Intrachannel Four-wave Mixing Research Articles

Intrachannel Four-Wave Mixing Compensation in Dispersion-Managed Transmission Links with Mid-Span Optical Phase Conjugation

Intrachannel Four-Wave Mixing Compensation in Dispersion-Managed Transmission Links with Mid-Span Optical Phase Conjugation

Improved compensation of intrachannel four-wave mixing in dispersion-managed transmission links with mid-span optical phase conjugation

Recently, a novel approach to satisfy the nonlinearity compensation criteria by mid-span optical-phase-conjugation (OPC) was proposed and excellent transmission performance was achieved, there the OPC propagation symmetry was obtained through optimized dispersion management with inverse-dispersion fiber (IDF). In this work, the author numerically investigates the possibilities of using dispersion-compensating fiber (DCF) instead of IDF for construction of the link. Nonlinearity compensation effectiveness of the two links are compared with respected to the intrachannel four-wave mixing (IFWM) induced intensity fluctuation of the ‘1’ bits and the generation of the ghost pulse. It is found that, by launching different powers (or energy of a limited bits) into the spans before and after the OPC, nonlinearity mismatch between the spans of the DCF-managed link can be counterbalanced with significantly improved transmission performance. For a given input energy, there exists an optimum ratio of the energies into the spans before and after the OPC, at which optimum nonlinearity compensation can be achieved, and the compensation effectiveness is very close to that of the IDF-managed link. Further studies show that the optimum energy ratio increases with the input energy but is independent of the span number of the link.

Improved Compensation of Intrachannel Four-Wave Mixing in Dispersion-Managed Transmission Links with Mid-Span Optical Phase Conjugation

Improved Compensation of Intrachannel Four-Wave Mixing in Dispersion-Managed Transmission Links with Mid-Span Optical Phase Conjugation

Field and lab experimental demonstration of nonlinear impairment compensation using neural networks

Fiber nonlinearity is one of the major limitations to the achievable capacity in long distance fiber optic transmission systems. Nonlinear impairments are determined by the signal pattern and the transmission system parameters. Deterministic algorithms based on approximating the nonlinear Schrodinger equation through digital back propagation, or a single step approach based on perturbation methods have been demonstrated, however, their implementation demands excessive signal processing resources, and accurate knowledge of the transmission system. A completely different approach uses machine learning algorithms to learn from the received data itself to figure out the nonlinear impairment. In this work, a single-step, system agnostic nonlinearity compensation algorithm based on a neural network is proposed to pre-distort symbols at transmitter side to demonstrate ~0.6 dB Q improvement after 2800 km standard single-mode fiber transmission using 32 Gbaud signal. Without prior knowledge of the transmission system, the neural network tensor weights are constructed from training data thanks to the intra-channel cross-phase modulation and intra-channel four-wave mixing triplets used as input features.

Comparison of Different Chromatic Dispersion Compensation Schemes in Quasi-linear Transmission System with Intrachannel Four-wave Mixing

In this paper, different chromatic dispersion compensation schemes like pre-, post-, and symmetrical schemes are compared numerically in the presence of intrachannel four-wave mixing (IFWM) for return-to-zero quasi-linear transmission systems. The transmission performances have been compared in terms of the average intensity deviation of the “1” bits and the relative intensity of the ghost pulse (the “0” bits). It is found that, for a fixed amplifier spacing, optimal compensation scheme depends on transmission bit rate. As bit rate increases the performance of pre-compensation becomes better. On the contrary, post-compensation exhibits its advantage more and more as bit rate decreases.

DWDM混合光学系统中帧间和信道内四波混频效应的抑制

In this study, a hybrid system of optical Code Division Multiple Access(optical CDMA) and Dense Wavelength Division Multiplexing(DWDM) is proposed with a comprehensive investigation into the effect of four-wave mixing(FWM). In such system, two major FWM problems exist, inter and intra-channel FWM, including multiple access interference(MAI) and inter-symbol interference(ISI). Results show that the optimum transmitted power is 18dBm in order to control the trade-off between inter and intra-channel FWM, where an increase in the BER of the hybrid system at transmitted power above 18 dBm is indicated. Hence, an electro-optic phase modulator(EOPM) module is proposed and placed after the WDM multiplexer to simultaneously modulate the phase of all wavelengths signals to increase the nonlinear tolerance in the hybrid system by suppressing the impact of intra-channel FWM, which is shown to greatly improve the performance of the optical CDMA-DWDM hybrid system based OOK transmission. In addition, the effect of MAI can be reduced by the use of multi-diagonal(MD) identification sequence code, due to the zero cross-correlation property of MD. The results also reveal that the CDMA technology in conjunction with chromatic dispersion helps to reduce the effect of inter-channel FWM. Moreover, the identification sequence code interval plays crucial role in the mitigating of ISI as the results expose that the best performance of the proposed hybrid system can be achieved when the identification sequence code interval squeezed into 25% of bit duration where the avoidance of ISI is guaranteed.

Performance Comparison of Different Dispersion Compensation Schemes in Quasi-linear Transmission System with Intrachannel Four-wave Mixing

Intrachannel four-wave mixing (IFWM) is the dominate source of bit errors in high-bit-rate quasi-linear fiber-optic transmission systems. Previous studies have shown that IFWM can be reduced by proper dispersion compensation scheme. In this paper, different schemes like pre-, post-, and symmetrical-dispersion compensations are compared numerically in the presence of IFWM in return-to-zero quasi-linear transmission systems. The performances of the three compensation schemes have been compared in terms of the average intensity deviation of the “1” bits and the relative intensity of the ghost pulse (the “0” bit). It is found that, for a fixed amplifier spacing, optimal compensation scheme (with minimum average intensity deviation of the “1” bits and minimum intensity of the ghost pulse) depends on transmission bit rate. As bit rate increases the performance of pre-compensation becomes better and better. On the contrary, post-compensation exhibits its advantage more and more as bit rate decreases.

Range of Influence and Impact of Physical Impairments in Long-Haul DWDM Systems

In long-haul dense wavelength-division multiplexing (DWDM) systems with periodic dispersion compensation and amplification, system performance is adversely affected by severe physical impairments due to fiber losses, dispersion and nonlinearity. Fiber modeling is a prerequisite for the development of physical impairment mitigation techniques to improve system performance. The distance between two interacting symbols in time and wavelength, i.e., the range of influence (RoI) of each physical impairment, plays an important role in the development of these mitigation techniques. In this paper, we use the Volterra series transfer function (VSTF) method to define impairment characteristic coefficients that capture intersymbol interference (ISI), self phase modulation (SPM), intrachannel cross phase modulation (IXPM), intrachannel four wave mixing (IFWM), cross phase modulation (XPM) and four wave mixing (FWM), to characterize the impact of these impairments individually on the system output. We then investigate the impact of system parameters, namely, duty cycle, spectral efficiency, frequency chirp, and span length, on the RoI for long-haul DWDM systems.

强色散管理抑制160 Gb/s光时分复用传输系统中的带内四波混频效应

强色散管理抑制160 Gb/s光时分复用传输系统中的带内四波混频效应

Analytical modeling of a single channel nonlinear fiber optic system based on QPSK

A first order perturbation theory is used to develop analytical expressions for the power spectral density (PSD) of the nonlinear distortions due to intra-channel four-wave mixing (IFWM). For non-Gaussian pulses, the PSD can not be calculated analytically. However, using the stationary phase approximations, we found that convolutions become simple multiplications and a simple analytical expression for the PSD of the nonlinear distortion is found. The PSD of the nonlinear distortion is combined with the amplified spontaneous emission (ASE) PSD to obtain the total variance and bit error ratio (BER). The analytically estimated BER is found to be in good agreement with numerical simulations.

Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing

By extending a well-established time-domain perturbation approach to dual-polarization propagation, we provide an analytical framework to predict the nonlinear interference (NLI) variance, i.e., the variance induced by nonlinearity on the sampled field, and the nonlinear threshold (NLT) in coherent transmissions with dominant intrachannel-four-wave-mixing (IFWM). Such a framework applies to non dispersion managed (NDM) very long-haul coherent optical systems at nowadays typical baudrates of tens of Gigabaud, as well as to dispersion-managed (DM) systems at even higher baudrates, whenever IFWM is not removed by nonlinear equalization and is thus the dominant nonlinearity. The NLI variance formula has two fitting parameters which can be calibrated from simulations. From the NLI variance formula, analytical expressions of the NLT for both DM and NDM systems are derived and checked against recent NLT Monte-Carlo simulations.

A 2-D Discrete-Time Model of Physical Impairments in Wavelength-Division Multiplexing Systems

Dense wavelength-division multiplexing (DWDM) is a promising approach to design ultrahigh-capacity fiber-optic communication systems ( >; nn50 Tb/s). However, DWDM gives rise to severe physical impairments that adversely affect system performance. To mitigate various physical impairments in DWDM systems and exploit their system capacity, there is a need to develop a 2-D (time and wavelength) discrete-time input-output model of physical impairments that can become the foundation of signal processing for optical communications. This paper develops such a model based on the Volterra series transfer function (VSTF) method. We overcome the well-known triple integral problem associated with the VSTF method and reduce it to a simple integral. This model takes into account multiple channel effects, fiber losses, frequency chirp, optical filtering, and photo detection, which are ignored in the current literature. The model is in excellent agreement with results obtained by split-step Fourier simulation. Furthermore, with this model, we define coefficients that capture intersymbol interference, interchannel interference, self-phase modulation, intrachannel cross-phase modulation (XPM), intrachannel four-wave mixing (FWM), XPM, and FWM to characterize the impact of these effects individually on the system performance. We also apply this model to analyze the effects of varying system parameters and pulse shapes on the individual physical impairments.

Polarization scattering by intra-channel collisions

We show that polarization modulated and polarization multiplexed transmission may be significantly impaired by the polarization scattering induced by intra-channel cross-phase modulation and four-wave mixing. In polarization multiplexed transmission, channel interleaving may be used to mitigate the effect when two-pulse collisions are dominant.

Suppression intra-channel four-wave mixing by strong dispersion management in 160 Gb/s OTDM RZ 100 km transmission

The effect of intra-channel four-wave mixing on the performance of a 160 Gb/s OTDM RZ 100 km transmission system is analyzed. Strong dispersion management to suppress the detrimental effects of intra-channel four-wave mixing is presented theoretically and verified experimentally. Results demonstrate that amplitude fluctuation and ghost pulses are well suppressed by strong dispersion management. Stable (>2 h) error-free (10−12) transmission over 100 km is achieved without forward-error correction, and the power penalty is ∼3.6 dB.

Suppression of intra-channel four-wave mixing in 40Gbit/s RZ-DQPSK transmission with alternate-polarization

In this paper, we show that the suppression of intra-channel four-wave mixing (IFWM) in 40 Gbit/s RZ-DQPSK transmission system based on different dispersion maps through using alternate polarization of adjacent symbols. The suppression of IFWM results in significant improvement of system performance. Simulation results show that the amplitude fluctuation is efficiently reduced due to the suppression of the IFWM with alternate-polarization.

A fiber-optic transmission system based on differential polarization-shift keying

A differential polarization-shift keying (DPolSK) scheme in which information is encoded as a differential polarization state with respect to the previous symbol is considered. A novel DPolSK demodulator consisting of optical delay interferometer and a pair of birefringence plates that do polarization rotation are proposed. Numerical simulations of the long haul fiber-optic systems based on differential phase-shift keying (DPSK) and DPolSK are carried out and it is found that DPolSK has a higher nonlinear tolerance than DPSK. This is because the ghost pulse generation due to intra-channel four-wave mixing (IFWM) is less efficient for DPolSK signals as compared to DPSK.

Intra-Channel Four-Wave Mixing Impairments in Dispersion-Managed Coherent Fiber-Optic Systems Based on Binary Phase-Shift Keying

In this paper, we mathematically derive the probability density function (PDF) of the received electrical signal for coherent fiber-optic transmission systems. Both amplified spontaneous emission (ASE) noise and fiber nonlinearity are taken into account. The results show that the PDF of a bit ldquo0rdquo or ldquo1rdquo is asymmetric when intra-channel four-wave mixing (IFWM) is dominant. However, the PDF becomes nearly symmetric when the variance of ASE is much larger than that due to IFWM. The standard deviation of the received signal is calculated analytically. It is shown that the variance varies quadratically with launch power. We also investigate the optimum system scheme, including optimum dispersion map and pre-compensation ratio, for the coherent fiber-optic systems based on analytically calculated variance of IFWM.

Experimental and numerical investigation of bit-wise phase-control OTDM transmission

The impact of varying the phase relationship between adjacent OTDM channels is investigated in 80 Gbit/s transmission experimentally and numerically. A fiber-based coherent multiplexer is proposed for OTDM experiments - a phase shifter in the multiplexer and an external phase control circuit are used to set and maintain the phase difference. It is demonstrated that the optimum modulation format for maximum transmission distance strongly depends on pulse width, e.g. 120 degrees-RZ provides the best performance for pulse width of 8 ps; however, 90 degrees-RZ is advantageous when pulse width is reduced to 2 ps. Power in 'zero' bit slots and amplitude jitter are calculated to demonstrate that the performance variation is due to intra-channel four-wave mixing (IFWM) and different receiver sensitivity at back-to-back. We also show that phase modulation formats are sensitive to optical filtering.

Study on the suppression of IFWM in 40 Gb/s WDM systems

The paper analyses the effects of intra-channel four-wave mixing (IFWM) on the high-speed optical fiber communication system. A new code format is developed with double 0 and double π phase separating 1 code; it can decrease the transmission penalty from fiber nonlinearity by counteracting the perturbation terms of IFWM. From the simulation of transmission of two classic code data “11011” and “11100”, we find that our proposed code format has a better suppression effect than the alternative modulation inversion (AMI) or the normal RZ format and supports a wider pulse mode. In a 40 Gbps system, the AMI format is 2 dB less than the RZ format, and our proposed format is 1 dB less than the AMI format when a 1 dB eye open penalty is taken as a metewand. Moreover, it can be realized as easily as the AMI format.

Pseudolinear optical system reach enhancement via runlength-limited coding

This paper demonstrates that the transmission distance of an ON-OFF-keyed high-speed pseudolinear optical communication system can be dramatically improved by means of runlength-limited coding. The key idea is to impose constraints on transmitted sequences such that the minimum interpulse spacing increases, and the average transmission power decreases. Both effects help suppress intrachannel four-wave mixing, a major nonlinear penalty in pseudolinear long-haul links. Several coding schemes with different properties are designed for various constraints and compared against a prototypical reference system. Finally, numerical simulations are performed for a benchmark system employing differential phase-shift keying. The results obtained indicate that the runlength-limited coding approach can be considered a legitimate alternative to this more advanced modulation format.