1. Introduction

Recently, long-haul wavelength-division multiplexed (WDM) transport systems have utilized high-level quadrature amplitude modulation (QAM) based formats to achieve high spectral efficiency. Since the required optical signal-to-noise ratio (OSNR) increases quickly with the constellation size, a number of enabling technologies have been employed in such experiments [1–4]. Apart from coded modulation, powerful forward error correction, advanced digital signal processing, and Raman assisted amplification, the use of large-effective-area, low-loss fibers has proved to be crucial. As fiber technologies continue to advance [5–7], quantitative characterization of the benefit brought about by the use of these fibers becomes necessary.

Previously, a few figures of merit (FOM) [8–11] have been proposed to estimate the performance improvement over a reference system in terms of OSNR or Q² factor, link reach, or span loss margin, as a function of fiber and link parameters. Specifically, the OSNR and Q²-factor improvement predicted by the FOM in [8] matched the 112-Gb/s experiments employing polarization-division multiplexed quadrature phase-shift keying (PDM-QPSK) and lumped erbium-doped fiber amplifiers (EDFAs); the FOM for maximum reach in [9] was validated by PDM-QPSK experiments and PDM-16QAM simulations; in [11] the FOM for OSNR estimate was extended to include hybrid EDFA/Raman and all Raman amplification schemes. According to these FOMs, the performance of a fiber link continues to improve with decreasing attenuation coefficient and increasing effective area. Recently, it was pointed out that excess noise, which originated at amplifiers compensating for filtering and switching losses located between fiber spans, caused noticeable performance deviations from the FOMs and more importantly, led to the undermined benefit of low-loss fibers [12]. The investigation in that work was limited to EDFA amplified links. Here, it is extended to systems that are amplified via hybrid EDFA/Raman or all Raman scheme. In order to accurately assess the performances of such systems, the enhanced Gaussian noise (EGN) model [13], which corrects the nonlinearity noise overestimate of the GN model, is adopted, and the analytical methods employed in this work are checked against experiments [14]. For ease of comparison, this work focuses on 256-Gb/s PDM-16QAM WDM transmissions, using the same bit rate per optical carrier and modulation format as in the experiments [14]. The performances of such links of various large-effective-area, low-loss fibers are assessed via the experimentally verified analytical methods, and the corresponding OSNR improvements over a reference system are compared with the FOMs in [8,9,11]. Our results show that the advantage of low-loss fibers can be compromised due to the excess inter-span amplifier noise, especially if distributed Raman amplification is employed, which explains the difference between our analysis and the predictions of the FOMs. On the other hand, the impact of the fiber effective area is essentially independent of the amplification scheme or the excess noise, and agrees with the FOMs. These findings can be extended to high-spectral-efficiency coherent transmissions employing other bit rates and modulation formats.

The rest of the paper is organized as follows. In Sec. 2, the analytical methods for approximating the signal power evolution and nonlinearity noise power are described and then confirmed by 10-channel 256-Gb/s PDM-16QAM experiments, which employed three amplification schemes: EDFA only, hybrid EDFA/Raman, and all Raman [14]. In Sec. 3, the analytical methods are used to investigate the impact of fiber attenuation coefficient and effective area on the received generalized OSNRs, following an explanation of the scaling rules for estimating the Raman gain efficiency and fiber attenuation at the pump wavelength. The analysis starts with the 10-channel 256-Gb/s PDM-16QAM transmissions and then extends to broader bandwidth systems. Additionally, the influence of the excess amplifier noise on fiber comparisons is explored and believed to be the major cause of the difference between our analytical results and the FOMs. Finally the paper is summarized and concluded in Sec. 4.

2. Analytical methods and comparison with experimental data

Consider the experimental system setup in [14], which is also sketched here as Fig. 1. The recirculating loop consists of four fiber spans, a gain-flattening wavelength selective switch (WSS), and an EDFA compensating for the losses of the loop switch and the WSS. Each fiber span is configured such that three amplification schemes can be implemented: EDFA only, hybrid EDFA/Raman with 50:50 gain split, and all Raman. For the hybrid and all Raman schemes, the transmission fibers are backward pumped.

 

Fig. 1 Schematic diagram of the span and recirculating loop configuration. WSS: wavelength selective switch.

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2.1 Analytical models

Throughout this work a generalized OSNR, defined as $OSNR=P_{ch}/(P_{ASE}+P_{NLI})$, is used to assess the system performances of WDM uncompensated coherent transmissions. In this definition, noise powers due to amplified spontaneous emission, $P_{ASE}$, and nonlinear processes, $P_{NLI}$, are taken into account, and $P_{ch}$ is the launch power of a PDM WDM channel. For the setup in Fig. 1, the total accumulated $P_{ASE}$ is $P_{ASE}=N_{span}{P}_{ASE-span}+N_{loop}{P}_{ASE-loop}$, where $N_{span}$ is the number of spans, $P_{ASE-span}=E{F}_{eq}B$ is the ASE noise power contributed by a single span ($E$: photon energy, $F_{eq}$: equivalent noise figure of a single span, $B$: signal bandwidth), and $P_{ASE-loop}$ denotes the additional ASE noise (i.e., excess noise) from the fifth EDFA in the recirculating loop with $N_{loop}$ being the number of loops. For fiber links that are partially or entirely compensated for via distributed Raman amplification, $P_{ASE}$ and $F_{eq}$ can be found by referring to [15,16]. The nonlinearity noise power $P_{NLI}$ can be estimated via the EGN model [13] as the following.

Incorporating distributed Raman amplification, the normalized power evolution of a dual-polarization WDM channel along the propagation distance $z$ can be approximated as [15,16]

Equation (1) is then taken into the EGN model to calculate the power spectral density of the nonlinearity noise. Specifically, Eq. (11) in [13] needs to be rewritten as

2.2 Experimental validation

The analytical methods were verified by comparing with the experiments in [14]. Figure 1 depicts the schematic of the system setup. The WDM comb was centered at 1552 nm and consisted of 10 PDM-16QAM channels at 32-Gbaud symbol rate with 37.5-GHz channel spacing. A WaveShaper was programmed to flatten the signal spectrum over 32 GHz. The fiber had a loss coefficient of 0.185 dB/km at 1550 nm, an average effective area of 122 μm², a chromatic dispersion coefficient of 20 ps/(nm·km) at 1550 nm, and a nonlinearity index of 2.3 × 10⁻²⁰ m²/W. The total extra insertion loss in each 101.3-km long fiber span was estimated to be 1.3 dB. An average noise figure of 5.5 dB was used for the EDFAs in the recirculating loop. Fiber lasers at 1450-nm wavelength provided 500-mW and 900-mW pumping powers, respectively, for the hybrid EDFA/Raman and all Raman amplification. The fiber loss at the pump wavelength and the Raman gain efficiency at 1550 nm were measured to be 0.224 dB/km and 0.248 /km/W, respectively.

Making use of the experimental parameters in the analytical models, the link performances were calculated and compared with the experimental transmission data, and the results are shown in Fig. 2, where the lines represent the calculations and the markers represent the measurements. The amplification scheme is indicated by the color of the markers or line, with blue for EDFA only, red for hybrid Raman/EDFA, and magenta for all Raman. Referring to the bit error ratio (BER) vs. OSNR relationship in [14], which provides the noise loaded back-to-back characterization of the 256 Gb/s PDM-16QAM system, the corresponding Q² factors of the transmissions were obtained from the calculated OSNRs. A center channel of the WDM comb was chosen for the comparison as it suffered the most from the nonlinearity impairment. By fitting the analytical models to the experimentally measured Q² factor at a transmission distance of 2431 km, the total loss of the WSS and the loop switch was estimated to be 16 to 18 dB depending the amplification scheme, which was then used to calculate the excess noise powers at other transmission distances.

 

Fig. 2 Comparison between the calculations (lines) and experimental measurements (markers) for the 10-channel 256-Gb/s PDM-16QAM system using three different amplification schemes. Blue: EDFA only, red: hybrid EDFA/Raman, magenta: all Raman.

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Figure 2 depicts the system performance in terms of Q² factor versus the transmission distance, where the launch powers per channel were all set at the optimal levels. For each of the three different amplification schemes, good agreement has been found between the calculations and the measurements. In the following section, the same analytical approaches will be applied to assess the impact of fiber parameters on the performances of 256-Gb/s PDM-16QAM WDM systems with 37.5-GHz channel spacing.

3. Results and discussion

Utilizing the same system setup as described in Sec. 2 except for the transmission fiber, the performances of different fiber links were analytically investigated and compared. Specifically, the fiber attenuation coefficient at 1550 nm was varied from 0.13 to 0.19 dB/km and the effective area was varied from 80 to 160 µm². Given that the recently proposed large-effective-area, low-loss fibers are mostly the type of pure silica core [5–7], for ease of comparison, the dispersion coefficient was set at 21 ps/(nm∙km) and the nonlinearity index was set at 2.2 × 10⁻²⁰ m²/W for all the fibers in the analysis. These values are slightly different from the corresponding experimental parameters provided in Sec. 2. Once again, the fiber loss was compensated for with one of the three different amplification schemes as previously described. Particularly for the hybrid EDFA/Raman amplifier, the span gain was evenly divided between the EDFA and Raman.

3.1 Scaling of fiber loss at Raman pump wavelength and of Raman gain efficiency

For the systems employing distributed Raman amplification, the attenuation coefficient at the Raman pump wavelength, ${\alpha }_{p-dB}$, as well as the Raman gain efficiency, $C_R$, were scaled using ${\alpha }_{p-dB}={\alpha }_{dB}{\lambda }_s{}^4/{\lambda }_p^4$ [17] and $C_R=C_{R-\exp }{A}_{eff-\exp }/A_{eff}$ [18], respectively, and the errors of the scaling rules were estimated to be less than 10%. Here, ${\lambda }_s$ and ${\lambda }_p$ are the signal and pump wavelengths, $C_{R-\exp }$ and $A_{eff-\exp }$ are the experimental values of the Raman gain efficiency and effective area as described in Sec. 2. In order to understand the influence of the errors on the system performance, the received Q² factors in Fig. 2 for the case of all Raman amplification were recalculated with either ${\alpha }_{p-dB}$ or $C_R$ altered by ± 10%, and the results are plotted in Fig. 3. Specifically, in Fig. 3(a), $C_R$ is fixed at 0.248 /km/W, and the lines correspond to three values of ${\alpha }_{p-dB}$, i.e., 0.224, 0.246, and 0.202 dB/km. The very little difference between the lines indicates that the system performance is not sensitive to the fluctuation in ${\alpha }_{p-dB}$. A closer examination of the calculations revealed that a shift in ${\alpha }_{p-dB}$ resulted in changes in both the amplified spontaneous emission (ASE) and nonlinearity noise powers, however, since the changes were in opposite directions, the total accumulated noise power differed by a very small amount. In Fig. 3(b), ${\alpha }_{p-dB}$ is fixed at 0.224 dB/km. It can be seen that there is virtually no difference between the three lines, which correspond to $C_R=$0.248, 0.273, and 0.223 /km/W, respectively. This is because in our analytical approaches $C_R$ always appears in the form of a product of itself and the backward Raman pump $P_b$, which is determined by the Raman gain in Eq. (2). Therefore, as long as the product remains the same, the system performance will not be affected by the change in $C_R$. In other words, for a fixed Raman gain a higher $C_R$ corresponds to a lower $P_b$ and vice versa. It is worth mentioning that efficient Raman pumping occurs with small-effective-area, low-loss fibers, which can be readily seen from Eq. (2) and the scaling rules for ${\alpha }_{p-dB}$ and $C_R$.

 

Fig. 3 Effect of the scaling error of (a) the fiber loss at the Raman pump wavelength (with $C_R=0.248$/km/W), or (b) the Raman gain efficiency (with ${\alpha }_p=0.224$dB/km), on the performance of the 10-channel 256-Gb/s PDM-16QAM system with 37.5-GHz channel spacing.

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3.2 Impact of fiber loss and effective area on the received OSNRs

The influence of fiber parameters on the performance of a 256-Gb/s PDM-16QAM WDM system with 37.5-GHz channel spacing is illustrated with the contour maps in Fig. 4, where the horizontal and vertical axis are fiber attenuation coefficient and effective area, respectively. As in the previous section, the amplification scheme is color-coded, with blue for EDFA only, red for hybrid Raman/EDFA, and magenta for all Raman. Figure 4(a) shows the received OSNRs in dB/0.1 nm after 2431-km transmission of 10 WDM channels. In Fig. 4(b), the fiber link with an attenuation coefficient of 0.19 dB/km and effective area of 80 µm² is used as the reference, and its performance or system parameter is referred to as the baseline for comparisons. The contours illustrate the OSNR improvements with respect to the baseline. In order to extend the investigation to broad bandwidth transmissions, the performances of 40-channel 256-Gb/s PDM-16QAM systems were also analytically investigated for the range of fiber parameters considered in this work. The same center channel wavelength as in Sec. 2, 1552 nm, was assumed for the 40-channel systems. It was found that as the channel count went beyond 40, further increasing it caused negligibly small change in the received OSNRs, whereas the numerical integrations for estimating the nonlinearity noise power became drastically time consuming. Hence the reason for not going for a larger channel count. The OSNR improvements with respect to the corresponding baseline are depicted as the dotted lines in Fig. 4(b), along with the solid lines representing the 10-channel systems. With a small difference of no more than 0.06 dB between them, both the 10-channel and 40-channel contours indicate up to 4.5, 2.5, and 2.2-dB OSNR upgrade from the baseline for the case of EDFA only, hybrid EDFA/Raman, and all Raman amplification scheme, respectively, as the fiber attenuation and effective area vary. Each OSNR upgrade can be dissected as the following. By increasing the effective area from 80 to 160 µm² while keeping the attenuation coefficient unchanged, a 2-dB OSNR improvement can be achieved for all the three types of amplification. This feature agrees with the FOMs in [8,9,11]. On the other hand, if the effective area remains constant, reducing the attenuation from 0.19 to 0.13 dB/km results in 2.5, 0.5, and up to 0.2-dB OSNR improvement for the cases of EDFA only, hybrid EDFA/Raman, and all Raman scheme, respectively. Figure 4(b) shows that as the attenuation is decreased to below 0.15 dB/km, the performance improvement is very limited for the links that are amplified by hybrid EDFA/Raman, whereas the links that are entirely amplified by Raman suffer from a small performance degradation. In other words, fiber loss has little impact on the system performance if distributed Raman amplification is employed. This is drastically different from the FOM in [11].

 

Fig. 4 (a) Contours of the received OSNRs in dB/0.1 nm after 2431-km transmission of 10 WDM channels. (b) Contours of the OSNR improvements in dB/0.1 nm over the respective baseline performances. Horizontal axis: fiber attenuation coefficient, vertical axis: fiber effective area, blue lines: EDFA only, red lines: hybrid EDFA/Raman, magenta lines: all Raman, solid lines: 10 WDM channels, dotted lines: 40 WDM channels.

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In order to understand the substantially different impacts of the fiber attenuation coefficient on systems employing the three different amplifiers, the received OSNRs of the 10-channel systems after 2431-km transmission were reassessed with the $P_{ASE-loop}$ artificially removed from the total noise. Note that $P_{ASE-loop}$ denotes the excess ASE noise power from the fifth EDFA in the recirculating loop, which was employed to compensate for the insertion losses of the loop switch and the WSS. For each amplification scheme, contours of the OSNR improvements over the respective baselines with and without $P_{ASE-loop}$ taken into account are plotted, respectively, in solid and dotted lines, in the same subfigure of Fig. 5. It can be seen that the excess noise results in significant discrepancy between the solid and dotted lines, especially in the lower loss regions of Figs. 5(b) and 5(c), which respectively represent the links that are partially and entirely amplified via Raman. The explanation is that as the attenuation coefficient decreases, $P_{ASE-loop}$ evolves into a more dominating portion of the total ASE noise power since it is independent of the fiber parameters. At this point, further reducing the fiber attenuation yields little performance enhancement. With the excess noise eliminated from the total noise power, an OSNR upgrade of up to 3.4 dB can be obtained for EDFA only systems, shown in Fig. 5(a), and up to 2.2 dB for hybrid EDFA/Raman and all Raman systems, shown in Figs. 5(b) and 5(c), as the attenuation is reduced from 0.19 to 0.13 dB/km while the effective area remains unchanged. Such investigation was also conducted for the 40-channel systems, and similar findings were obtained. These results suggest that the excess noise in a transmission system should be minimized in order to benefit from low-loss fiber technologies. It is worth mentioning that the impact of the fiber effective area remains virtually unchanged throughout Figs. 5(a)–(c). For instance, at any given value of the attenuation coefficient, an increase in the effective area results in approximately the same amount of OSNR improvement.

 

Fig. 5 Contours of the OSNR improvements in dB/0.1 nm over the respective baseline performances after 2431-km transmission for (a) EDFA only (blue lines), (b) hybrid EDFA/Raman (red lines), and (c) all Raman (magenta lines) amplification scheme. Horizontal axis: fiber attenuation coefficient, vertical axis: fiber effective area, solid lines: with $P_{ASE-loop}$ included in the total noise power, dotted lines: without $P_{ASE-loop}$ in the total noise power.

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Although the work presented here focuses on 256-Gb/s PDM-16QAM transmissions, analyses for other bit rates and modulation formats have been conducted, and since the results and conclusions are similar they are not included in this paper.

3.3 Comparisons with previously proposed FOMs

Our findings were compared with the previously proposed FOMs [8,9,11], assuming the same setting as in the 10-channel 256-Gb/s PDM-16QAM 2431-km transmissions described above. The link performance enhancements (ΔOSNR) of three fibers, labeled as A, B, and C, with respect to the baseline, are listed in Tab. 1. As before the fiber with an attenuation coefficient of 0.19 dB/km and an effective area of 80 µm² is used as the reference. Predictions of the FOMs are also included respectively for systems employing the three different amplification schemes. Due to the same system setup except for the transmission fiber, the FOMs in [8] and [9] can be reduced to the same form, which explains their identical predictions. It can be seen that the difference between the FOMs and our analytical results is 0.4 dB or less if the excess noise is completely eliminated, indicating very good agreement. With the excess noise included in our analysis, the agreement is still reasonable for the case of EDFA only scheme with up to 0.7-dB difference, but no longer holds for the case of hybrid EDFA/Raman or all Raman amplification with up to 2.1-dB difference. From the viewpoint of fiber comparison, although Fiber C has lower attenuation coefficient than B, its advantage is limited to systems employing EDFA only scheme due to the presence of the excess noise.

Table 1. Comparisons of fibers and with previous FOMs

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4. Conclusions

The impact of the fiber attenuation coefficient and effective area on the system performances of high-spectral-efficiency coherent WDM transmissions has been investigated by applying the experimentally validated EGN model. The analytical results were compared with the previously published FOMs, and conditions for good agreement have been understood. When the excess ASE noise is minimized, our results have shown that the link performance continuously improves with the decreasing attenuation coefficient, and agrees with the predictions of the FOMs in [8,9,11]. However, when the excess noise becomes significant, the FOMs tend to overestimate the link performance. As is the case with recirculating loop experiments employing distributed Raman amplification, the excess noise may reach a level where very little or even negative performance gain can be obtained as the fiber attenuation is reduced to below 0.15 dB/km. On the other hand, the magnitude of performance enhancement owing to increased fiber effective area remains approximately the same regardless of the amplification scheme or the excess noise, and agrees with the FOMs. For links that are amplified via hybrid EDFA/Raman and all Raman, efficient pumping occurs with small-effective-area, low-loss fibers, therefore, a tradeoff between high system performance and low power consumption needs to be found for such systems.