The second way to increase the transported capacity per fiber is to employ a higher number of channels. For this purpose, two options can be envisaged: a) populate the low loss attenuation spectrum of the single mode fiber (around 365 nm) with channels, extending in this way the transmission beyond the C-band, realizing Ultra-Wideband (UWB) transmission (or named as Multi-Band transmission, however throughout the text we use the term UWB) and/or b) the space dimension can be exploited, e.g. populating a bundle of SMFs, or considering transmission within a Multi Core/Multi Mode/Few Mode Fiber, performing in this way SDM. Both UWB and SDM are candidate approaches for F6G and have their own merits, which will be presented at the rest of this sub-section.
4.3.1. Ultra-Wideband transmission
Ultra-Wideband transmission allows for a ten-fold increase in the number of channels compared with the case of C-band transmission only. However, populating the entire low loss attenuation spectrum of the SMF with channels is not trivial, as to-date, optical components such as amplifiers, filters and commercially available transceivers are mainly focused on C and L and parts of S-band. To further understand the current state,
Figure 22 illustrates the attainable gain and the noise figure of indicative available doped fiber amplifiers for the five bands of an UWB system. As it can be observed, in O and E-bands, the technology at the component level has to be further developed in order to unlock the transmission of these frequencies. We expect that future research will be able to provide components with the desirable characteristics, such as amplifiers with sufficient gain, with low noise figure and with a significantly wider amplification gain.
To realize UWB transmission, various types of amplifiers can be employed, such as Doped Fiber Amplifiers (DFAs), Semiconductor Optical Amplifiers (SOAs) and Raman amplifiers. The pros and cons of each method are discussed in [
71]. According to our opinion, DFAs are currently the dominant amplification technology, as they (a) are a well-known technology due to the extensive use of EDFAs in the C-band, (b) allow for a modular engineering, introducing amplifiers on an as-needed basis, and (c) provide the desirable characteristics such as low noise figure, gain flatness, and high output power. The full potential of an UWB (when all 365 nm are fully exploited) is to transmit more than 1,000 channels (e.g. with 37.5 GHz channel spacing). However, the true number of transmitted channels is expected to be lower, due to the current absence of optical components with the desirable characteristics, especially in O and E-bands as well as the catastrophic impact of nonlinear effects, such as Nonlinear Interference (NLI) and Stimulated Raman Scattering (SRS), the impact of which scales nonlinearly with the increase of the total injected power in the fiber. In particular, [
85] showed that by using the currently available technology, the transmission of 871 channels in all five bands can be feasible. However, the attainable capacity of an UWB system depends also on the modulation format “carried” by each channel. For example, if PM-16QAM is considered, an overall rate of 174 Tb/s can be envisaged. Next, the estimation of the transparent reach strongly depends on the impact of the physical layer effects which are a function of various system parameters. In particular, the estimation of transparent reach is a more complex procedure, since each band “sees” different transmission parameters, such as attenuation parameter, local dispersion parameter, effective area etc., and for this reason the attainable reach in each band (even in different channels of the same band) is different, unless an optimization strategy, like [
86,
87,
88], which can ensure similar physical layer performance in all bands is considered.
The attainable reach and bit rate are antagonistic target metrics, as when migrating to a higher modulation format, an increased physical layer performance is required in order to attain the same BER. This eventually leads to a lower transparent reach compared with the case of lower cardinality format, e.g. PM-QPSK. This means that rates of > 250 Tb/s can be theoretically achieved in metro, access and inter/intra data center networks while in longer networks, such as submarine and regional, a capacity of up to around 100 Tb/s can be achieved.
Figure 23 summarizes the relation between transported capacity and transparent reach up to 10,000 km for experimental works over the past decade [
89,
90,
91,
92,
93,
94,
95,
96,
97,
98,
99,
100,
101,
102,
103,
104,
105,
106,
107,
108,
109,
110,
111,
112,
113]. As it is evident from this figure, using either EDFAs alone or in combination with Raman amplifiers, UWB transmission is feasible in long-haul and submarine networks while for shorter distances, e.g. access/DCI and metro, there is a broader gamut of available options for optical amplification. This allows to select the most cost-effective technology between DFAs (e.g. Thulium DFA and EDFAs in parallel), hybrid-Raman amplifiers and SOAs. SOA technology particularly is a very cost-effective option for short distances as it can offer a large amplification bandwidth, e.g. 100 nm with only one amplifier [
97,
110].
Hollow-core fibers for further increasing the transmission spectrum
The low loss attenuation spectrum of SMF spans over about 50 THz (O to L bands). However, signal transmission beyond this range, in particular from 1800 to 2350 nm, is possible, allowing an about 37 THz additional range using hollow core fibers [
64]. In practice, the light in the hollow core fiber propagates within a hollow region, in a way that only a small portion of the optical signal propagates in the solid fiber material. Hollow-core fibers with the proper manufacturing can attain a low fiber loss within a range that spans around 2000 nm. However, the transmission within hollow-core fibers, requires installation of new fibers, which leads to high installation costs and buying prices. This fiber alternative as well as the SDM concept are included in the category of “green-field”, where new fiber types need to be deployed while the UWB transmission are part of the “brown-field” category, where the existing fiber infrastructure is used as the basis for installing new fiber subsystems and elements, such as amplifiers, filters, etc.
An important metric that shows the current state of the technological progress in the optical transmission is the “relative bandwidth”, which equals to the total system bandwidth divided by the central frequency [
64]. This metric relates the system bandwidth to its central frequency, and the ultimate target is to approach as close as possible to 100%. For example, a C-band only system shows a relative bandwidth of less than 3%, while a theoretically fully populated UWB system can attain a relative bandwidth of about 25%. Finally, when the transmission spectrum is extended using hollow-core fibers the relative bandwidth can exceed 65%. As the value of this metric increases, the overall system costs are becoming higher, as novel components, such as amplifiers, transceivers, band filters etc. need to be deployed. These components are more costly than those used in C and L-bands, because the technology in C and L-bands bands is more mature and widely adopted, as well as the economy of scale can lead to reduced costs, compared e.g. with E and S-bands. This high cost is a significant constraint for network operators that desire to upgrade their infrastructure towards engaging more bands on optical transmission and can steer them towards exploiting SDM techniques, which are analyzed in the next section.
4.3.2. Space Division Multiplexing
Space Division Multiplexing is in principle a system that incorporates at least one subsystem (e.g. a transmission fiber, an amplifier, a switching node or a terminal equipment) which implements the concept of “spatial integration of network elements”. SDM is of great interest as it promises to increase the overall transported capacity by multiple times compared with one standard SMF. In particular, the main options that can be considered to increase the number of spatial channels within the transmission link are [
13]:
Multiplication of the number of conventional fibers (thus implementing a parallelism that consists of single-core/single-mode fibers), considering the existence of at least one element that performs spatial integration, e.g. an amplifier with sharing pumps, a switching node, or terminal equipment; named as bundles of Single-Mode Fibers (Bu-SMFs).
Multiplication of the number of cores; within the fiber multiple cores arranged within the cladding with each supporting a single spatial mode (Multi-Core Fiber - MCF), or multiple cores each supporting multiple modes (Multi-Core-Mode Fiber - MCMF). Coupled Core (CC) fibers. CC can provide strong mode coupling between the different cores, attaining shorter core-to-core distance and higher spatial density compared with the uncoupled MCFs.
Multiplication of the number of modes in MMF fibers; within a single core supporting a discrete number of spatial modes (Multi-Mode Fiber - MMF, Few-Mode Fiber - FMF).
A combination of the above categories, e.g. MCF/FMF is also feasible.
All these combinations are illustrated in
Figure 24.
As mentioned above, in the case of Bu-SMFs, a Bu-SMF to be considered as an SDM, it needs to incorporate at least one sharing scheme, e.g. a pump-sharing scheme in the optical amplifiers/repeaters. It is worth mentioning that the main target of SDM, especially in submarine networks is not to simply increase the number of spatial channels targeting to a higher attainable capacity, but to exploit multiple spatial channels and pump-sharing schemes to achieve a reduction of cost/bit and power/bit quantities, while providing the obvious modular capacity scaling [
13].
The comparison between SDM and UWB can designate three main advantages of SDM; the first is its better physical layer performance. In particular, when SDM transmission utilizing the C-band is compared against the lower bands of an UWB system, SDM system benefits from the a) absence of SRS, b) lower attenuation and c) higher dispersion, leading to both decreased ASE and nonlinear effects and eventually to an improved physical layer performance. This not only increases the modulation format cardinality (and so the data rate per channel), but also increases the transparent reach. The latter will lead to a lower number of 3R regenerators in the network (especially in long-haul networks), making SDM systems the ideal candidates for e.g., long-range terrestrial and submarine networks, when compared with UWB. The second advantage of SDM is the use of “spatial integration of network elements”, such as optical amplifiers etc., leading in this way in significantly lower OpEx and CapEx. The third advantage of SDM over UWB is the lower component associated costs, e.g. costs for transceivers, amplifiers and filters.
However, SDM comes with two significant drawbacks. The first is the need to deploy new fibers in links where is an insufficiency of available fibers, however, this is not the case in most links, where abundant dark fibers are present. The second is that SDM cannot attain a diversity on connectivity compared with UWB. More specifically, UWB systems can attain a diversity in connectivity, as the lower bands can employ less costly components employed for shorter links, although these bands result to shorter reach when they are compared with SDM. On the other hand, in UWB, only the C and L-bands can be exploited for the more distant links of a network, which cannot be the case in C-band SDM systems, where the entire available spectrum is considered as “premium” due its high-quality physical layer performance.
Certainly, a combination of SDM/UWB is possible, e.g. by considering a multiple fiber transmission, e.g. Bu-SMFs, exploiting both C and L-bands. However, in order to select the optimal solution between a) the various SDM variants, b) the exploited amplification bands of an UWB system and c) a combination between them, we need to take into account a number of different factors, where many of them are antagonistic, such as attainable capacity, node connectivity, cost/energy-effectiveness, transparent reach, node scalability, system upgradeability and node/spectrum flexibility.
Cost-effectiveness is obviously one of the most important factors when designing an optical network. SDM can reduce the overall component associated costs by exploiting “spatial integration of network elements”, e.g. amplifiers. Considering transmission within multiple modes and/or cores, the most important concern is if these modes/cores intermix. This is an important issue, as a possible energy transfer between them will result in a lower physical layer performance, increasing in this way, the BER of the transmitted channels. For example, in multi-mode fibers, degenerate spatial modes exhibit mixing during fiber propagation while bundles of SMF do not. Proper system design may suppress the impact of this mixing. Further, MCFs’ coupling can be reduced by considering different neighboring core properties and increasing the pitch [
114]. Note also, that the placement of identical cores in proximity leads to mutual coupling [
115] allowing a more precise control. Mixing between the modes in an MMF can be reduced by breaking the mode group degeneracy [
116]. Optical amplification in UWB systems when DFA technology is adopted can be achieved with the use of multiple amplifiers. More specifically, employing a single amplifier for each band, which is placed either in parallel or serial [
87]. On the other hand, power feeding in SDM systems utilizing the C-band can be implemented by groups of EDFAs, e.g. one per guided mode, core or fiber [
117,
118]. A significant benefit of SDM over UWB here is the ability of sharing common pumping lasers [
119] reducing in this way the number of laser pumps. SDM is also advantageous when compared with UWB as it possesses the ability to share the lasers in the transmitter and receiver parts [
120]. In particular, if mode mixing exists, a common laser source leverages the post-detection signal processing required to unravel the original information, as the phase relationship is fixed. However, SDM shows higher costs than UWB in cases of limited fiber availability or in cases where, due to regulatory aspects, network operators are forced to pay a rent to a government body/agency for any occupied fiber resources. For example, the CAPEX to roll-out a new fiber is ∼25 keuro/km in rural areas, and up to ∼500 keuro/km in metropolitan areas [
121]. In particular, for a European country, the lease cost is approximately 0.33x (~
$1308) per fiber/km/year for five years of leasing package; but the lease cost in Indian network is about 0.007x (~
$ 29) per fiber/km/year [
122]. These leasing costs need to be quantified during the selection of the optimal solution between UWB and SDM.
The exploitation of SDM in terrestrial networks will not only aid to attain the target of 10 Pb/s by 2030 (
Figure 17) but will also significantly boost the node connectivity through the introduction of additional channels which are transmitted through the additional cores and fibers. In particular, the number of parallel cores can reach up to 32 for fiber diameters ≤250 μm, where glass remains flexible, transporting a capacity of 1 Pb/s over more than 200 km [
123]. Moreover, with the use of 8D-16QAM format, the transmission distance can exceed 1,200 km with a capacity of 0.75 Pbit/s. Further, in [
124] it is demonstrated that the efficient operation of an SDM network is feasible, as the channels are adaptively (re)configured, taking into account the inter-core crosstalk with the aid of a software-defined network (SDN) controller. Towards the introduction of SDM in terrestrial networks, the availability of multi-/core/fiber/mode amplifiers is a prerequisite. In particular, a Multi-Core Erbium/Ytterbium-Doped Fiber Amplifier (MC-EYDFA) can be a promising solution for the power restoration of the channels in multiple cores, however, some challenges need to be addressed, such as the reduction of its size and power consumption. Authors in [
125] showed that a 32-core EYDFA can reduce the overall power consumption when benchmarked against a multiple EDFA scheme. This efficiency improvement for cladding pumping originates from increasing the effective area of active cores. Authors in [
126] showed increased cladding pump efficiency for 19-core EDFA in C or L-band while a cost-analysis designates that the common amplifier brings long-term cost savings of 33% and up to 55% power savings [
127]. In order to realize SDM within the limits of a terrestrial network, the existence of Optical Cross Connects with SDM capabilities is a prerequisite. Scalability is the most important issue in order to accommodate several types of switching granularity demands and a layered switching architecture is mandated. In future SDM networks, when the capacity per path will exceed several Tb/s, the introduction of spatial Optical Cross Connect (OXC) based architectures [
128,
129] will be a must. The successful migration from current Wavelength Selective Switches (WSS)-based networks towards layered and scalable SDM switches [
130,
131] will be a key for the success of SDM based networks.
The era of SDM deployments in submarine networks has already started. The first generation of SDM-based submarine systems has been announced and started its deployment phase since 2020, before any terrestrial SDM network of any kind had been deployed. It is characterized by early technology advancements that implement the concept of “spatial integration of network elements” with optical amplifiers. The spatial integration/sharing of resources, is implemented at the submarine optical amplifiers via the so-called “Repeater Pump Farming” (RPF) technique. RPF consists of a group (named “farm”) of repeaters which are cross connected to each other. Each RPF farm supports a certain group of Fiber Pairs (FPs) and utilizes a group of optical pumps that are shared among groups of FPs [
132,
133]. A significant advantage of RPFs is that they can continue the pumping of FPs even in the cases that one or more pumps fail, offering a promising solution for network survivability, by assuring redundancy. A schematic of an RPF system is illustrated in
Figure 25.
SDM in terrestrial and submarine networks
For the realization of SDM, several networking components do exist, such as WSSs and Reconfigurable Optical Add Drop Multiplexers (ROADMs) compared with UWB, in which WSS and ROADMs that can incorporate O, E or S-bands are not in general commercially available. Usually, a submarine OADM node comprises both a Branch Unit (BU) and a Wavelength Management Unit (
Figure 26). Fiber pairs may bypass the node (through the BU) if they are routed directly to other destinations or may enter the node to be switched through the WMU BU to their destination. Although flexibility may lead to higher cable utilizations in the case of a reconfigurable OADM, strict security protocols must run to prevent unwanted or faulty node configurations and possible unauthorized access. A comparative analysis between UWB and SDM for the submarine cables is tabulated in
Table 5. As it is evident, the SDM can support a significantly larger number of fiber pairs along with very high-power repeaters to rectify the power of the optical signals, which are expected to be significantly larger in number compared with traditional cables. Moreover, the transmission within SDM cables is restricted in C-band, while PCS can be employed to improve the channel performance.
To further understand the potential of SDM systems in increasing the transportation capacity,
Figure 27 illustrates the total capacity of deployed submarine cables with and without the use of SDM. From this figure we can observe the trend to migrate to SDM in order to overcome the 100 Tb/s capacity crunch, showing the potential to reach 1 Pb/s by 2030, satisfying in this way the challenging demands of F6G services as they were presented in section 2.
SDM in wireless fronthaul/backhaul
It should be also emphasized that SDM is also an excellent option to support the ever-increasing demands of traffic in the wireless part of the network by offering enhanced fronthaul/backhaul capabilities, as the antenna cell sites (or remote units) are attached via an optical distribution network (ODN), which can exploit SDM [
135] (
Figure 28). As a consequence, the deployed infrastructure can concurrently support multiple heterogeneous streams of digital and/or analog radio over fiber (DRoF/AroF, respectively), which can distribute heterogeneous traffic in a coordinated fashion through a converged infrastructure. The Central Office (CO) has the capability to exploit space and spectrum resources in an automated way allowing channel establishment between the CO and the cell sites in a 2D space (WDM+SDM), pairing baseband units (BBU) with remote radio units (RRU). As the access requires cost and energy efficient solutions, it will significantly benefit from SDM, using mainly passive components, such as couplers and AWGs. However, the use of active components, such as WSSs, can be considered if the cost needs to be traded with flexible resource allocation.
SDM in inter/intra data center networks
The intra and inter data center communication can greatly benefit from the exploitation of the spatial dimension. The data rates in these two types of networks are usually low, such as 25 Gb/s and up to 100 Gb/s per fiber exploiting mainly direct detection methods, such as NRZ and PAM-4. However, they can be further boosted up to 220 Gb/s OOK, and 408 Gb/s 8-PAM, as shown in [
67], increasing the transported capacity (per channel) when needed. Based on the characteristics of currently deployed intra and inter data center networks, a very large number of parallel single mode fibers (>10,000s) is exploited in order to attain Pb/s rates. As a consequence, SDM is an already adopted solution here, where each fiber is populated with only a limited number of channels, e.g., four or eight, giving the opportunity to increase one or two orders of magnitude the overall transported capacity both through the use of a larger number of channels and through increasing the data rate per channel, e.g. via scaling the baud rate.
4.3.3. Summarizing the benefits of UWB and SDM-based systems
Before we conclude this sub-section, we wish to highlight the need to exploit all available capacity scaling dimensions (polarization, amplitude, phase, number of spectral and spatial channels) and tailor them to specific applications and network domains. On one hand, SDM systems based on bundles of SSMFs are an already adopted solution in submarine networks and in intra-datacenter networks. However, the need for their deployment in terrestrial network segments is yet unclear. SDM has also very good potential to support the capacity and connectivity demands of the fronthaul. On the other hand, UWB (i.e. with mainly C and L-band transmission) systems have been a reality for over a decade now. The main question is if UWB is more economically feasible than e.g., a 3-fiber SDM system that achieves the same capacity. To answer this question, one needs to delineate the most cost-effective solutions between SDM, UWD and their combination, accounting for fiber availability, maturity – both at the component and system level – as well as the target total capacity, capacity per lane/channel, transmission reach and the targeted specifications for cost-power consumption per transmitted bit. Towards this target, a technoeconomic analysis on the basis of a network planning study is missing from the literature and needs to be performed for indicative network types, e.g., submarine, access etc.
Regarding the fiber availability, UWB can reach up to 100% availability, as there is at least one fiber present in all network links. On the other hand, SDM in terrestrial links shows a lower fiber availability as the existence of a bunch of dark fibers is not always guaranteed. Next, SDM is advantageous over UWB, as it exploits a well-known and mature technology for various components, such as transceivers, amplifiers, filters etc. since it focuses on the third transmission window. Moreover, the physical layer performance of Bu-SMF is significantly higher when it is compared with UWB systems (beyond C, L-bands), allowing to attain a higher transmission reach, prohibiting the use of UWB applicability in submarine and long-haul transmission systems, as they require a large number of regenerators, especially for the channels in the lower bands. However, in the core domain, as shown in [
85], four out of five bands of an UWB system can interconnect even the most distant nodes of a core network, while O-band can be used to interconnect less distant nodes (e.g. up to 600 km), showing that UWB is a very good candidate for the terrestrial domain. This diversity of UWB systems is highly plausible, as different bands can be assigned to different network paths and/or carry different data rates balancing in this way the cost/transparent reach ratio. Merging the advantages of both worlds, we can say that a combination between UWB and SDM systems seems to be the most efficient solution to maximize the terrestrial network connectivity, allowing to transport a multi-thousand number of channels through each optical link.
Next, both UWB and SDM systems have excellent upgradeability capabilities, as a new band or fiber can be engaged when the already active bands or fibers are reaching an utilization threshold, e.g. 60 or 70%, allowing in this way to follow a pay-as-you-grow policy reducing the first-day capital expenditure. Another important advantage of SDM systems compared with UWB ones is the possibility of using common components for a large number of cores/fibers/modes, reducing in this way the overall costs and power consumption. On the other hand, UWB can exploit amplifiers in multiple bands, such as C+L bands EDFA, UWB SOAs and Raman amplifiers, however these components are confined in two or three bands at most. A comparative study between UWB and bundles of C-band SMFs for their most important qualitative features is tabulated in
Table 6.
Concluding this sub-section, we wish to underline that using currently available commercial components, it is possible to use in a complementary way UWB alongside SDM systems based on bundles of SMFs. SDM systems based on new fiber types (e.g. MCFs or FMFs) are expected to be further commercialized in the future, due to the immaturity of the technology, performance limitations and the requirement for new fiber deployments that are very costly compared to their alternative solutions. In addition, UWB systems alone can be readily employed, extending the capacity of already deployed SMFs and providing a short to medium-term cost-effective solution for network operators. However, there is a strong need to migrate to the spatial dimension with a rapid pace as it offers a theoretically unbounded capacity multiplier potential allowing to exceed 1 Pb/s rates and can efficiently underpin the upcoming network transformation in order to support 6G and F6G services.
4.3.5. Towards the ultimate capacity limits of optical transmission
In this sub-section, we briefly elaborate the main factors which can stress the optical transmission towards its practical capacity limits. In order to achieve this, we need to maximize the following three quantities: a) the bit rate per channel, b) the number of employed channels per spatial element, e.g., fiber/core/mode and c) the number of spatial elements. Given that each channel has a specific bandwidth, the bit rate per channel is maximized by selecting a more spectrally efficient modulation format, e.g., 16 or 32QAM instead of QPSK. However, there is a clear tradeoff between the spectral efficiency and the physical layer performance, as the higher cardinality modulation formats require a significantly larger SNR in order to attain the same BER. This is more clear when the Shannon-Hartley theorem is considered, which calculates the spectral efficiency (Sp.Ef.) in the presence of noise as follows:
where
C is the channel capacity in Gb/s,
B the bandwidth of the channel in GHz and S/N the signal to noise ratio. From Eq.(1), it is clear that a high SNR is required to transmit multiple b/s/Hz, which cannot be attained within, e.g. a core network, via for example PM-32QAM, PM-64QAM or even higher cardinality formats, for long distances more than a few hundreds of kilometers [
88], mainly due to the accumulation of ASE noise and fiber nonlinearity. In a core network, PM-QPSK or even PM-16QAM can be exploited to interconnect distant nodes [
87], as these modulation formats have relaxed SNR requirements compared with higher cardinality formats, in order to attain the same BER. For sure, the spectral efficiency can be boosted using a) sophisticated DSP modules, which can significantly improve the signal’s performance, however with additional computational complexity and added cost/power consumption and b) using more sophisticated forward error correction codes, but at the cost of an increased number of redundant bits. Next, increasing the number of transmitted channels within the same spatial element, e.g. fiber, will directly result to a
Nch multiplier. This can be realized by exploiting the low loss attenuation spectrum of the optical fiber as analyzed in section 3.3.1. The ultimate limit of UWB is the 365 nm spectrum, which is obviously finite and after its exploitation, only the third method can be used, which is the space division multiplexing. This method can pack a very large number of spatial elements, in practice much larger than 24, which is the number of the largest SDM system offering another capacity multiplier, allowing to attain multi-Pb/s rates within a single transmission link. The aforementioned analysis is summarized in
Figure 31 where the three methods are combined to maximize the number of transmitted data in an optical system.
Predictions on the attainable capacity
Based on the announced capabilities of submarine cables we can perform predictions about the transported capacity for the coming years based on data taken from the previous decades. For this purpose,
Figure 32 illustrates the announced transported capacity of various submarine fiber cables [
13] with and without SDM. As it is evident, SDM is the key technology that can assist exceeding the limit of 100 Tb/s and reach 1 Pb/s by 2030. These predictions are fully aligned with the predictions of various research works summarized in
Figure 17 where it was also highlighted that the capacity of commercially available systems will reach 1 Pb/s at 2030.
Predictions on the attainable capacity times length product can be also performed using the Optical Moor’s Law (OML) formula introduced in [
136] for submarine networks as follows
where the parameter
Year denotes the year selected to estimate the predicted C
.B product and
F is a parameter that characterizes how fast in time the C
.B product is increasing. In the original work of [
136],
F equals to 3.75, which means a doubling every 3.75 years or every 45 months. In this work, we exploit this formula and based on recent experimental results for ultra-long haul and/or submarine transmission (taken from
Figure 23), we slightly update the value of F. In particular, from
Figure 33 we can observe that by setting in Eq.(2) an
F value equal to 3.125 the fitting error is smaller. This is translated into a doubling of C
.B product about every 37.5 months which designates a faster scaling comparing with the value of F equal to 3.75, which to our opinion can be mainly attributed to the unlocking of new amplification bands, which allowed to increase the transported capacity C.