We demonstrate a nonlinear signal processing approach for compensating nonlinear distortion caused by the Kerr effect in optical fiber transmission. The concept relies on propagating the signal through a separate all-optical module outside the link to apply tunable nonlinear distortion and phase-conjugation in series. We show this uniquely enables tunable regeneration of phase-encoded 40 Gb/s signals of different data-formats and number of WDM channels, to allow significantly higher transmission powers through single and multi-span fiber links. An improvement in the receiver power penalty by 3~4 dB for a bit-error-rate (BER) of ≈10−5 is achieved.
©2012 Optical Society of America
Advances in optical fiber communications led by the expansion of wavelength division multiplexing (WDM) of signals modulated onto many tens or hundreds of unique wavelengths of light have achieved data capacities of several Tb/s . But with the available spectrum for transmission over fiber exhausted, the race to higher capacity to meet the ever increasing demand has turned towards encoding more information within the limited spectrum by multi-logic level modulation of both the amplitude and phase of the optical field [2–5], beyond conventional binary amplitude modulation. This solution comes at a price however. Information theory proves that encoding more logic levels at the same modulation rate requires a higher optical signal to noise ratio (OSNR) after transmission through a noisy channel to avoid a loss of information due to bit-errors . This can be achieved by boosting the signal power, but that increases its susceptibility to nonlinear distortion from the Kerr effect of optical fiber , which produces a linear change in the refractive index with optical field intensity . This gives rise to self phase modulation (SPM), whereby the time varying power of the signal modulates its phase and frequency . For signal transmission in a dispersive fiber, the Kerr effect leads to nonlinear mixing between the fields of neighboring bits, that have temporally dispersed and overlap . For WDM systems, the Kerr effect also causes cross phase modulation (XPM) and four wave mixing (FWM) between neighboring channels . These distortions cap the maximum data capacity and transmission distance in optical fiber.
A promising solution to this problem is digital signal processing (DSP) [2,4,10–13]. This operates on the electrical rather than optical signal to compute an algorithm that cancels the distortion. However, practical limits on the circuit size and power consumption [11,12] limit the number of computation steps, at the expense of signal regeneration performance. While advanced algorithms can relax this compromise , every channel in a WDM system still requires its own circuit (or a pair for a polarization diversity receiver implementation ).
Nonlinear optics offers a potentially simpler yet powerful approach that can suppress the nonlinear distortion all-optically by propagating the signal through a nonlinear medium. Phase sensitive amplification using FWM with a CW pump that is phase locked to the signal has demonstrated impressive regeneration of phase encoded signals , although only for individual WDM channels. Simultaneous compensation of nonlinear distortion for WDM signals on the other hand, has been demonstrated using optical phase conjugation (OPC) [9,15–17]. This also uses FWM (or an equivalent process ) with a CW pump but without the need for phase locking. In that scheme, the new field produced at a new wavelength by FWM has an amplitude, Ai (t)∝ As*(t), where As is the time (t) varying signal field amplitude, and the asterisk denotes phase-conjugation of the complex field vector from As = x + jy, to As* = x − jy. This operation allows OPC for different signal bit-rates, data formats [9,16,17], and multiple WDM channels (exceeding one hundred ).
The traditional approach for compensating nonlinear signal distortion is to position OPC along the link, where reversing the sign of the nonlinear phase distortion leads to its optimal cancellation at the receiver (Rx) [9,17]. This, however, has the drawback of limited flexibility, since the primary design variable is the OPC position, which is dictated by the fiber link parameters, and must therefore be tailored to the specific link length, fiber type and signal. It also must be deployed at a distant and likely remote location, where the signal’s state of polarization and wavelength conversion [18,19] must also be managed.
This paper presents a different approach for enabling optically tunable compensation of nonlinear signal distortion by pre-processing the signal outside the link to apply an additional nonlinear phase distortion, that when combined with OPC, produces an opposing distortion to that produced in the link. We show this is capable of regenerating 40 Gb/s DPSK signals in optical fiber transmission to reduce the bit-error rate (BER) power penalty by ≈4 dB, and improve the equivalent Q-factor by up to 2.6 dB. The same module also demonstrates operation for different signal formats, and transmission distances, and the parallel processing of multiple WDM channels.
Figure 1 illustrates the concept. In traditional OPC, maximizing regeneration relies on matching the nonlinear phase distortion induced in the transmission fibers both before and after OPC. This requires accounting for the non-zero propagation loss and chromatic dispersion of the optical signal by ensuring the fiber dispersion map in the nonlinear regions of the link is symmetric about the OPC point . The nonlinear region is dictated by the exponential decrease in signal power over distance, z, due to fiber loss, which confines the major nonlinear behavior in a fiber span (of length, L) to a shorter effective length indicated by Leff = (1/α)⋅[1−exp(-α⋅z)], where α is the loss coefficient (related in decibel units as αdB = 4.343 α) . In practice, optical communication fibers typically have αdB ≈0.2 dB, which gives a corresponding Leff ≈22 km in the mathematical limit of z→□∞. Therefore, since long distance optical fiber links generally employ L » Leff to reduce the number of in-line EDFAs needed for optical amplification, fiber nonlinearity dominates for only a fraction of L. It is noted that the nonlinear region would be modified by the use of distributed gain based on Raman amplification.
Our approach for enabling optically tunable compensation of nonlinear signal distortion is shown in Fig. 1 and relies on propagating the signal through an all-optical module outside the link to apply tunable nonlinear distortion (TD) in combination with OPC. The TD-OPC module modifies the field vector of a signal in the complex plane to acquire an opposite phase rotation to that produced in the fiber link, and thereby enable regeneration of the signal phase.
The flexibility of the TD-OPC module in contrast to traditional OPC is the ability to arbitrarily tailor the TD stage by tuning the input optical power, PNL, and choosing a waveguide of particular length, LNL, nonlinearity coefficient, γNL and dispersion, so that the locus of the field vector intersects the phase rotation induced by the nonlinear distortion of the link. Figure 1 illustrates how dispersion symmetry can be satisfied for a single TD stage in the TD-OPC. It uses a fiber of the same type as that in the fiber link, and of length comparable to each span’s nonlinear region, which in Fig. 1 is approximated to Leff, with an average power Peff. Note, the negative Peff in the TD-OPC represents the reversal of the sign of nonlinear phase distortion due to OPC. In the fiber link, every span is post dispersion-compensated (with dispersion compensating fiber (DCF) for example) to assure the signal dispersion in the TD-stage is symmetric with respect to that in the nonlinear region of each fiber span.
By this approach, TD-OPC enables the accumulated nonlinear phase distortion from the cascaded nonlinear regions for multiple fiber spans to be replicated in a single TD-stage by simply tuning PNL depending on both the signal input power to the link, Pin, and the number of spans. This enables the scalability of the scheme to multi-span fiber links. Unlike in conventional OPC, the power profile versus distance can therefore be highly asymmetric as shown in Fig. 1.
The flexibility of the TD-OPC scheme is that it is designed to compensate fiber nonlinearity only and not dispersion, even though an OPC module could potentially do both . Instead, dispersion management in the link is left to conventional methods, such as inserting DCF. This avoids the complexity of designing the dispersion of the TD medium to match the entire link dispersion , and scaling it to impractically large size for longer links. Moreover, changing the TD medium’s dispersion and length unavoidably impacts nonlinear propagation as well, thereby constraining the design flexibility for maximizing regeneration. Also, managing the fiber dispersion slope (variation with wavelength) would require tailoring a separate module for every WDM channel . This is energy inefficient and less practical.
In contrast, the TD-OPC module with the experimental set-up shown in Fig. 2(a) demonstrates flexible, all-optical nonlinear distortion compensation for different data formats, multi-span fiber links, and multiple WDM channels (highlighting its parallel processing capability). This in turn permits longer fiber between optical amplifiers. We compared transmission of 40 Gb/s signals encoded by differential phase-shift keying (DPSK) with either return-to-zero (RZ), carrier-suppressed-RZ (CS-RZ) or non-return-to-zero (NRZ) amplitude modulation.
3.1 Transmitter(Tx) & Receiver (Rx)
The signal Tx for all experiments used a WDM multiplexer (MUX) to combine as many as three co-polarized CW lasers separated by 100 GHz on the ITU grid. In the case of not using TD-OPC, the center wavelength was 1558.98 nm (ITU Ch. 23). The lasers were simultaneously modulated by a pair of Mach-Zehnder modulators (MZM) connected in series– the first for encoding a DPSK pseudo random bit sequence of 231−1 pattern length, and the next for carving the amplitude into 40 GHz pulses in the case of CSRZ and RZ formats, whose pulse duty cycles were 66% and 33%, respectively.
The Rx for all experiments incorporated an EDFA as a pre-amplifier, followed by a 43 GHz DPSK demodulator, 0.55 nm bandwidth tunable bandpass optical filter (BPF) and 40 Gb/s photo-receiver. The input optical power to the photo-receiver, Prx, was monitored via the 1% port of a 99:1 coupler connected at its input. Although a balanced photo-detector was not used in this work, it was not essential for evaluating the BER improvement by TD-OPC.
3.2 Fiber link
Signal transmission was initially investigated for a single span fiber link of length 177 km assembled from an arbitrary mix of 78 km of standard single mode fiber (SMF) (with dispersion of 16.5 ps/nm.km at 1550 nm wavelength), and 99 km of a similar fiber with slightly larger dispersion of 20 ps/nm.km at 1550 nm. Notably, such long L was not essential for the technique, and a shorter more typical 50-80 km length could have been used without significantly changing the results since L » Leff (i.e. ≈22 km). Rather, it served to highlight the capability for using higher Pin enabled by nonlinearity compensation to overcome higher span loss and maintain the minimum output OSNR requirement. In this case, the span loss was 37 dB. However, for all fiber link configurations considered in this paper, every span was followed by a variable optical attenuator (VOA) that fixed the span loss to 39 dB to ensure a consistent output OSNR at the Rx for a given Pin. The higher Pin in turn enabled a larger nonlinear distortion to be produced with a small number of spans. This could equivalently be produced for a larger number of spans with lower Pin. The link dispersion was optimally post-compensated using DCF after boosting the signal to an optimum power of 1~3 mW per channel to minimize the signal BER at the Rx. Signal transmission through a dual-span fiber link was also investigated by simply splitting the 177 km span in two of length 91 and 86 km. The DCF at the link output was also divided, allowing a spool with dispersion of −1653 ps/nm to be inserted after the second span. Observing the output signal waveform from the Rx on an oscilloscope confirmed that the residual dispersion for the first span with the remaining DCF was close to zero.
The signal Pin for each span was set by an EDFA that was followed by a BPF to remove amplified spontaneous emission (ASE) noise, and a 99:1 coupler for monitoring Pin at the 1% port. For WDM signals, both Pin and PNL per channel were calculated from the total input power divided by the number of channels. Also, the input channel powers were adjusted so that their output powers after transmission differed by within ± 0.1 dB, as observed on an optical spectrum analyzer with resolution bandwidth (RBW) of 0.5 nm. For the dual span link, an equal input power reading was set for both spans, but because of the slight coupling differences for the 99:1 couplers, the second span Pin was 33% higher than for the first. Thus, the average Pin of both spans was used for reference.
3.3 TD-OPC module
The TD stage for nonlinear signal distortion used SMF with LNL = 17.6 km (comparable to the link’s Leff ≈22 km). Optimizing the choice of LNL and the other physical parameters of the TD stage allows signal regeneration to be maximized. In this experiment, this was achieved by tuning PNL using a low noise EDFA followed by a high power EDFA preceding the SMF.
The OPC stage shown in Fig. 2(a) used FWM of the signal with a CW laser as the pump in a 100 m long highly nonlinear optical fiber (HNLF) with γ = 21 W−1km−1, and zero dispersion wavelength of 1551 nm. While this used χ(3) nonlinearity, the OPC operation can equivalently be performed using the χ(2) nonlinearity in different media [9,18,19], and in either case, using a compact chip scale device [9,16–21]. For all experiments, the CW laser wavelength was fixed at 1555.36 nm, and the Tx laser center set to 1551.7 nm so that the phase conjugated signal formed at ITU Ch. 23 (1558.98 nm) and therefore matched the no-OPC case. The polarization of the signal and CW laser were optimized by polarization controllers (PC) to maximize the power of the converted signal, which was extracted by a cascade of two tunable BPFs of bandwidth 4 and 3 nm, and one notch fiber Bragg grating filter to reject the CW pump. The CW pump power into the HNLF was fixed at 130 mW for all experiments, while the total signal power was ≈15 mW. The output signal power from the TD-OPC module was 30~50 μW.
Using the TD-OPC required extending the fiber link from 177 to 191 km by adding extra fiber to near its output in order to compensate for the dispersion of the TD-stage. In the case of the dual span link, the second span was extended from 86 to 100 km.
3.4 Pre-dispersion module
Since TD-OPC introduces normal sign group velocity dispersion (GVD), which itself alone can impact signal transmission in fiber [22,23], the effect of applying only pre-GVD to the signal was also investigated to confirm the origin of signal regeneration. This was implemented by simply re-arranging spools of SMF and DCF in the original 177 km long link so that the overall total dispersion remained unchanged. In order to apply a pre-GVD matching the ≈−290 ps/nm for the TD-OPC, the pre-GVD module incorporated an EDFA at its input, followed by a 23 km SMF (relocated from the link’s output) and a VOA before a DCF (−661 ps/nm). The reconfiguration shortened the fiber link length from 177 to 154 km, (which had minimal impact on nonlinear transmission since L » Leff). The optimum input signal power to the module’s fibers was optimized to around a few milliwatts to minimize the link output BER. Nonlinear distortion in the pre-GVD module was therefore negligible.
4. Results and discussion
Signal transmission without TD-OPC was initially investigated. Figure 3(a) plots the BER versus Pin for transmission of a CSRZ signal over 177 km, and shows a minimum BER at Pin ≈24 mW. For either lower or higher Pin, the BER was degraded due to increased ASE from amplifying a weaker signal after transmission, and nonlinear distortion from enhanced SPM and intra-channel mixing , respectively.
The TD-OPC module was then inserted with the set-up shown in Fig. 2(a). Figure 3(a) shows its flexibility for regenerating signals with Pin up to 120 mW. Inserting it before the 191 km link nearly doubled the optimum Pin for minimum BER to 46 mW (equivalent to a further ≈15 km transmission for the same output OSNR), and the BER was significantly reduced by ≈3 orders of magnitude, despite the output OSNR not being higher. Figure 4 shows for each Pin, the optimum PNL for minimum BER followed PNL ≈1.7Pin. Figure 3(b) shows an optimum PNL exists where the output signal BER is minimized and the signal spectrum can be restored to nearly its original.
The effect of applying only normal dispersion to the signal in place of TD-OPC was also investigated by substituting the TD-OPC module with the pre-GVD module described in Section 3.4. However, Fig. 3(a) shows its use only degraded the output BER, which confirmed that signal regeneration achieved with the TD-OPC module was not due to simply applying pre-GVD to the signal.
Similar results were also observed for RZ-DPSK signals. Figure 5 shows by using TD-OPC with Pin = 72 mW, the floor in the BER was reduced to enable error free transmission (BER = 10−9) with a 1.5 dB power penalty compared to the “back-to-back” (B2B) BER measured with the signal Tx connected directly to the Rx.
The TD-OPC also enabled error free transmission in the dual span fiber link. For a 40 Gb/s RZ DPSK signal with average Pin per span of 47 mW and input spectra shown in Fig. 2(b)iii, the link output BER was improved by almost four orders of magnitude (at Prx = −6 dBm), and the receiver power penalty reduced by 4.3 dB at a BER of 5 × 10−6, as shown in Fig. 5(a). Comparing the output signal spectra at the Rx in Fig. 5(b) highlights the reduced distortion from using TD-OPC. The equivalent Q factor improvement was 2.6 dB. The scheme can also be scaled to compensate the nonlinear distortion in a larger number of spans. It is noted that a comparable degree of regeneration is also predicted for a similar magnitude of nonlinear distortion induced over a larger number of fiber spans with lower Pin, (and correspondingly lower span loss to meet the minimum output OSNR requirement).
The TD-OPC module also demonstrated the flexibility to regenerate WDM signals. Transmission in a single span link was investigated for a 3 × 40 Gb/s NRZ-DPSK signal with 100 GHz channel spacing and input spectrum shown in Fig. 2(b)iii. Figure 6 shows NRZ suffers more nonlinear distortion than CSRZ or RZ, and although pre-GVD before the link improved the BER, TD-OPC with optimized PNL (Fig. 4) still enabled the lowest BER for all channels at higher Pin. Similar results were observed for the single channel signal (Fig. 6).
Regeneration of both channels of a 2 × 40 Gb/s RZ-DPSK signal with 200 GHz channel spacing was also demonstrated for transmission through a dual span fiber link. Calculation of the equivalent Q-factor from the output BER at fixed Prx, revealed a significant Q-factor improvement (ΔQ) of close to 2 dB for both channels. Table 1 summarizes the regeneration achieved in the various experiments from calculation of the equivalent Q-factor and corresponding ΔQ when comparing TD-OPC to either pre-dispersion or no TD-OPC cases. It shows ΔQ of 1.3 to 2.7 dB, which is comparable to that reported for DSP .
In conclusion, we demonstrated a novel approach for optically tunable signal regeneration that extends the maximum transmission distance beyond the power limits imposed by fiber nonlinearity. We showed that an all-optical module applying both nonlinear distortion and phase conjugation to the signal outside the link enabled tunable regeneration for multiple DPSK signal formats, multiple WDM channels, and both single and dual-span fiber links. The scheme is also capable of simultaneously compensating both XPM and FWM. More sophisticated parameter tailoring will further improve the regeneration capability for longer distance, unrepeated transmission, and transmission through a larger number of fiber spans.
M.D. Pelusi was supported by the Australian Research Council (ARC) Future Fellowship program. B.J. Eggleton was supported by the ARC Federation Fellowship program. This research was also supported by the ARC Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (project number CE110001018).
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