Interchannel Four-wave Mixing Research Articles

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.

Modeling interchannel four-wave mixing for 8-Ary modulated dense wavelength division multiplexing systems over dispersion map

Semianalytic models are developed to deterministically calculate the variances of degenerate and nondegenerate four-wave mixing (FWM) noises for dispersion-managed dense wavelength division multiplexing (DWDM) systems with 8-Ary modulations [i.e., 8-level amplitude- and differential phase-shift keying (8APSK) and constant-amplitude optical differential 8-level phase-shift keying (D8PSK)]. The semianalytic models include various important propagation effects for exact numerical results. A 5.28-Tb/s (40-Gs/s/ch) 100-GHz-spaced 33-channel DWDM system with a dispersion map is then numerically analyzed by using the newly derived semianalytic models. It is numerically validated that FWM impacts coming from 8APSK pump channels are more severe than those coming from D8PSK ones, where pump channels denote the channels whose energies are transferred to a probe channel through the FWM process. The numerical results show that although FWM tolerance of a central channel with 8APSK is worse than that with D8PSK, a central channel with 8APSK is still superior to that with D8PSK when some linear noises and FWM noise are simultaneously taken into account for our given system conditions, which is mainly attributed to a relatively larger minimum Euclidean distance for the 8APSK constellation than the D8PSK one.

4 × 160-Gbit/s multi-channel regeneration in a single fiber.

Simultaneous regeneration of four high-speed (160 Gbit/s) wavelength-division multiplexed (WDM) and polarization-division multiplexed (PDM) signals in a single highly nonlinear fiber (HNLF) is demonstrated. The regeneration operation is based on four-wave mixing in HNLF, where the degraded data signals are applied as the pump. As a result, the noise on both '0' and '1' levels can be suppressed simultaneously in our scheme. The stimulated Brillouin scattering (SBS) from the continuous wave (CW) is suppressed by cross-phase modulation (XPM) from the data pump, relieving the requirement of external phase modulation of the CW light. Mitigation of the inter-channel nonlinearities is achieved mainly through an inter-channel 0.5 bit slot time delay. Bidirectional propagation is also applied to relieve the inter-channel four-wave mixing. The multi-channel regeneration performance is validated by bit-error rate (BER) measurements. The receiver powers at the BER of 10(-9) are improved by 1.9 dB, 1.8 dB, 1.6 dB and 1.5 dB for the four data channels, respectively.

Simultaneous 3R Regeneration of 4 $\times$ 40-Gbit/s WDM Signals in a Single Fiber

We experimentally demonstrate simultaneous 3R regeneration of 4 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\times$ </tex></formula> 40-Gbit/s WDM channels, which is based on the four-wave mixing (FWM) in a single dispersion-shifted fiber. The multichannel 3R regeneration performance is validated by bit-error rate (BER) measurements. Receiver powers at a BER of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$10^{-9}$</tex></formula> are improved by 5.2 dB, 4.8 dB, 3.3 dB, and 3.9 dB for the four WDM channels, respectively. Mitigation of the interchannel nonlinearities is achieved mainly through an interchannel 0.5-bit slot time delay, which is introduced by differential group delay. Bidirectional propagation and polarization multiplexing are also applied to relieve the interchannel FWM.

Analysis of Nonlinearities on Coherent Ultradense WDM-PONs Using Volterra Series

This paper addresses transmission aspects on very high aggregate wavelength-division multiplexing based passive optical networks (WDM-PON). The ultradense WDM-PON system evaluated in this paper transports high-order modulation formats such as M-ary phase-shift keying (PSK) and M-ary quadrature amplitude modulation (QAM) in which coherent detection is performed at the optical network unit (ONU), after transmission over 25 km, 60 km, and 100 km of standard single-mode fiber (SSMF). The first part of this work covers the impact on the system's performance of the most relevant fiber nonlinearities such as self-phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM), and their interplay between transmission distance and modulation format. Using a Volterra series method allows estimating the error vector magnitude (EVM) of the received constellation related to different fiber nonlinearities. In a 32 × 625 Mbaud system spaced by 3 GHz (0.025 nm), the FWM to XPM ratio (F/X) varied from 25 up to 30 dB for phase-modulated signals (1.25 Gb/s-QPSK and 1.875 Gb/s-8PSK). On the other hand, this ratio ranged from 2.6 to 7.4 dB for amplitude-modulated signals (2.5 Gb/s-16QAM, 3.75 Gb/s-64QAM and 5 Gb/s-256QAM). After applying a frequency-allocation scheme at both transmitter and local oscillator lasers, some of the FWM crosstalk is mitigated by 2.4 to 3.5 dB. This EVM reduction confirms that increasing the transmission distance and the order of the constellation, the system's performance becomes limited by both interchannel FWM and XPM.

Adaptive delay control for time-interleaved multi-channel amplitude limiter based on saturation of four-wave mixing in a fiber

An adaptive delay control to maintain time-interleaving condition of multi-channel input signals of all-optical amplitude limiter based on saturation of four-wave mixing (FWM) in a nonlinear fiber is demonstrated. The delay control utilizes as a monitor signal the optical power after the nonlinear fiber at a wavelength that is affected by interchannel FWM in the fiber. When the scheme is applied to 2 x 10 Gbit/s return-to-zero differential phase-shift keying signals where the time separation between the input channels is intentionally changed randomly, the delay control works well and error free detection after transmission is obtained.

Analysis and experiment of all-optical time-interleaved multi-channel regeneration based on higher-order four-wave mixing in a fiber

Simultaneous all-optical multi-channel regeneration based on second-order four-wave mixing (FWM) in a single highly nonlinear fiber (HNLF) is studied. Interchannel crosstalk, especially cross gain saturation and generation of interchannel FWM, is avoided by properly time-interleaved channels. Preliminary experiment of 2 ch × 10 Gbit/s operation shows simultaneous noise reduction of the two channels and good agreement with numerical analysis. Numerical investigation on 2 ch × 40 Gbit/s operation using the same parameters as the experiment shows that the regeneration can improve qualities of both channels. For more number of channels and higher speed of operation, several parameters need to be adjusted to avoid interchannel crosstalks. Time synchronization techniques for the input channels are also discussed.

Transmission performance of 10-Gb/s DPSK WDM signals due to phase-error and four-wave mixing in SOAs

We present a complete dynamic model of semiconductor optical amplifiers (SOAs) including the inter-channel four-wave mixing (FWM). The model has been implemented using the time-dependent transfer matrix method (TMM) and applying the discretization scheme in both the spatial and spectral domains. In SOA-based wavelength division multiplexing transmission systems using 10-Gb/s differential phase shift keyed (DPSK) signals, the system performance due to the SOA-induced phase-error and the FWM effect has been analyzed. By the injection of a reservoir channel into SOAs, the transmission performance of non-return-to-zero (NRZ) DPSK signals can be improved through the phase-error reduction. Both the NRZ-DPSK and return-to-zero (RZ) DPSK signals are found to be suffered from the FWM-induced crosstalk. The overall nonlinear tolerance of RZ-DPSK is shown to be better than that of NRZ-DPSK.

Modeling Interchannel FWM With Walk-Off in RZ-DPSK Single Span Links

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> An analytic model for interchannel four-wave mixing (FWM) is developed for return to zero differential phase shift keying (RZ-DPSK) single span transmission including interchannel walk-off for degenerate FWM (D-FWM) and nondegenerate FWM (ND-FWM). The model is verified by simulations and reasonable agreement is obtained for a 10-Gb/s single span link. Results are presented for different channel spacing, launch pulse duty-cycle, and launch power. The model is strictly valid for systems with low fiber dispersion as it ignores dispersion related pump pulse distortion. It is found that the walk-off effect makes a significant contribution to the detected unfiltered FWM noise and this contribution is mostly concentrated at high frequencies determined by the channel spacing alone. The contribution of the walk-off and its frequency content is understood in terms of intracollision and intercollision interference. In the typical situation when a sub-bit-rate electrical low-pass filter is used, the walk-off effect is effectively removed for all types of FWM. The analytic model is validated by comparing to split-step-Fourier (SSF) simulations. Extension to the general case of multiple FWM lines is considered. It is found that the FWM noise standard deviation is 2 times smaller for RZ-DPSK as compared to that for return to zero on-off keying (RZ-OOK) at the same average launch power for a system with 25-GHz channel spacing. </para>

Optimal bidirectional Raman pumping in dispersion-shifted fibres for WDM inter-channel FWM reduction

Bidirectional Raman pumping schemes for C-band dense-WDM transmission in dispersion-shifted fibres are experimentally investigated taking into account both pump-to-signal and inter-channel four wave mixing (FWM) interactions, as well as optical signal-to-noise ratio (OSNR) performance. For the first time it is shown that an optimal combination of co- and counter-propagating pumping technologies leads to acceptable OSNR performance allowing, at the same time, for an effective reduction of inter-channel FWM crosstalk with limited pump-to-signal FWM interaction.

COMPARISON OF INTERCHANNEL FOUR-WAVE MIXING WITH CONTINUOUS WAVES, QUASI-CONTINUOUS WAVES AND ULTRASHORT PULSES

We compare the interchannel four-wave mixing (FWM) in dense wavelength division multiplexing (DWDM) systems with continuous waves, quasi-continuous waves and ultrashort pulses. The differences are theoretically analyzed for the three inputs. We investigate the FWM conversion efficiency as a function of the channel spacing, the fiber length, the single bit energy and the pulse width. It is shown that the FWM effect in DWDM systems with quasi-continuous waves is the strongest and with ultrashort pulses is the lowest among the three cases. The FWM conversion efficiency changes periodically with the propagation length, and it is approximately an exponential function of the single bit energy. The performance of the pulse FWM effect versus the pulse width is different from that of the quasi-continuous wave FWM, which may be one possible way to suppress the interchannel FWM.