Rigorous assessment of small-signal analysis for linear anddispersive optical communication systems operating near zero-dispersionwavelength

This paper presents a rigorous small-signal theory for linear single-mode fibers taking into account the first- and second-order fiber dispersion. From this theory, exact small signal intensity modulation (IM) and frequency modulation (FM) fiber transfer functions are presented. Exact expressions of the intensity and frequency noise spectra at fiber output due to laser noise taking into account all Langevin noise terms are also derived. Accurate numerical simulations of the IM and FM fiber transfer functions, and intensity and frequency noise spectra after linear transmission along single-mode fiber are compared with theoretical predictions and very good agreement is achieved. In addition, the theoretical predictions are compared with other author's results and the discrepancies are thoroughly explained. A new expression for the transmission distance which can lead to further significant reduction of intensity noise spectrum in systems using single-mode lasers with reduced linewidth enhancement factor is presented. The theoretical and simulation results show that the magnitude of the small-signal IM and FM fiber transfer functions, and the intensity and frequency noise spectra after linear single-mode fiber transmission are not affected by second-order fiber dispersion. The theory indicates that second-order fiber dispersion solely introduces delay distortion in the IM and PM fiber transfer functions. So, with linear transmission second-order dispersion effects on the intensity and frequency noise have proved to be irrelevant even for very long broad-band fiber systems     

Exact compensation for both chromatic dispersion and Kerr effect ina transmission fiber using optical phase conjugation

We propose a new method to compensate exactly for both chromatic dispersion and self-phase modulation in a transmission fiber, where the light intensity changes due to fiber loss and amplifier gain. This method utilizes optical phase conjugation (OPC). The pulse shape is precompensated before OPC by transmission through a fiber with large dispersion. A computer simulation demonstrates effective compensation for waveform distortion in a 40 Gb/s NRZ intensity-modulated light transmission     

Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection

The spectrum of an intensity modulated (IM) and a combined intensity-frequency modulated (IM-FM) monochromatic light source has been generated. The amplitudes of the modulated carrier and the first three pairs of sidebands are plotted showing the influence of IM on an FM signal. The effects of first order chromatic dispersion on the baseband amplitude response and harmonic distortion are determined. The manner in which modulation type and depth, modulating frequency, wavelength, and fiber length alter harmonic distortion is presented. Numerical examples giving the amplitude response of a single-mode fiber system as well as the magnitude of the second- and third-harmonic distortion caused by chromatic dispersion are presented. Based on this material, the limits placed on analog transmission due to chromatic dispersion may be assessed.     

FM subcarrier fiber optical transmission system design and itsapplication in next-generation wireless access

This paper presents a design method of optical frequency modulation (FM) subcarrier (with super carrier) transmission modem. The nonideal link characteristics, including laser chirping, fiber dispersion, voltage controlled oscillator (VCO) phase noise, relative intensity noise (RIN), and equivalent network model of laser diode of such a system that may bring about signal distortion are discussed first. We then propose a hierarchical methods to establish the system equivalent model. Finally this FM modem is applied to a GSM wireless system, in which multichannel signals are transmitted over fiber between radio port and basestation, and system performance is appraised by its dynamic range. It is found that optical FM subcarrier (with super carrier) transmission technique can improve the system dynamic range, compared with the intensity modulated direct detection (IMDD) method, and this is a economical and efficient method     

Long-haul WDM transmission using higher order fiber dispersionmanagement

We propose a fiber dispersion management scheme for large-capacity long-haul wavelength division multiplexing (WDM) transmission systems that considers not only second- but also third-order dispersion characteristics using transmission fibers with opposite dispersion signs. It eliminates the waveform distortion of WDM signals that originates from the existence of third-order dispersion, which is a constraint placed on WDM capacity in conventional dispersion management, while reducing the interchannel interaction caused by the interplay of fiber nonlinearity and second-order dispersion. Design concept of the scheme is discussed to show the feasibility of using actual fiber parameters. An experimental investigation on transmission performance regarding the signal pulse format, nonreturn-to-zero (NRZ) and return-to-zero (RZ), and interchannel interaction caused by four-wave mixing (FWM) and cross-phase modulation (XPM) is described for optimizing WDM system performance. It is experimentally shown that RZ pulse transmission is possible without significant spectral broadening over a wide wavelength range in dispersion managed fiber spans. Using these results together with a wideband optical amplifier gain-bandwidth management technique, yields long-distance WDM transmission with the capacity of 25×10 Gb/s over 9288 km     

自陡峭效应对相位共轭系统脉冲传输的影响

光学相位共轭(OPC)技术能够同时且高效地补偿光纤传输过程中色散及非线性效应所导致的信号失真，且该技术同脉冲调制方式无关。从理论上分析了在自陡峭效应(SS)作用下高斯脉冲信号在中距相位共轭系统中的传输演化特性，数值模拟了在其作用下超短飞秒高斯脉冲的动态传输过程，讨论了自陡峭效应对中距相位共轭系统复原性能的影响。结果表明自陡峭效应将导致高斯脉冲信号发生峰值漂移和脉冲后沿变陡，相位共轭系统不能补偿由此导致的脉冲失真和畸变。引入合适的色散可以减小这种信号失真，并使得相位共轭系统能够同时补偿由于色散、自相位调制和自陡峭效应而引起的信号失真。     

Nonlinearly strain-chirped fiber Bragg grating with an adjustabledispersion slope

In this letter, we demonstrate an adjustable dispersion slope compensator for waveform distortion compensation based on a nonlinearly strain-chirped fiber Bragg grating. The dispersion slope of the device can be tuned up to -18.9 ps/nm² with a bandwidth >2.4 nm. After transmission through a 120-km-long dispersion-shifted fiber, the resulting waveform distortion for a 2.65-ps pulse is successfully compensated by using this device     

色散对光纤中高斯光脉冲传播特性的影响

从麦克斯韦方程组出发,建立了光脉冲在光纤中传播的理论模型。在只考虑色散效应的情况下,对该理论模型进行进一步的研究,数值模拟出高斯光脉冲在光纤中的传输状态,并讨论了色散对光脉冲传播特性的影响。结果表明,群速度色散会增加光脉冲的宽度而波形保持不变;三阶色散会引起光脉冲的畸变。该结论对光纤的色散补偿具有一定的理论参考价值。     

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     

光纤通信系统中色散补偿的研究

本文从光纤色散和啁啾光栅所提供的延时两方面对光通信系统中的色散补偿进行了分析，表明每隔放大器的中继距离插入一啁啾光栅进行色散补偿可实现信号无失真传输，在此基础上提出了在中继器中同时实现全光信号放大和色散补偿的光纤通信系统方案。     

Performance of smart lightwave receivers with linear equalization

Signal processing techniques can be used to reduce linear and nonlinear distortion in high-speed lightwave systems caused by fiber dispersion and nonideal responses of optoelectronic and electronic components. The improvement in the performance of 2.5 and 10 Gb/s intensity modulation, direct detection systems is assessed for receivers which utilize an analog taped delay line equalizer to compensate for signal distortion. Synchronous and fractionally spaced equalizers are evaluated. Smart receivers that jointly optimize the decision time, decision threshold, and equalizer tap weights under a minimum bit error ration criterion are considered. This yields the optimum system performance and allows consideration of both reduced distortion and enhanced noise arising from the signal processing. The effectiveness of the equalization is determined as a function of several important system parameters. Three-tap and five-tap synchronous equalizers yield virtually the same improvement in receiver sensitivity. Depending on the system, a five-tap fractionally spaced equalizer with half-bit-period tap spacing may or may not be significantly more effective than a three-tap synchronous equalizer     

Impact of Optical Transmission on Multiband OFDM Ultra-Wideband Wireless System With Fiber Distribution

Multiband (MB) orthogonal frequency-division multiplexing (OFDM) ultra-wideband (UWB) wireless, which provides high data rate access, is required to be distributed by using optical fiber. The performance of MB-OFDM UWB over fiber transmission system is investigated considering optical modulation and demodulation impact. Theoretical analysis of the effect of fiber dispersion, optical transmitter, and optical receiver response on system performance is carried out considering amplitude and phase distortion. Experiments are conducted and verified by our theoretical analysis and good agreement is obtained. It is found that RF modulation index of $sim {hbox {4}}%$ is optimum for optical transmitter with Mach–Zehnder modulator, and optical receiver with Chebyshev-II response is the best for MB-OFDM UWB over fiber. Compared to back-to-back UWB over fiber, optical transmission is mainly limited by laser phase noise converted relative intensity noise and phase distortion induced by fiber dispersion when optimum modulation index is used. Higher modulation index is limited by amplitude and phase distortion to OFDM signal induced by optical transmitter and receiver response nonlinearities and fiber dispersion and the spectral mask. It is also found that highly received optical power is required for transmission of MB-OFDM UWB signal over fiber.      

模间色散为零的双芯光子晶体光纤

设计一种在短波长处可以实现零模间色散的双芯光子晶体光纤,该光纤的包层气孔直径具有渐变结构。利用全矢量有限元法进行分析,得到光纤耦合系数、模间色散及走离距离特性随传输频率和结构参数的变化曲线。数值分析结果表明,可以通过调节双芯间小孔的直径,灵活控制耦合系数的变化。在特定的传输频率处,模间色散存在过零点。且双芯间小孔的直径越大,模间色散过零点所在的传输频率越低。当模间色散为零时,可以完全消除模式间相位不匹配导致的脉冲失真,从而实现能量的完全交换。     

Computationally Efficient Nonlinearity Compensation for Coherent Fiber-Optic Systems

Split-step digital backward propagation (DBP) can be combined with coherent detection to compensate for fiber nonlinear impairments.A large number of DBP steps is usually needed for a long-haul fiber system,and this creates a heavy computational load.In a trade-off between complexity and performance,interchannel nonlinearity can be disregarded in order to simplify the DBP algorithm.The number of steps can also be reduced at the expense of performance.In periodic dispersion-managed long-haul transmission systems,optical waveform distortion is dominated by chromatic dispersion.As a result,the nonlinearity of the optical signal repeats in every dispersion period.Because of this periodic behavior,DBP of many fiber spans can be folded into one span.Using this distance-folded DBP method,the required computation for a transoceanic transmission system with full inline dispersion compensation can be reduced by up to two orders of magnitude with negligible penalty.The folded DBP method can be modified to compensate for nonlinearity in fiber links with non-zero residual dispersion per span.     

Three-level modulation scheme on standard fibers to extend thedispersion limit

Numerical simulations show that the impact of the pulse shape on the power penalty in intensity modulated systems with standard, nonlinear fibers is decisive. This can be used to define a three-level modulation scheme that makes use of the interaction between fiber dispersion and fiber nonlinearities. By adjusting the pulse shape and peak power in a three-level modulation scheme, the standard dispersion limit of 65 km at 10 Gb/s can be extended to 170 km. The control of the pulse shape can be accomplished in the electrical domain, and therefore the effects of fiber dispersion can be compensated electrically. This is very advantageous compared with dispersion compensation schemes in the optical domain     

Design of Dispersion Compensation and Nonlinear Distortion Self-compensation in Co-network Transmission Systems

Dispersion and nonlinear distortion have an effect on transmission performances of optical fiber transimission systems,The schemes of dispersion compensation and nonlinear distortion self-compensation in telecom-CATV co-network transmission systems are reported,followed by investigation on (1) the impact of dispersion compensation fiber (DCF) on fiber nonlinear effects with a cascade of erbium-doped fiber amplifiers (EDFAs) and different dispersion compensation schemes,(2) the impact of the complex on the total nonlinear distortion induced by EDFA gain tilt and the light source.As a result,dispersion compensation optimal scheme and EDFA negative gain tilt are suggested as a solution to dispersion compensation optimal scheme and EDFA negative gain tilt are suggested as a solution to dispersion compensation and the nonlinear distortion self-compensation.     

Effects of nonlinear dispersion in EDFA's on optical communicationsystems

The signal-induced change of the refractive index in an erbium-doped fiber amplifier (EDFA) causes a phase modulation imposed on a signal when passing the EDFA. In this paper, we apply our extended EDFA model on an optical communication system. The model includes this phase modulation, by including the nonlinear dispersion in an EDFA, and the spontaneous emission noise. The influence of these effects on an optical communication system is examined by means of Q-factor and eye diagram. We assume an intensity modulated-direct detection (IM-DD) system operating at 193 THz (1552.5 nm) with a bit rate of 10 Gb/s in the anomalous dispersion regime and a total fiber length of 500 km. The fibers are assumed to be dispersion shifted ones, EDFAs are used to compensate for the fiber loss. By numerical simulation we obtain results for the influence of the phase modulation (nonlinear dispersion) due to the signal induced change of the refractive index in an EDFA and the spontaneous emission noise at different input peak powers. Neglecting the signal-induced change of the refractive index strongly underestimates the Q-factor in the anomalous dispersion regime. Therefore it should be included for reliable system simulations. This can be done with the numerical model presented here     

零模间色散双空芯光子晶体光纤

分析了双空芯光子晶体光纤(HC-PCF)在纤芯填充液态高折射率温敏物质后的传输特性,应用全矢量有限元法(FEM)研究温度均匀变化时光纤耦合特性、模间色散特性的变化规律。结果表明,在特定温度下,耦合特性随传输波长的增大呈现出先减弱、后增强的变化趋势,且光纤的模间色散存在过零点。通过调节温度或占空比,可以在1.31μm和1.55μm两个常用通信波段内实现零模间色散传输,由此能够完全消除模式间相位不匹配导致的脉冲失真,实现能量的完全交换。     

On the joint effects of fiber parametric gain and birefringence andtheir influence on ASE noise

Parametric gain (PG) in optical fibers may substantially enhance amplified spontaneous emission (ASE) noise, especially in long-haul amplified links. We present new results that permit to accurately characterize the effects of PG on ASE noise, as well as the interplay of PG and ASE noise with fiber dispersion in both the anomalous and normal dispersion regions. In a recent letter, we introduced the concept of a PG transfer matrix, that allows the easy evaluation of ASE noise enhancement over chains of amplified fiber spans. In the same letter we showed that the transfer matrix can be expressed in analytical closed-form when a scalar (single polarization) fiber is assumed. In this paper we extend the analysis to a more realistic two-polarization fiber model that accounts for both linear and nonlinear polarization coupling effects. We show that the new transfer matrix does not have an analytical expression, but can be easily evaluated using standard numerical algorithms. ASE noise enhancement due to PG turns out to be slightly lower in a realistic birefringent two-polarization fiber than a single-polarization fiber. An interesting result is that the single polarization model yields a convenient approximation to ASE noise enhancement, that can be evaluated analytically     

Pulse restoration by filtering of self-phase modulation broadened optical spectrum

Restoration of distorted optical pulses is achieved using nonlinear fiber self-phase spectral broadening and subsequent optical band-pass filtering of a single sideband. Using this technique, the output pulsewidth is shown to remain constant for input pulse-widths between 9-20 ps. A detailed investigation of the signal-to-noise ratio shows that best performance is obtained by operating in normal fiber dispersion regime. This technique is also applied to restore 40 Gb/s RZ-data suffering distortion from polarization mode dispersion. The high-bandwidth fiber nonlinearity shows promise to scale to higher bit rate pulse distortion correction.