Inter-channel Nonlinear Effects Research Articles

Optical back propagation for compensating nonlinear impairments in fiber optic links with ROADMs.

An optical back propagation (OBP) technique is investigated to compensate for nonlinear impairments in fiber optic communication systems with reconfigurable optical add-drop multiplexers (ROADMs). An OBP module consisting of an optical phase conjugator (OPC), amplifiers and dispersion-decreasing fibers (DDFs) fully compensates for the nonlinear impairments of a transmission fiber. The OBP module can be placed after each transmission fiber (inline OBP case) or at each network node (node OBP case). For a wavelength division multiplexing (WDM) system with 2400 km transmission distance and 32-quadrature amplitude modulation (QAM) format, inline OBP and node OBP bring Q-factor improvements of 4.9 dB and 5.6 dB as compared with linear compensation, respectively. In contrast, receiver-side digital back propagation (DBP) only provides 1.3 dB Q-factor gain, due to its incapability of mitigating inter-channel nonlinear effects in fiber optic networks.

Multi-channel nonlinearity compensation of PDM-QPSK signals in dispersion-managed transmission using dispersion-folded digital backward propagation

We demonstrate nonlinearity compensation of 37.5-GHz-spaced 128-Gb/s PDM-QPSK signals using dispersion-folded digital-backward-propagation and a spectrally-sliced receiver that simultaneously receives three WDM signals, showing mitigation of intra-channel and inter-channel nonlinear effects in a 2560-km dispersion-managed TWRS-fiber link. Intra-channel and adjacent inter-channel nonlinear compensation gains when WDM channels are fully populated in the C-band are estimated based on the GN-model.

Fiber-Nonlinearity-Tolerant Superchannel Transmission via Nonlinear Noise Squeezing and Generalized Phase-Conjugated Twin Waves

We present fiber-nonlinearity-tolerant transmission of polarization-division multiplexed binary phase-shift keying (PDM-BPSK) through a nonlinear noise squeezing (NLNS) effect that is achieved by optimized digital electronic dispersion precompensation. With the improved nonlinear tolerance, a 406.6-Gb/s superchannel consisting of eight 37.5-GHz-spaced 32-Gbaud Nyquist-filtered PDM-BPSK signals is transmitted over a 12800-km (160 × 80-km) EDFA-only amplified dispersion-unmanaged nonzero-dispersion-shifted fiber link. We establish a connection between the beneficial NLNS effect and the recently reported phase-conjugated twin wave (PCTW) concept and further generalize the PCTW concept to vector twin waves that are traveling through a fiber link along orthogonal dimensions such as time and space. Moreover, we apply the PCTW concept to wavelength-division-multiplexed (WDM) superchannel transmission by treating the entire WDM superchannel as a twin wave to further mitigate interchannel nonlinear effects. Through numerical simulations, we show that the generalized PCTW technique can effectively mitigate interchannel nonlinear impairments, in addition to mitigating intrachannel nonlinear impairments.

Characteristics of XPM in coherent optical OFDM WDM transmission systems

We use a self-correlation technique to extract the inter-channel nonlinear effects i.e. cross phase modulation (XPM) induced phase noise and XPM-induced polarization scattering for analyzing the characteristics of XPM in coherent optical orthogonal frequency division multiplexing (CO-OFDM) wavelength-division-multiplexed (WDM) transmission systems under different dispersion compensation (DC) ratios and different walk-off values. Through the analysis, we can clearly see how the DC ratio acts on the XPM by applying this technique. After transmitting 1500km standard single-mode fiber (SSMF), 12.3dB phase noise is induced when the DC ratio is changed from 0% to 105%. While the walk-off is varied from 1.6ps/km to 12.8ps/km, almost 10.6dB phase noise is eliminated. Additionally, the phase noise is verified as the dominant distortion in dual-polarization OFDM systems while the XPM-induced polarization crosstalk is proved to be the decisive distortion in dual-polarization QPSK coherent experiment.

Nonlinear Tolerant Spectrally-Efficient Transmission Using PDM 64-QAM Single Carrier FDM With Digital Pilot-Tone

We propose nonlinear tolerant single carrier frequency-division-multiplexing (SC-FDM) signal enhanced by digital pilot-tone for future high speed Ethernet transport like 400 G Ethernet. First, we discuss system configuration and the wavelength-division-multiplexed (WDM) transmission of SC-FDM signals employing polarization-division-multiplexed (PDM) 64-ary quadrature amplitude modulation (64-QAM). Next, we describe the long-haul transmission characteristics of 50 GHz-spaced 538 Gb/s × 7 ch WDM signals. We compare digital back-propagation (DBP) and digital pilot-tone for nonlinearity compensation and experimentally show that digital pilot-tone can effectively compensate the phase noise induced by inter-channel nonlinear effects with less computational complexity than DBP. Then we discuss a high-capacity transmission experiment employing 548 Gb/s PDM-64QAM SC-FDM; 102.3 Tb/s (224 × 548 Gb/s) C- and extended L-band WDM transmission is demonstrated over 240 km (3 × 80 km) of pure-silica-core fiber (PSCF) with all-Raman amplification. Thanks to the high nonlinear tolerance enhanced by pilot-tone, we can employ the 80 km repeater spacing used in conventional terrestrial systems. Assuming 20% forward error correction (FEC) overhead, a spectral efficiency of 9.1 b/s/Hz is achieved.

Application of a digital non-linear compensation algorithm for evaluating the performance of root-raised-cosine pulses in 112 Gbit s−1 DP-QPSK transmission

In this paper, we numerically investigate the non-linear tolerance of root-raised-cosine (RRC) pulse shaping by interpolating finite impulse response (FIR) filters in conjunction with digital backward propagation (DBP) in coherent 112 Gbit s−1 dual-polarization quadrature phase shift keying (DP-QPSK) transmission. The results depict that RRC pulses are more tolerant to intra-channel non-linearities, i.e. self-phase modulation (SPM), as compared to standard RZ-33 and NRZ pulses. The non-linear threshold point is improved by using RRC pulses by a factor of 2 dB signal input power as compared to RZ pulses and by 4 dB signal launch power as compared to NRZ pulses. The behavior of RRC pulses is also investigated with standard single mode fiber (SMF), non-zero dispersion shifted fiber (NZDSF) and next-generation large Aeff pure silica core fiber (LA-PSCF). Most importantly multi-span DBP is implemented and in the case of RRC pulses the computational efforts of the conventional DBP algorithm are reduced by 80% with a diminutive Q-penalty of 0.74 dB. The duty cycle of the RRC pulses is further optimized for efficient system performance. We have also compared the performance of single-channel transmission with the multi-channel transmission, where the performance is limited due to inter-channel non-linear effects. Furthermore, the non-linear tolerance of RRC pulses is investigated with; (a) different amplifier spacing and (b) variation in transmission link design information for the DBP algorithm.

Nonlinear Shannon Limit in Pseudolinear Coherent Systems

In this paper, we develop a general first-order perturbation theory of the propagation of a signal in an optical fiber in the presence of amplification and Kerr nonlinearity, valid for arbitrary pulse shapes. We obtain a general expression of the sampled signal after optical filtering, coherent detection, and optimal sampling. We include intrachannel and as well as interchannel nonlinear effects. We obtain simplified expressions in the case in which the accumulated dispersion is high (equivalent to the far-field limit in paraxial optics). This general theory is applied in detail to the special case of spectral-efficient sinc pulses. This exercise shows that the characteristics of the neighboring wavelength-division multiplexed channels are essential in determining the nonlinear impairments.

Improved digital backward propagation for the compensation of inter-channel nonlinear effects in polarization-multiplexed WDM systems

An improved split-step method (SSM) for digital backward propagation (DBP) applicable to wavelength-division multiplexed (WDM) transmission with polarization-division multiplexing (PDM) is presented. A coupled system of nonlinear partial differential equations, derived from the Manakov equations, is used for DBP. The above system enables the implementation of DBP on a channel-by-channel basis, where only the effect of phase-mismatched four-wave mixing (FWM) is neglected. A novel formulation of the SSM for PDM-WDM systems is presented where new terms are included in the nonlinear step to account for inter-polarization mixing effects. In addition, the effect of inter-channel walk-off is included. This substantially reduces the computational load compared to the conventional SSM.

Performance Dependence on Channel Baud-Rate of PM-QPSK Systems Over Uncompensated Links

We investigated through simulation the performance of dense wavelength-division-multiplexing transmission systems based on polarization-multiplexed quadrature phase-shift keying over long-haul uncompensated links. We looked at three system configurations, whose per-channel Baud-rate was 14, 28, and 56 GBaud, respectively. Their total net capacity in the C-band (8 Tb/s) and net spectral efficiency (2 b/s/Hz) were exactly the same. We found that the systems long-haul performance is almost the same in the three cases, with the 56-GBaud configuration only slightly under-performing. By means of backward-propagation, we also found that the balance between intrachannel and interchannel nonlinear (NL) effects is completely different in the three cases, with 14-GBaud dominated by interchannel NL effects and 56-GBaud dominated by single-channel NL effects. We also show that, where possible to actually exploit backward-propagation, the 56-GBaud per channel system would outperform the lower Baud-rate configurations.

Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission

An advanced split-step method is employed for the digital backward-propagation (DBP) method using the coupled nonlinear Schrodinger equations for the compensation of inter-channel nonlinearities. Compared to the conventional DBP, cross-phase modulation (XPM) can be efficiently compensated by including the effect of the inter-channel walk-off in the nonlinear step of the split-step method (SSM). While self-phase modulation (SPM) compensation is inefficient in WDM systems, XPM compensation is able to increase the transmission reach by a factor of 2.5 for 16-QAM-modulated signals. The advanced SSM significantly relaxes the step size requirements resulting in a factor of 4 reduction in computational load.

Interchannel Nonlinearities in Coherent Polarization-Division-Multiplexed Quadrature-Phase-Shift- Keying Systems

We study with simulations interchannel nonlinear effects on a 42.8-Gb/s coherent polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) system with and without dispersion management. We find that interchannel cross-phase-modulation induced nonlinear polarization scattering can severely degrade the performance of a dispersion-managed PDM-QPSK system. We demonstrate that the time-interleaved return-to-zero PDM-QPSK, where the symbols of the two polarizations are shifted by half a symbol in time, can significantly suppress the nonlinear polarization scattering in dispersion managed systems, and make systems with inline dispersion-compensation fiber (DCF) achieve better performance than those without DCF.

Performance Evaluation of Dispersion Managed Optical TDM-WDM Transmission System in the Presence of SPM, XPM, and FWM

Optical time division multiplexing - wavelength division multiplexing (OTDM-WDM), intensity modulation (IM) systems employing optical amplification and dispersion management (DM) are analyzed. Interchannel nonlinear effects present the input power limit to system performance. Therefore, a lumped DM system performed better than a fully inline DM system through reduction of coherent channel interaction. With proper channel spacing, all demultiplexed OTDM channels and the multiplexed signal show the same performance.