Effect of dispersion on nonlinear phase noise

The variance of nonlinear phase noise is analyzed by including the effect of intrachannel cross-phase modulation-induced nonlinear phase noise. Consistent with Ho and Wang [IEEE Photon. Technol. Lett.17, 1426 (2005)] for a lightwave transmission system but contrary to the conclusions of both Kumar [Opt. Lett.30, 3278 (2005)] and Green [Opt. Lett.28, 2455 (2003)] with different initial conditions, the variance of nonlinear phase noise does not decrease much with the increase of chromatic dispersion. The results are consistent with each other after a careful reexamination.     

Effect of phase noise on optical minimum-shift keying transmission systems

Phase-modulated (PM) signals have recently been used in long-haul lightwave communication systems to reach record distances. Added directly to the signal phase, linear and nonlinear phase noise cause performance degradation in PM systems. Minimum-shift keying (MSK), as a special format of PM signals, presents some different features of phase noise tolerance. This paper investigates the effect of phase noise on the performance degradation in the 10 Gb/s optical MSK systems and analyzes the contribution of phase noise to the bit error rate (BER), compared with the conventional PM format, 50% duty cycle optical return-to-zero differential phase-shift keying (RZ-DPSK) signals, in several typical local fiber dispersion transmission systems. The effect of intensity noise on the performance degradation in the corresponding transmission systems is also investigated.     

Mitigation of phase noise in dispersion compensated quasi-linear optical transmission systems: Analysis

We theoretically investigate the phase noise in quasi-linear optical transmission systems and study the mitigation of phase noise by properly choosing periodic dispersion compensation and amplification. Variational method is used to deduce the analytical formula for calculating the phase fluctuations of a Gaussian pulse. The analytical predictions are then checked against direct simulations by numerically solving the nonlinear Schrödinger equation. We find that stronger dispersion compensation maps can be used to reduce phase noise and it can be further mitigated by modifying the dispersion map appropriately. It is also found that shorter amplifier spacing yields lower phase noise. We also explore the effect of pre-, post- and bi-end dispersion compensation configurations on phase noise with full compensation and check the reduction of phase noise along the fiber link.     

Effect of chromatic dispersion on nonlinear phase noise

We consider the combined effects of amplified spontaneous emission noise, optical Kerr nonlinearity, and chromatic dispersion on phase noise in an optical communication system. The effect of amplified spontaneous emission noise and Kerr nonlinearity were considered previously by Gordon and Mollenauer [Opt. Lett. 15, 1351 (1990)], and the effect of nonlinearity was found to be severe. We investigate the effect of chromatic dispersion on phase noise and show that it can either enhance or suppress the nonlinear noise amplification. For large absolute values of dispersion the nonlinear effect is suppressed, and the phase noise is reduced to its linear value. For a range of negative values of dispersion, however, nonlinear phase noise is enhanced and exhibits a maximum related to the modulation instability found in amplitude fluctuations. Nonlinear phase noise is quenched by these effects even in dispersion-compensated systems; the degree of suppression is sensitively dependent on the dispersion map. We demonstrate these results analytically with a simple linearized model.     

Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems

Self-phase modulation and intrachannel cross-phase-modulation- (IXPM) induced nonlinear phase noise is investigated by the variational method. IXPM can cause a considerable increase of phase noise. We show, however, that IXPM leads to a partial correlation between the phase noises of adjacent pulses, which tends to reduce the influence of nonlinear phase noise in return-to-zero differential phase-shift keying transmission. In highly dispersive transmission systems, intrachannel four-wave mixing-induced differential phase fluctuations are typically larger than differential nonlinear phase noise. The analysis is validated by Monte Carlo simulation.     

Classical and quantum noise in nonlinear optical systems

In quantum optics noise plays an important role, since many of the nonlinear optical systems are quite sensitive to the subtle influences of weak random perturbations, being either classical of quantum mechanical in nature. We discuss the origin of quantum noise emerging from the reversible or the irreversible part of the dynamics and compare it with the properties of purely classical fluctuations. These general features are illustrated by a number of physical examples, such as the laser with loss or gain noise, nonlinear optical devices, and the phenomenon of quantum jumps. These processes have been chosen mainly to illustrate the different aspects of noise, but also because, to a large extent, they can be described in analytical terms.     

Influence of phase noise on OFDM data transmission systems

We discuss the influence of the phase noise on OFDM data transmission systems. It is shown that intercarrier interference appearing due to the influence of the phase fluctuations on the OFDM communication system can be represented as two components, one of which has a uniform distribution across all the subcarriers, while the other has a nonuniform frequency-selective distribution determined by the transmission function of the communication channel. Therefore, the total distribution of intercarrier interference is frequency-selective with a higher power concentrated at stronger subcarriers. It is shown that the phase-noise influence on the OFDM communication system in frequency-selective communication channels is relatively weaker than that in frequency-flat channels without time dispersion.     

Cross-phase modulation induced phase fluctuations in optical RZ pulse propagating in dispersion compensated WDM transmission systems

The basic mechanism of cross-phase modulation induced phase fluctuations in optical RZ pulse propagating in a periodically dispersion compensated transmission line has been investigated. Ordinary differential equations have been derived using variational analysis to estimate the phase fluctuation and the analytical result is verified by numerical simulations based on split-step Fourier method. We therefore explore the impact of different dispersion compensation maps on phase fluctuation for 10 Gb/s and 40 Gb/s WDM transmission systems. The effects of initial pulse spacing between channels, channel spacing and residual dispersion on phase shift have been studied. We find that cross-phase modulation induced phase fluctuation can be mitigated by proper adjustment of channel spacing and/or residual dispersion.     

Compensation of third-order dispersion using time reversal in optical transmission systems

It is shown that the third-order dispersion of an optical fiber can be compensated for using a time-reversal system that can be implemented with periodic time lenses.     

Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion

Soliton propagation in a cascaded dispersion-managed optical amplifier system with zero net dispersion is examined. We present a qualitative physical explanation for the recently discovered fact that a soliton with finite energy can propagate down a fiber line with zero or normal average dispersion. We describe a specific practical system for the main properties of such a soliton, namely, the dependence of the soliton power on the pulse width at chirp-free points and the soliton average energy and width at chirp-free points as functions of the dispersion-allocation (strength of the map) parameter.     

Effect of noise on characteristics of optical waveguide systems

Transient regimes of an optical waveguide system in the presence of additive and multiplicative noises are studied. The presence of noise is shown to result in a transformation of the spectrum of radiation modes. The effect of noise on the efficiency of input of electromagnetic energy into a waveguide system is studied.     

The characters of dense dispersion managed soliton in optical fiber transmission systems

The properties of ultra-short dense dispersion-managed soliton (DBMS) in optical fiber links are investigated. They show some excellent characters, such as, reducing pulse's breathing extent greatly, facing fewer mutual interactions and tolerating larger local dispersion. In general, DBMS is more stable than a conventional dispersion-managed soliton in high-capacity systems. Excessively dense dispersion compensation is more suitable for systems with weak nonlinear effect.     

Effect of transmission fiber and amplifier noise on optical chaos synchronization

Optical chaos propagation has few constraints peculiar to itself which do not become as significant in conventional nonchaotic optical communication. We have investigated the effects of transmission fiber nonlinearities, dispersion and noise of erbium doped fiber amplifier (EDFA) on chaotic signal synchronization in lumped and distributed configuration. It is found that the effects of fiber dispersion can be easily compensated; however, the effects of fiber nonlinearity on chaos cannot be overdone and must be avoided. Three distinct configurations with different combinations of standard telecommunication fiber, dispersion compensation fiber and lumped and distributed EDF for amplification are analysed. The results are compared in terms of sync diagrams and noise figure. The chaos after propagation through distributed amplification performs better as compared to lumped amplification. Also, a new quantitative measure for the calculation of deviation in sync diagram of chaos is introduced.     

Suppression of nonlinear effects by phase alternation in strongly dispersion-managed optical transmission

The nonlinear effects of amplitude jitter and ghost pulse generation, which are present in strongly dispersion-managed optical communication systems can be suppressed by alternation of the phase of the bits. A physical explanation for this effect is given that shows that with suitably chosen phase modulations the processes that give rise to the nonlinear effects will counteract each other.     

Power-weighted dispersion distribution function for characterizing nonlinear properties of long-haul optical transmission links

Based on the first-order perturbation theory, we introduce the power-weighted dispersion distribution (PWDD) function to characterize nonlinear properties of fiber-optic transmission links. This technique offers a new perspective on dispersion management for pseudolinear transmission. A rectangular PWDD model is used to describe the formation of ghost pulses analytically in the time domain without relying on the assumption that the pulse shape is Gaussian.     

Weighted nonlinear phase shift with group velocity dispersion to assess the nonlinear penalty in C+L band long-haul fiber optical amplified transmission link

To assess the penalty due to nonlinear effect in C L band long-haul optical amplified transmission link,a new parameter of modified nonlinear phase shift (φD) is proposed,which is the accumulated nonlinear phase shift weighted by a normalized group velocity dispersion (GVD).Based on the numerical simulation result of broadband long-haul hybrid Raman/erbium-doped fiber amplified transmission line,it is validated that φD is more reasonable and suitable than the previous proposed nonlinear phase shift (φNL) for broadband applications.     

Laser phase noise to intensity noise conversion by lowest-order group-velocity dispersion in optical fiber: exact theory

An exact result for the spectral density of intensity variations that occur after propagation of ergodic light in a medium having lowest-order-only group-velocity dispersion is obtained and applied to the problem of semiconductor laser phase noise to intensity noise conversion in a single-mode optical fiber. It is shown that the intensity spectrum after propagation formally approaches, for a large laser linewidth or a long (or high-dispersion) fiber, the intensity spectrum of a thermal source having the same line shape as the laser.     

Effect of nonlinear gain on the phase noise of Y-branch lasers

Effect of nonlinear gain on the phase noise of modulated grating Y-branch (MGY) lasers is investigated by experiments and simulations. The phase noise is first characterized by measuring the frequency modulation noise spectrum of the MGY laser, and some interesting phenomena are observed. In order to understand the underlying physic mechanism of those phenomena, simulations are performed with taking Langevin noise sources and nonlinear gain terms into account. Simulated results show that, in the presence of the nonlinear gain, fluctuations of side-modes can bring excess phase noise to the lasing mode, especially when the side-modes are on the long-wavelength side of the main mode. Furthermore, it has been found that the phase noise hopping phenomenon can be induced by a bi-stable state of the laser, which is also closely related to the nonlinear gain. The investigation is helpful for explaining the complicated phase noise characteristics of the MGY laser.     

Modeling of semiconductor optical amplifier RIN and phase noise for optical PSK systems

Phase modulation schemes are attracting much interest for use in ultra-fast optical communication systems because they are much less sensitive to fibre nonlinearities compared to conventional intensity modulation formats. Semiconductor optical amplifiers (SOAs) can be used to amplify and process phase modulated signals, but with a consequent addition of nonlinear phase noise (NLPN). Existing SOA NLPN models are simplistic. In this paper we show that a more accurate model can be used, which results in simple expressions for SOA nonlinear noise, in particular when used to amplify differential phase shift keyed modulated data. The model is used to calculate the optical signal to noise ratio introduced by a power booster SOA and the first inline amplifier of a 40 Gb/s NRZ-DQPSK single channel link.

     

非线性相位噪声对DQPSK调制系统性能影响研究

为了研究非线性相位噪声对差分正交相移键控（DQPSK）调制系统性能的影响,在理论推导非线性相位噪声数学模型的基础上,通过固定接收端信噪比不变,仿真分析了40Gb/s速率时DQPSK调制系统误码率随输入信噪比的变化情况。结果表明:与二进制差分相移键控（DPSK）调制相比,DQPSK调制对非线性相位噪声的影响更为敏感,当非线性效应较大时,非线性相位噪声将使系统误码率显著增大,严重影响系统通信质量。因此,当采用DQPSK调制时,必须考虑非线性相位噪声对系统性能的影响。