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Abstract
The practical cable design for optical submarine communications has a limited fiber pair count due to the mechanical considerations of cable weight and size. Consequently, multi-core fibers (MCFs) could exhibit higher capacity than conventional single-mode fibers (SMFs) thanks to space division multiplexing (SDM). That is because the power supply to a submarine cable is fed by the voltage difference between shores. Under the power-limited condition, SDM improves the cable capacity by using more paths which outperforms the SMF link whose capacity approximately complies with a logarithmic relationship to optical power. At the same time, fiber nonlinearity can be alleviated by the reduced power density of transmitted light in MCFs, due to the increased spatial diversity and mode coupling among coupled cores. In this work, we theoretically investigate the potentials of MCFs including weakly-coupled multicore fiber (WC-MCF) and strongly-coupled multicore fiber (SC-MCF) as the propagation media for submarine communications across the Atlantic and the Pacific. To fairly compare the performances of SMFs- and MCFs-based submarine cables, the Gaussian noise (GN) model for SDM links is employed to optimize the systematic settings including spatial multiplicity and single span length. Then, we develop an SDM and wavelength division multiplexing (WDM) fiber transmission model based on coupled nonlinear Schrodinger equations (CNSE) to investigate the optical filed coupling effect in MCFs-based cables. The developed transmission model has been self-examined by measuring the inter-core crosstalk (IC-XT) and spatial mode dispersion (SMD), referring to the set values. As indicated by the theoretical analysis, the WC-MCFs cable exhibits a larger capacity than the SMFs cable, when the fiber pair count is limited below 32. Moreover, the SC-MCFs cable outperforms the WC-MCFs cable thanks to the reduced fiber nonlinearity due to the random mode coupling and the assistance of multiple-input and multiple-output digital signal processing (MIMO-DSP). At last, the marginal influences of IC-XT, SMD, and insertion loss of Fan-in and Fan-out couplers are also analyzed for the MCFs cable.
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1. Introduction
Optical submarine communication cables act as the backbone of communications on earth which carry on a huge amount of communication data. Due to the fact that the electrical power supply to the repeaters of submarine cables is fed by the stepped voltage decreasing between shores, power efficiency is a specific consideration for optical submarine cable design. Under the limitation of power-feeding equipment, it has been proved that repeaters in submarine cables should be equally spaced for achieving maximum power feeding efficiency. Optical power supplied by all repeaters can be given by Eq. (1) when the feeding electrical current is optimized [1],
where $V$ is the feeding voltage, $R$ is the resistance of feeding electrical cable in $\Omega /km$, $L$ is the cable length, then the span length can be obtained by $l=L/(N+1)$ and $N$ is the number of repeaters. $\eta$ is the overall electrical-to-optical (E/O) conversion efficiency of repeaters, taking consideration of the power overhead for controlling and optical amplifier’s E/O efficiency.In addition to the power feed equipment (PFE) optimization, the other parameters also influence the capacity of submarine cables, including $l$, spatial multiplicity $M$, signal-to-noise ratio (SNR), and modulation format. For the SMFs-ribbon-based submarine cables, i. e. SMFs cable, the optimal SNR to achieve the best power efficiency (PE) performance has been derived to be $1.72$ [2], which provides guidance to choose the appropriate modulation format and FEC implementation for submarine cables. However, the optimization of span length and the spatial number has been discussed with the consideration of the droop effect in SMF-based submarine cable [2].
It is worth mentioning that, the fiber nonlinearity can not be neglected even for the power-limited submarine cable because the transmission distance is over several thousands of kilometers. Taking fiber nonlinearity into consideration, the power saving of submarine cables has been theoretically proved to be efficient by SDM using the SMFs ribbon [3]. This advantage can be attributed to two reasons: 1) SDM improves capacity with an approximately linear relationship to optical power, that outperforms an SMF link complying with the logarithm relationship between capacity and optical power. 2) Reduced power density by SDM results in less fiber nonlinearity. On the other hand, the SDM of optical submarine cables using multi-core fiber (MCF) has also been theoretically evaluated. Gaussian noise (GN) model without considering inter-core crosstalk (IC-XT) has been developed for analyzing MCFs submarine cable performances [4]. It concludes that when the overall spatial multiplicity is constant, the MCFs cable is not better than the SMFs one in the aspect of capacity, due to the additional losses by Fan-in and Fan-out (FIFO) and the corresponding splicing points. However, the practical submarine cable design has a certain fiber count limit due to the considerations of cable size and weight [5]. That is because severe bending will occur if the cable has a large cross-sectional area. Consequently, the MCFs cable possesses the capacity advantages over the SMFs one under the fiber count limitation, because the higher density of SDM can be achieved. Additionally, the strongly-coupled MCF (SC-MCF) could further reduce the impact of fiber nonlinearity thanks to the random mode coupling among cores [6]. As a result, it is worthwhile to investigate the capacity of weakly-coupled MCFs (WC-MCFs) and SC-MCFs cables with a comprehensive consideration of inter-core crosstalk (IC-XT), insertion loss of FIFO, and spatial mode dispersion (SMD), under the limited power supply and fiber count.
In this work, we first conducted a GN model with the IC-XT consideration for evaluating the MCFs cables, then theoretically optimize the system settings of the cables across the Atlantic and the Pacific, including span length and spatial multiplicity. Based on the optimized settings, fair comparisons between the SMFs- and WC-MCFs-based submarine cables under certain fiber counts are performed, with a comprehensive consideration of fiber nonlinearity, signal droop effect, and insertion loss of FIFO and IC-XT. Results indicate that 4-core WC-MCFs outperform SMFs in submarine cables when fiber count is limited below 32. Then, we further develop an MCF transmission model based on CNSE, to evaluate the transmission performances of SC-MCFs cables. By using dual-polarization quadrature phase shift keying (DP-QPSK) format, SC-MCFs cable could improve Q-factor by 0.75- and 2-dB over the WC-MCFs cable for the trans-Atlantic and -Pacific cases respectively, thanks to the random coupling and the use of multiple-input and multiple-output digital signal processing (MIMO-DSP). At last, the marginal influences of FIFO, IC-XT, and SMD are also analyzed.
2. Systematic settings optimization strategies for optical submarine cables
For maximizing the capacity of a submarine cable under the power and fiber count limitations, the system parameters including span length and spatial multiplicity need to be optimized. It should be noted that accumulated ASE noise along the cable dominates rather than the noise generated by the electrical-optical devices at the transmitter and receiver on the shores, due to the larger number of repeaters deployed in a submarine cable. That is also because the utilization of coherent detection has a high receiving sensitivity, in which case the thermal noise of electrical-optical devices can be ignored. Capacity (in directions) of a submarine cable can be formulated by Eq. (2).
where $B$ is the amplifiers’ bandwidth, $SNR$ is the cable end-to-end SNR, $M$ is the bidirectional spatial multiplicity that equals to the production of fiber pair count $M_{fiber}$ and core number per fiber $M_{core}$. When optical power maintains the same at the output of every repeater, the signal power will be reduced along the cable due to the accumulated ASE noise power added by every repeater [7]. That is called as signal droop effect. Then, SNR at the end of a submarine cable can be derived as follows, where $N$ is the repeater number, $P_1$ is the output optical power per spatial dimension at the end of a cable, which can be obtained by $P_1=P_{tot}/(M\cdot N)$. $P_{ase+NLN}$ is the ASE and nonlinearity power per spatial path at the end of a cable, which can be approximated by Eq. (4) when amplifiers work in the saturated mode [3].In Eq. (4), $\alpha$ is the fiber attenuation coefficient, $F$ is the amplifier’s noise figure. $h$ is Plank’s constant. $v$ is the central frequency of the ASE spectrum. Firstly, we extract the second-order noise contribution coefficient $\chi _1$ using the source codes provided in the appendix of [8]. Then we derive the coefficient $\chi '$ in Eq. (4) which is independent of $B$ and single channel bandwidth $B_{ch}$ by
Consequently, capacity in the non-droop case can be calculated by [3],
While for the long-haul submarine cables with the signal droop effect, the corresponding capacity estimation should be written as
For achieving the highest capacity, optimizations of systematic settings are quite different for these two cases. Without considering the signal droop effect, the highest capacity will be achieved at an infinite spatial path [3]. That results in zero SE, which is not practical. Consequently, the systematic settings including $B$, $l$, $SNR$, and $M$, need to be optimized considering the signal droop effect:
- Optical bandwidth, fiber pair count and core number per fiber
There are two main approaches to boosting the capacity of optical communication systems, namely ultra-broad band modulation and high-density SDM. However, for obtaining the optimal capacity performance of a submarine cable, there is an intrinsic trade-off between $B$ and $M$. In detail, when $M$ is at a relatively small value, $P_{tot}$ can support a larger range of $B$. On the contrary, the increasing of $M$ results in the decreasing of $B$. To coarsely estimate the optimal value of $M$, NLN is neglected here and it has been proved to be accurate when $M$ is more than 16 [3]. Substitute $P_{ase+NLN}$ in Eq. (7) by $B$ and neglect the NLN term, then can get
From the formalization of Eq. (8), we can know that $C(B\cdot M)$ is convex, and its global maximization can be achieved at the zero of the derivatives $B\cdot M = \frac {4P_{tot}}{(e^3 F-e)\cdot hv (L\cdot \alpha -2)^2}$. MCF has a larger core number $M_{core}$ than SMF, so the MCFs cable could provide a much higher $M$ than the SMFs cable. According to $B\cdot M = \frac {4P_{tot}}{(e^3 F-e)\cdot hv (L\cdot \alpha -2)^2}$ for maximizing PE, the MCFs solution could alleviate the requirement of the broad-band WDM modulation and amplification.
- Single span length
According to Eq. (7), $l$ affects the power density of ASE noise $P_{ase}$ by $P_{ase}=(e^{\alpha l}F-1)hvBN$. Then we could define the function $N\cdot P_{ase}$ as $F(l)$, which is also convex. So the optimal value can be found with $F'(l)=0$. Then, the optimal span length can be obtained by $l=2/\alpha$. It indicates that optimal span length is only relevant to fiber attenuation.
$SNR$ per spatial path needs to be optimized to realize the overall capacity at its maximum. Based on Eq. (8), we can get SNR by
Based on the above derivations, the optimized $B\cdot M$ equals to $\frac {4P_{tot}}{(e^3 F-e)\cdot hv (L\cdot \alpha -2)^2}$ and the optimized $N$ equals to $\frac {\alpha L}{2}-1$. Then we can get the corresponding optimal SNR is $e-1$. That agrees with the result of the optimization strategy for achieving the highest power efficiency of the submarine cable in [2]. According to Shannon capacity theory, SE over two polarizations when $SNR=1.72$ is 2.89 bits/s/Hz. That corresponds to the DP-QPSK formats with the ideal entropy of 4. In addition, forward error corrections (FEC) are also mandatory for recovering the transmitted signals in submarine cables.
3. Capacity comparison for the SMFs, WC-MCFs, and SC-MCFs optical submarine cables
3.1 Shannon capacity comparison between SMFs and WC-MCFs based submarine cable
Here, we investigate two typical scenarios of sub-sea communications across the Atlantic and the Pacific with transmission distances of 6000km and 11000km respectively. Corresponding PFE voltages are 15kV and 30kV respectively, representing the practical upper limit for the modern submarine systems [3,9]. The power supply cable resistance $R$ is 1 $\Omega /km$. The overall E/O conversion efficiency of repeaters $\eta$ is $1.5\%$. The higher E/O efficiency of repeaters could further improve the cable capacity. Especially for the MCFs cables, advanced amplification schemes like the cladding pumping and co-doped active fiber are promising solutions to further boost the submarine cable capacity [10,11]. The quantitative influence of the repeaters’ E/O efficiency on the cable capacity will be analyzed later. Then, the total optical power generated by all repeaters $P_{tot}$ for the Atlantic and Pacific cables can be calculated at 140.6W and 306.8W according to Eq. (1). The optical amplifier bandwidth is 4.3THz, for the full-C band transmission. For optimizing the capacity of the submarine cables across the Atlantic and Pacific, the fixed settings are given in Table 1. Then, the achievable capacity can be theoretically estimated by GN model [12], with modeling the NLN interference as a Gaussian-type noise as given in Eq. (4).
Table 1. Systematic settings of the trans-Atlantic and trans-Pacific cables
Figure 1 depicts $M$ vs. capacity curves for the trans-Atlantic and trans-Pacific cables. As indicated by Fig. 1, in the trans-Atlantic case, fiber nonlinearity can be neglected when $M$ is larger than 40. Similarly, fiber nonlinearity becomes insignificant when $M$ is larger than 40 for the trans-Pacific cable. Moreover, the maximum capacity for the trans-Atlantic cable is achieved with $M$ at 351. However, the traditional submarine cables can hardly tolerate such a large size of fiber ribbons if utilizing SMFs [5]. In this case, the MCF technology could provide a higher spatial density, so that posses a much closer performance to the optimal capacity. As for the trans-Pacific cable, the maximum capacity is achieved with $M$ at 226, which is also difficult to approach by manufacturing SMFs in cables. As conclusion, the MCF technology having a much larger spatial multiplicity can improve the capacity of the trans-Atlantic and trans-Pacific cables when the cable size is mechanically limited, although the additional loss by FIFO and the splicing points concern. In addition, fiber nonlinearity can be alleviated using MCF technology. It also can be observed that, for the trans-Pacific cable, the capacity improvement by the space multiplexing is not as significant as in the case of the trans-Atlantic cable. That is because the power supplying resistance and the span number of the trans-Pacific cable are higher, the signal droop-induced capacity reduction occurs earlier when the spatial multiplicity is increasing. As a result, it is worthwhile to quantitatively investigate the capacity gain by MCFs under the constraint power and fiber count.
Fig. 1. Cable capacity vs. spatial multiplicity with the constrained feeding voltages and $1.5\%$ EO efficiency of optical amplification for (a) the trans-Atlantic and (b) the trans-Pacific cables.
It should be noted that the results in Fig. 1 are based on the 15-kV and 30-kV feeding voltages and the unlimited fiber count in submarine cables. For the more practical analysis, we consider four fiber pair count scenarios at 8, 16, 24, and 32 pairs. At first, we investigated the weakly-coupled MCFs (WC-MCF) with core numbers below 16 For the standard cladding diameter at 125um. Performance degradation due to the IC-XT of WC-MCF will be analyzed in the next part. Figure 2 depicts the relative capacity (the ratio between the MCFs and SMFs cable capacity) as the function of core number per fiber and optical power supply (power generated by all repeaters for all spatial paths), with different fiber pair count for the trans-Atlantic cable.
Fig. 2. Relative capacity of WC-MCFs cable to SMFs cable as the function of core number and optical power with different fiber counts for the trans-Atlantic cable.
In general, the relative capacity of MCFs cables increases with the increase of optical power. Moreover, when more fiber pair counts are available, more improvement in cable capacity can be achieved. Typically, when the fiber pair count is 8 and the optical power supply is sufficient at 300W for the trans-Atlantic cable, more than 11 times of capacity gain by MCFs to SMFs cable can be obtained. As the increasing of fiber pair count, the relative capacity of MCFs cable to SMFs cable becomes smaller. That is because the capacity of SMFs cable also increases with spatial multiplicity. While for MCFs cables, the signal droop effects will lead to the capacity decreasing at larger spatial multiplicities. That agrees well with the results in Fig. 1 which describes the signal droop effect’s influence at larger spatial multiplicities. In addition, it is notable in Fig. 2 that there exist the optimal values of core number for achieving the highest capacity gain of MCFs-based cable, at different fiber pair counts. As the typical case of 15-kV feeding voltage and $1.5\%$ E/O conversion efficiency of repeaters, MCF solution could provide more than 6, 3, 2, and 2 times capacity gains over the SMFs cable, with fiber pair count at 8, 16, 24, and 32 respectively.
For the trans-Pacific cable, capacity gain by MCFs is relatively smaller compared to the case of the trans-Atlantic cable as indicated by Fig. 3. That can also be explained by the results in Fig. 1(b) that the signal droop occurs earlier for a longer cable. Due to the larger cable resistance of the trans-Pacific power feeding equipment, the overall optical power supply should be higher than that of the trans-Atlantic cable. As the typical values of the trans-Atlantic cable, the 30-kV voltage supply and $1.5\%$ E/O efficiency results in 306.8-W optical power. In this case, by optimizing the core number of MCFs, more than 5, 2.5, 1.5 and 1.5 times capacity gains can be obtained over SMFs cable.
Fig. 3. Relative capacity of WC-MCFs cable to SMFs cable as the function of core number and optical power with different fiber counts for the trans-Pacific cable.
3.2 Q factor evaluations for the WC-MCFs and SC-MCFs submarine cables
Strongly-coupled MCF (SC-MCF) has been proven to be advantageous over WC-MCF with reduced fiber nonlinearity [6] and lower spatial mode dispersion (SMD) [13]. It requires multiple-input and multiple-output (MIMO) DSP implemented at the receiver to demodulate coupled optical fields. Above-utilized GN model has its limitations to predict SC-MCF cable performance because the joint influence of IC-XT and SMD can hardly be accurately evaluated for coupled fields transmitted in SC-MCFs. Consequently, we further develop a transmission model based on CNSE [14,15], to compare the WC-MCFs cable and SC-MCFs cable. For MCFs, the IC-XT evolution over $z$ axis can be approximated as,
where $z$ is the integer index of the split-step Fourier (SSF) process, $K_{ab}$ is the coupling coefficient between core $a$ and $b$. The exponential part in the right-hand side (RHS) of Eq. (10) describes the phase-matching condition of mode coupling between two cores. Due to the optical phase is randomly perpetuated by the ambient environment, the phase deviation during inter-core coupling can be treated as a Gaussian random process [14]. In addition, there is a relationship between $K_{ab}$ and the mean crosstalk value by $\mu _{XT}=|K_{ab}|^2$, assuming one-time phase matching within a step size [14]. This assumption is accurate when the step size of SSF is smaller than or equal to the coupling length $L_c$. In this paper, we utilize the coupling length $L_{c}=1/K_{ab}$ as a parameter to investigate IC-XT influence to submarine cables [16]. Here, we typically investigate the 4-core SC-MCF [13] to compare the 4-core WC-MCF for the trans-Atlantic and Pacific cables. Numerical solving of CNSE is performed by the SSF method with a short step size of 100m. Systematic settings of the transmission cable are in agreement with Table 1 with 15-kV and 30-kV feeding voltages for the trans-Atlantic and trans-Pacific cables respectively. 80 subcarriers are modulated by 50-Gbaud DP-QPSK signals with the 53-GHz spacing, so those cover the 4.3-THz spectrum at C band. DP-QPSK has been proved to be the optimal format for submarine cables, according to Eq. (9). XPM and SPM effects are emulated among 5 adjacent subcarriers. With a sufficient power supply at 240W to the trans-Atlantic cable with 8 pairs MCFs, corresponding constellation diagrams with coupling lengths at 1000km and 100m are presented in Fig. 4. As indicated by Fig. 4, the stronger coupling of MCFs results in the improved performance. That is due to the alleviated fiber nonlinearity by the averaging of randomly-coupled optical fields. MCFs with coupling length at 1000km have individually transmitting cores, in which mode coupling only occurs between two polarization modes. For the case of coupling length at 100m, mode coupling occurs among all cores thus DSP requires 8-by-8 MIMO to demodulate signals.Fig. 4. Constellation diagrams for the trans-Atlantic 8-pair MCFs cable with optical power supply at 240W, with coupling length at 1000km (a), 100m (b).
To quantitatively evaluate the joint influences of fiber pair count, coupling length, and optical power supply, Q factors of the trans-Atlantic and trans-Pacific cables are calculated, with results plotted in Fig. 5. As indicated by the results in Figs. 5(a) and (b), for trans-Atlantic communications, fiber nonlinearity can be alleviated by the deployment of 16 pairs MCFs. As for the case of 8-pair MCFs, fiber nonlinearity leads to severe signaling distortion when the optical power is over 150W. In this case, the SC-MCFs cable with a coupling length of 100m has improved Q factors than those cables with longer coupling lengths. As for the trans-Pacific cable, the impact of fiber nonlinearity is more notable than that of the trans-Atlantic cable due to the longer transmission distance, for both 8- and 16-pairs MCFs cases. As indicated by the results in Figs. 5(c) and (d), the SC-MCFs cable with coupling length at 100m has the largest Q factor. If 8 pairs MCfs are deployed for the trans-Pacific cable, the 260-W optical power supply is sufficient because the further increase of optical power leads to Q factor degradation due to fiber nonlinearity. In the case of a 260-W optical power supply, the SC-MCFs cable with coupling length at 100m could induce over 1-dB Q factor gain than the WC-MCFs cable. When the fiber pair count can be increased to 16, a higher optical power supply of up to 440W is required to realize higher Q factors, as indicated by Fig. 5(d). In this case, the SC-MCFs cable with a coupling length of 100m still could provide a 1-dB Q factor gain over the WC-MCFs cable.
Fig. 5. Q factor of DP-QPSK signals as a function of optical power supply for 4-core MCFs with the different coupling length. (a) Trans-Atlantic cable with 8 pairs of MCFs, (b) trans-Atlantic cable with 16 pairs of MCFs, (c) trans-Pacific cable with 8 pairs of MCFs, (d) trans-Pacific cable with 16 pairs of MCFs.
4. Marginal influences of IC-XT, SMD, and FIFO insertion loss
4.1 Inter-core crosstalk
To deploy MCFs in the submarine cables, IC-XT and the additional insertion loss induced by FIFO are the main concerns for impeding the optimal performance of the MCFs cables. Here, we investigate the reported WC-MCFs with a standard 125-um cladding diameter for analyzing IC-XT effects, with the core number at 4 [17]. Supplied by the voltages at 15kV and 30kV between shores, the total optical powers of all repeaters for the Atlantic and the Pacific cable are 140.6W and 306.8W respectively, assuming the overall E/O efficiency of each repeater is 1.5$\%$ [3]. The emulation of IC-XT-induced noise variance is referred to [18]. Equivalent noise variance $\sigma ^2_{XT}$ by IC-XT can be derived from the mean value of IC-XT contributed by the other cores $\mu _{XT,total}$, which is given by
Figure 6 presents the IC-XT-induced capacity degradation for the MCFs cables. Overall crosstalk of the whole cable is induced by MCF and FIFO. It indicates that the influence of crosstalk below −40dB/100km for the 4-core MCFs cable can be ignored. In general, with the increase of fiber pair count, the capacity gain by MCFs becomes smaller. Typically, in the 24 fiber pairs case, the employment of 4-core MCFs cable could provide 1.4 times capacity to the SMFs cable, when IC-XT is below −40dB/100km. Up to −25dB/100km IC-XT can be tolerated to achieve the considerate capacity gain by using the 4-core MCFs. As for the trans-Pacific cable, less performance gain is achieved by 4-core MCFs when the fiber pair is increased to 24, as indicated by Fig. 6(b). Nevertheless, when the fiber pair count is limited at 8, 60$\%$ capacity gain can be obtained by using 4-core MCFs when IC-XT is below −40dB/100km. One thing is worthwhile to be noted that the results in Fig. 6 are based on the $1.5\%$ overall EO efficiency of repeaters. If the advanced amplifications with higher E/O conversion efficiency are used in submarine cables like the cladding pumping and Erbium/Ytterbium co-doped active fibers, the performance advantages of MCFs-based submarine cable can be much deeper explored even for the Pacific cables with longer distance.
Fig. 6. Relative capacity of 4-core WC-MCFs-based submarine cable to the SMF-based one under different IC-XT conditions with different fiber pairs number. (a) Trans-Atlantic cable. (b) Trans-Pacific cable.
4.2 SMD
If MCFs are designed with a small core pitch then belonging to the strongly-coupled regime, the IC-XT impact has to be eliminated through the MIMO DSP at the receiver. Moreover, extra performance improvement can be obtained by SC-MCFs, due to the alleviated fiber nonlinearity. However, in the practical case, the cores of MCFs are heterogeneous due to imperfect fabrication. As a consequence, the MIMO DSP performance would be degraded when equalizing the coupled signals with large delays. Thus, it is worthwhile to investigate the SMD impact to SC-MCFs cables. Fixing the fiber pair count at 8, it has been observed from Fig. 5(a) that SC-MCFs cables have better Q factors than the WC-MCFs ones. Typically with optical power supplies at 150 W and 300 W for the trans-Atlantic and trans-Pacific cables, SC-MCFs solution could offer more than 0.75- and 2-dB Q factor gains to the WC-MCFs cables. Pulse broadening of SC-MCFs due to SMD will place a heavy burden on MIMO-DSP. Q factor values vs. SMD curves for the Atlantic and Pacific are given in Fig. 7(a). Inserted figures are the constellations in the cases of 40-ps/100km Atlantic cable and 56-ps/100km Pacific cable, respectively. As shown in Figs. 7(b) and (c), pulse broadening can be indicated by the spreading of MIMO taps under large SMD values. Due to the fixed tap number, the equalization performance is degraded when SMD is over 50-ps/100km for the Pacific cable.
Fig. 7. (a) Q factors vs. SMD curves, and inserted figures are typical constellations. Convergent taps for (b) the Atlantic cable with 40-ps/100km SMD and (c) the Pacific cable with 56-ps/100km SMD.
4.3 FIFO insertion loss
FIFO deployed in the MCFs cables induces additional link loss, which degrades the SNR of the transmitted lightwave. For compensating the extra loss induced by FIFO, ASE emitted by the repeaters will increase at the same time. By setting the IC-XT at −40 dB/100km in the weakly-coupled regime, the relative capacities of the 4-core WC-MCFs submarine cable to the SMFs one under different FIFO insertion loss conditions are given in Figs. 8(a) and (b) for the trans-Atlantic and -Pacific cables respectively. In general, the longer trans-Pacific cable is more sensitive to the insertion loss of FIFO. That is due to the accumulated ASE noise is more remarkable by higher numbers of repeaters. Under the 24 fiber pairs counts limitation, the maximum tolerated FIFO insertion loss is 1.8 and 0.5 dB for the trans-Atlantic and -Pacific cables respectively. However, if the optical power supply is sufficient, the high FIFO insertion loss can be tolerated with capacity gain to the SMF-based submarine cable.
Fig. 8. Relative capacity of the 4-core WC-MCFs cable to the SMFs one under different FIFO insertion loss conditions with different fiber pairs number. (a) Trans-Atlantic cable. (b) Trans-Pacific cable.
5. Conclusion
In this work, we have comprehensively investigated and compared the capacities of WC-MCFs and SC-MCFs in applications of optical submarine communications with limited fiber count and power supply. A concrete optimization procedure of span length and spatial multiplicity has been detailed based on developing a GN model for the MCFs-based submarine cables. Comparative results have indicated that 4-core WC-MCFs could outperform SMFs in submarine cables when fiber count is limited below 32. Moreover, the SC-MCFs cable has exhibited further improved transmission performance compared to the WC-MCFs ones, due to the alleviated fiber nonlinearity by random coupling among cores. At last, we have concluded that the development of advanced amplification schemes with improved E/O conversion efficiency is beneficial to further explore the potentials of MCFs in applications of optical submarine communications.
Appendix
In this work, the transmission model over MCF is built based on the split-step Fourier (SSF) solution to the CNSE. Different from the classical SMF model, MCF transmission needs to further consider the effect of IC-XT and heterogeneous characters.
Verification of optical transmission model based on CNSE
To ensure concrete conclusions drawn by simulations, we conducted self-consistency examinations for verifying the developed transmission model. On the basis of the classical SMF model, the additional settings of IC-XT and SMD of heterogeneous cores need to be further verified. Through launching optical pulses into MCF, the statistical characters of MCF can be estimated by analyzing the receiving pulses at the end of the fiber. For characterizing the IC-XT of the 4-core MCF, a pulse with power at $P_t^1$ is launched into one individual core, then measures the outputs power of every cores $P_r^ i$ where $i = 1,2,3,4$. Because the mode coupling among cores is a random process due to the phase matching points deviation, the overall IC-XT can be measured by the mean value of $\frac {\sum _{i=2}^{4}{P_r^i}}{P_r^1}$. During the IC-XT examination, the fiber attenuation, dispersion and nonlinearity can be turned on. For characterizing the 4-core MCF modeled in this work, the error bar curve of the set IC-XT values versus the measured values according to 2000 times of measurements is given in Fig. 9.
As for the SMD, four synchronized pulses are launched into individual cores then we measure the relative delay among cores after 100-km fiber transmission with a neglected IC-XT. Received pulses with 100-ps SMD are plotted in Fig. 10(a), combined with the random coupling between polarization modes. The individual pulse shape maintains well due to the negligible fiber dispersion and nonlinearity. Results indicate that relative delays at 100ps are set accurately for all spatial modes. When IC-XT is set with coupling length at 10km, the Gaussian shape of received pulses can be observed, as shown in Fig. 10(b).
Funding
National Natural Science Foundation of China (62035018, 62105273, 62171175); Hong Kong Polytechnic University (HK-PolyU) postdoc matching fund scheme (1-W155).
Acknowledgment
We would like to thank Lin Gan for the useful discussions during developing optical submarine transmission models, and also acknowledge the support of The Hong Kong Polytechnic University through project S-ZG8N.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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