of diagonalization operators and delay time difference compensation. One is a type using physical rotation of quarter wave phase plates. The other is a type using variable phase shifters suitable for PLC integration. Waveform comparison algorithm was simulated to show the existence of multiple equivalent optimum points due to the symmetry and periodicity of optical circuits. The second order PMD equalization is discussed briefly on the case of cascading the first and the second PMD equalizing circuits with two different polarization state converters     

Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for Group-velocity dispersion compensation

We demonstrate unrepeated optical transmission of 20-Gb/s quadrature phase-shift-keying (QPSK) signals over a 200-km-long standard single-mode fiber (SMF) without using any optical dispersion compensator. By employing optical homodyne detection, which can restore the entire information of the complex amplitude of the transmitted signal, group-velocity dispersion (GVD) of the SMF can be compensated electrically by a linear equalizer at the receiver. From off-line bit-error-rate measurements, we find that a simple transversal filter implemented in digital signal processing circuits after homodyne detection can effectively cancel the fiber GVD of up to 4000 ps/nm, enabling successful 20-Gb/s QPSK transmission.     

Polarization mode dispersion compensation at 10, 20, and 40 Gb/swith various optical equalizers

Polarization mode dispersion (PMD), especially in “old” fibers, is considered harmful for installation and upgrading of trunk lines. An optical PMD equalizer should have several or many differential group delay (DGD) sections with polarization transformers in between which can endlessly transform any input polarization into a principal state of the following DGD section. The sections must practically have fixed DGDs unless there is only one section. The small-signal baseband transfer function for PMD, higher order PMD, and the necessary number of sections as well as their control by the output signals of an electrical filter bank in the receiver are also discussed in this context. Several PMD equalizers have been realized and successfully tested in transmission systems with bit rates of 10, 20, and 40 Gb/s. The systems operated stably with well-opened eye diagrams for DGDs ranging between 0 and 1.7 bit durations. Best performance is obtained from a distributed PMD equalizer with one piece of polarization-maintaining fiber twisted by 64 stepper motors. The principle can also be realized in LiNbO₃     

The stress-optic effect in optical fibers

The importance of the photoelastic effect in controlling polarization in optical fibers is discussed. Measurements of the stress-optic coefficient, its dispersion, and temperature dependence are reported using a fiber measurement method. The results compare closely to data obtained for bulk silica by an extrapolation technique. It is shown that the dispersion of the stress-optic coefficient can have a significant effect on the performance of birefringent fibers and of fiber birefringent devices. Furthermore, the temperature dependence is sufficiently large to be troublesome in fiber sensors.     

Dynamic PMD Mitigation at 10 Gb/s Using Viterbi Equalization in DPSK Systems

Compensating dynamically changing polarization- mode dispersion (PMD) is important for optical fiber transmission systems. We present simulations of a Viterbi equalization for dynamic PMD mitigation in 10-Gb/s nonreturn-to-zero differential phase-shift keying systems. The equalizer can dynamically track fast varying differential group delay (DGD) and achieve similar performance to static DGD.      

周期线性变化光子晶体用于色散补偿的研究

文章研究了周期线性变化的一维光子晶体的色散补偿特性.根据周期性介质中电磁场在界面处的传递规律,利用传输矩阵方法分析了不同频率的光波在周期线性变化的一维光子晶体中的反射特性,结果表明这种光子晶体对于不同频率的光波成分具有不同的延时,利用这种延时特性,可以制作用于密集波分复用(DWDM)系统的色散补偿器件.     

高速光纤通信系统中高阶PMD补偿技术研究

随着光放大器和色度色散补偿技术的不断提高，光纤的偏振模色散（PMD）已经成为超高速、超长距离光纤通信系统发展的主要障碍，在40Gbit/s或更高速率的光纤通信系统中，PMD的影响已不可忽略，必须考虑PMD的补偿问题，从高阶PMD对40Gbit/s NRZ系统影响的数值模拟发现，当光纤中PMD高阶效应比较明显时，将严重劣化一阶PMD补偿的效果，另外，通过对两种高阶PMD补偿器的比较介绍，认为两段级联的高队PMD补偿系统是一种比较现实的补偿方法。     

Statistical properties of the DGD in a long-haul optical fiber system with temporally drifting birefringence

Due to the temporal drift of the fiber birefringence in an optical fiber transmission system, the polarization mode dispersion (PMD) effects measured in a time window can be quite different for different time windows of the same duration. Every 10 s for 10 days, the accumulated differential group delay (DGD) was repeatedly measured at 5000 km in a 107-km recirculating loop with loop-synchronous polarization scrambling. In each DGD measurement, the polarization dispersion vector of the 107-km-long fiber was also measured. To model the measured temporal variation of the DGD, two different perturbation algorithms were used to construct random walks through the configuration space of birefringent fibers, where each fiber realization is determined by the standard coarse-step method. With these simulation models, the statistical properties of the spread of the DGD samples over a finite time period were reproduced.     

Design of a transversal equalizer for electronic dispersion compensation in optical communication links

A programmable transversal equalizer for electronic dispersion compensation(EDC) in optical fiber communication systems is developed.Based on the SiGe technology with a cut-off frequency of 80 GHz,the equalizer consists of 6 seriesparallel amplifiers as delay units and 7 Gilbert variable gain amplifiers as taps,which ensure that the equalizer can work at the bit rate of 10 Gb/s.With different tap gains,the forward voltage gain of the transversal equalizer varies,which demonstrates that the equalizer has various filtering characteristics such as low pass filtering,band pass filtering,band reject filtering,and notch filtering,so it can effectively simulate the inverse transfer function of dispersive channels in optical communications,and can be used for compensating the inter-symbol interference and other nonlinear problems caused by dispersion.The equalizer(including pads) occupies an area of 0.40 mm × 1.08 mm,and its total power dissipation is 400 mW with 3.3 V power supply.     

Fast Characterization of Dispersion and Dispersion Slope of Optical Fiber Links Using Spectral Interferometry With Frequency Combs

We demonstrate fast characterization ( $sim$1.4 $mu hbox{s}$) of both the dispersion and dispersion slope of long optical fiber links ( $sim$25 km) using dual quadrature spectral interferometry with an optical frequency comb. Compared to previous spectral interferometry experiments limited to fiber lengths of meters, the long coherence length and the periodic delay properties of frequency combs, coupled with fast data acquisition, enable spectral interferometric characterization of fibers longer by several orders of magnitude. We expect that our method will be useful to recently proposed lightwave techniques like coherent wavelength-division multiplexing and to coherent modulation formats by providing a real-time monitoring capability for the link dispersion. Another area of application would be in stabilization of systems which perform frequency and timing distribution over long fiber links using stabilized optical frequency combs.      

Dispersion slope equalizer for dispersion shifted fiber using alattice-form programmable optical filter on a planar lightwave circuit

This paper reports an integrated-optic dispersion slope (third-order dispersion) equalizer for dispersion shifted fiber which employs a lattice-form programmable optical filter on a planar lightwave circuit (PLC). This dispersion slope equalizer consists of nine symmetrical interferometers interleaved with eight asymmetrical interferometers. The performance of the equalizer is evaluated numerically. We confirm experimentally that this equalizer is effective in reducing the pulse waveform deterioration caused by the dispersion slope. In addition, the equalizer improves the power penalty of a 200-Gb/s, 100-km, time-division multiplexed optical transmission experiment     

单轴晶体双折射滤光片特性研究

本文研究了由单轴双折射晶体波片（光轴平行波片表面）和理想线偏振片组成的双折射滤光片倾斜旋转时的透过率,群延迟和二阶、三阶色散特性。推导出了双折射滤光片的透过率,群延迟表达式,给出了透过率、群延迟和二阶色散随光线入射角和光轴旋转角变化的等高线图,并对透过率的等高线图作了实验验证,取得了很好的一致性。群延迟和二阶色散的等高线图对双折射滤光片的优化设计和实际应用具有理论指导意义。     

Electrical Mitigation of Penalties Caused by Group Delay Ripples for Different Modulation Formats

Electrical equalizers are proposed to mitigate the distortions caused by group delay ripples (GDRs) of cascaded optical filters (e.g., fiber Bragg gratings for chromatic dispersion (CD) compensation). Different electrical equalizers including feedforward equalizer (FFE), decision-feedback equalizer (DFE), nonlinear FFE-DFE, and maximum-likelihood sequence estimator are investigated and compared comprehensively for four different modulation formats: ON-OFF keying, optical duobinary, optical single sideband, and differential phase-shift keying. Especially, we find that the relationship of electrical equalization performance on the modulation format is very similar for the mitigation of GDR and CD.     

Optical PSK synchronous heterodyne detection transmissionexperiment using fiber chromatic dispersion equalization

This letter demonstrates an 8-Gb/s optical PSK (phase shift keying) synchronous detection transmission experiment using external cavity laser diodes. A 188-km 1.3-μm zero-dispersion fiber is used as the transmission medium at the wavelength of 1.55 μm. Fiber chromatic dispersion is successfully compensated with a microstrip-line delay equalizer     

Transmission limitations due to self-phase modulation in opticalPSK heterodyne detection systems employing chromatic dispersionequalization

Even if the amplitude of a phase-modulated optical signal is constant before transmission, amplitude modulation is caused by fiber chromatic dispersion. As a result, self-phase modulation (SPM) is induced. In optical heterodyne detection, SPM cannot be compensated for by the delay equalizer (electrical domain) used to compensate fiber chromatic dispersion. However, the transmission distance limitation of multi-repeatered coherent transmission systems has not been investigated in the presence of SPM. This paper theoretically and experimentally investigates the transmission distance achievable with a phase-shift-keying (PSK) heterodyne detection system employing in-line optical amplifiers and delay equalization. The calculated results show that equalization is effective when γP₀/2B²|β₂|<10 in the normal dispersion regime, and γP₀/2B²|β ₂|<15 in the anomalous dispersion regime. Furthermore, the increase in transmission distance achieved by using equalization is experimentally shown in an 8 Gb/s PSK heterodyne transmission experiment using a conventional single-mode (SM) fiber and in-line fiber amplifiers