1. Introduction

Multimode fibres (MMF) are still considered a viable solution for short distance data links, especially with the 10 Gigabit Ethernet standard now ratified [1]. Until now, MMF modal bandwidth limitations were seen as an absolute limit to system performance [2, 3]. However, we have shown recently that subcarrier multiplexing (SCM) techniques [4], in conjunction with WDM can provide significant bandwidth enhancement, when used in a C-band high-density WDM (HDWDM) context [5, 6]. The MMF modal limitations were also thought to cause strong de-polarisation of any input signal, so precluding the possibility of polarisation division multiplexing (PDM). However this is not the case and we have recently demonstrated the practicality of polarisation multiplexing in MMF’s, opening the way to further capacity enhancement [7, 8].

In this paper, we now show how an efficient combination of PDM and WDM may be practically implemented to achieve high data rate capacity in existing legacy MMF networks. This allows a simple and efficient exploitation of the available optical bandwidth, using both polarisation and wavelength domains, with important application in the upgrading of MMF-based access networks.

The paper is organised as follows. To begin with (Section 2), we derive expressions using the Stokes parameters for the polarisation cross-talk and polarisation channel isolation. In Subsection 3.1, we present the variation of the polarisation channel orthogonality at the output of different samples of MMF as a function of wavelength, using variable orthogonal input states of polarisation (SOP’s) and we show that channel isolation is always sufficient (¿10dB) to achieve error-free data transmission. In Subsection 3.2 we show how the variation in orthogonality affects the polarisation demultiplexing of the PDM channels. In Section 4, we describe two different experiments to demonstrate the potential of combined polarisation- and wavelength-division multiplexing (PWDM). The experimental setup is based on an expansion of a design described in [8]. A first experiment (2P×2λ, 100GHz-ITU-grid spacing) employs a monochromator for both polarisation and wavelength demultiplexing, to prove that error-free data transmission is possible (Subsection 4.2). In this case, four data channels at 2.5 or 2.6Gb/s, over MMF lengths of up to 3km were successfully recovered in turn. Section 4.3 describes a more complex experiment, featuring eight channels (2P×4λ, 200GHz-ITU-grid spacing), and based on a commercially available, polarisation-insensitive, 62.5μm MMF pigtailed, WDM demultiplexing device. This allows each of the four wavelengths to be polarisation demultiplexed in parallel. As a result, we were able to transmit error-free eight channels at 2.5 or 2.6Gb/s, over MMF lengths of up to 300m. Finally (Section 5) we discuss potential improvements of the system, such as optimisation of the components, and a reduction of the channel spacing down to 20GHz [6]. Together, this would offer multi-Tb/s MMF data rate capacity, to still further maximise MMF bandwidth exploitation.

2. Theory of polarisation multiplexing

2.1. Orthogonality between two SOP’s

Any SOP can be represented by its Stokes vector s = (s ₀,s ₁,s ₂,s ₃), where s ₁,s ₂,s ₃ are the Cartesian coordinates in Stokes space of the SOP on the surface of a Poincar sphere. Its radius s ₀ is given by the average power of the incident beam [9]. Circular and right and left SOP’s are located at the north and south poles of the sphere respectively, whilst horizontal and vertical directions correspond to (+s ₁,0,0) and (-s ₁,0,0) respectively (Fig. 1). Normalising the Stokes parameters to s ₀, such that we have S ₁ = s ₁/s ₀,S ₂ = s ₂/s ₀ and S ₃ = s ₃/s ₀, allows us to compare different SOP’s on a sphere of unit radius.

To quantify the ability of MMF to transmit polarisation-multiplexed signals, we analyse the two SOP’s at the output of a MMF link corresponding to a particular input pair of orthogonal SOP’s. As can be seen on Fig. 1, the positions of the output SOP’s on the unit Poincar sphere are given by their normalised Stokes components

where their intensities are given by s _a0 and s _b0 respectively. The angle 2θ between the two SOP’s in the plane defined by $\overrightarrow{S_a}$ and $\overrightarrow{S_b}$ is a measurement of their relative orthogonality, and is found by their scalar product

In the case of perfectly orthogonal SOP’s, which are antipodal on the Poincar sphere surface (e.g. linear vertical and linear horizontal), $\overrightarrow{S_a}=-\overrightarrow{S_b}$ and 2θ = 180°. As expected, in real-space, this corresponds to the angle θ = 90°, e.g. between the horizontal and the vertical directions for orthogonal linearly polarised beams.

 

Fig. 1. Arbitrary pair of SOP’s on the Poincar sphere, before (S_a, S_b) and after (S′_a, S′_b) realignment to the plane of linear polarisations.

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Fig. 2. (a) Projection of SOP on the axis of a PBS for polarisation demultiplexing and (b) principle of PBS demultiplexing.

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2.2. Cross-talk and isolation between SOP’s

Polarisation demultiplexing can be achieved with the help of a polarising beam splitter (PBS). Computing the cross-talk between two SOP’s is equivalent to calculating their projections on the x- and y-axes of the PBS. Any SOP can be regarded as an ellipse of ellipticity χ, orientated with an angle ψ with respect to the PBS x-y coordinate system, as indicated in Fig 2, where the η-ξ coordinate system is aligned to the major and minor axes of the ellipse. The real-space angles of Fig. 2 are related to the appropriate Stokes parameters via sin2χ = S ₃ and sin2ψ= S ₂/cos2χ[9]. The projection of $\sqrt{s_{a0}}$ on the x- and y-axes is equivalent to computing the two transmissions through the PBS. The projections are

so that the intensities finally seen by the receiver are simply given by

and similarly for the second SOP channel

Assuming that channel $\overrightarrow{S_a}$ is to be detected on the x-axis and channel $\overrightarrow{S_b}$ on the y-axis, we define the cross-talk between the channels as

and the corresponding channel isolations are -Xt_x and -Xt_y.

Experimentally, we can arrange the PBS used for demultiplexing to be aligned with the S ₁ axis of the Poincar sphere, as indicated in Fig. 1. Using an appropriate combination of quarter-and half-wave plates (QWP and HWP) to rotate SOP’s, keeping in mind that a QWP transforms circular SOP’s into linear ones (rotation along a longitudinal line) and that a HWP changes the orientation of linear SOP’s (rotation along a line of latitude), any pair of two arbitrary SOP’s can be rotated on the Poincar sphere such as to be transformed into two linear SOP’s both lying on the equator. The angle 2θ is conserved by this transformation so that we now have χ_a = χ_b = 0 and ψ_b = ψ_a + θ. In addition, the bisector of the two realigned SOP’s is oriented at an angle φ with respect to the PBS, as shown in Fig. 1 (where in Stokes-space it appears as 2φ) and also in Fig. 2. The resulting cross-talk is now

The transmission is optimised when the cross-talk is the same for both channels, that is when φ = 45°. Assuming equal channel powers s _a0 = s _b0, Eqs. (11) and (12) further reduce to

which, as might be expected, is minimised when θ = 90°, and becomes zero when θ = 0.

3. Preservation of orthogonality and polarisation demultiplexing in multimode fibres

3.1. Measurement of SOP’s orthogonality

SOP orthogonality after propagation through MMF was measured using a polarisation controller and a Stokes analyser together with a tunable laser source (Fig. 3). For the particular wavelength of interest, the polarisation controller was set to a given input SOP, usually linear or circular, and the corresponding Stokes vector at the output of the MMF sample was measured. At the same wavelength, the Stokes vector of the orthogonal SOP was also measured. The process was repeated over the entire C-band. The acquisition was computer controlled, so that all measurements could be completed within the mechanical stability tolerances of the experiment. Finally, we computed the corresponding channel isolation curves by applying Eqs. (2) and (13) to each pair of SOP’s, which gave us the theoretical limits of the transmission system.

 

Fig. 3. Set-up for the measurement of Stokes parameters and orthogonality over C-band.

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As can be seen in Fig 4(a), channel isolations in the case of a 300m long MMF were higher than the 10dB limit normally required for error-free communication. Moreover, circular and linear cases were very similar, which means that no degradation is to be expected for these different input SOP’s. For the 3km long MMF (Fig 4(b)), there was a small reduction of channel isolation, however not sufficient to affect the error-free transmission. Of interest is to note that circular SOP’s yield slightly better performance than linear ones. This confirms previous findings [8]. Intuitively, this can be understood by the fact that linearly polarised light centre-launched into MMF will differentially excite spatial polarisation modes parallel and orthogonal to the original polarisation sense, whilst in the case of circularly polarised light, power is equally coupled into the two orthogonal spatial modes, thus reducing the depolarisation effects at the far end of the fibre [10, 11].

 

Fig. 4. Channel isolation over C-band at the output of 300m (a) and 3km (b) of MMF using an optimised PBS at each wavelength so that channel isolations are equalised to each other [equivalent to using Eqs. (2) and (13)].

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3.2. Effect of SOP’s wavelength variation on polarisation demultiplexing

Figure 4 shows that orthogonality is sufficiently maintained across the whole of the C-band. However, the SOP’s vary randomly with wavelength, and trace random trajectories over the surface of the Poincar sphere: their ellipticity χ and orientation ψ vary with wavelength. Thus the use of a single PBS demultiplexer optimised for one wavelength will not necessarily successfully demultiplex polarisation channels at other wavelengths. Assuming that a PBS has been optimised for a wavelength λ ₀, such that the corresponding SOP’s are defined by χ_a|_λ0 = χ_b|_λ0 = 0, the cross-talk is given by Eq. (13). However, calculation of cross-talk for the other wavelengths using the same PBS requires use of Eqs. (9) and (10), which takes into consideration the relative variation of χ and ψ.

Figure 5 shows the corresponding spectral variation of the channel isolation at the output of 300m and 3km of MMF for linear and circular input SOP’s respectively, where the SOP’s at λ ₀ = 1545nm have been optimised with respect to the PBS to achieve equal isolation for both polarisation channels. Channel isolation over 10 dB was still predominantly achieved, though not for all wavelengths. Even higher isolations are seen at some wavelengths for one of the two polarisation channels; however we note that the corresponding orthogonal polarisation channel is then seen to have a significantly reduced isolation, such that the desired equality between the isolations is not achieved. A null ratio can be seen in the bottom right corner of Fig 5 (b), which indicates that the output channel SOP’s were circular with respect to the PBS axis, and thus could not be successfully demultiplexed. We can assume that the locus of the trajectories on the Poincar sphere have a smaller rms radius for 300m MMF, than for the case of 3km MMF. Hence, the 3km MMF has a greater probability of reduced channel isolation. However, the fact that 50dB channel isolation is still occasionally achieved for 3km MMF indicates that depolarisation is not a significant factor. Overall, the results show that polarisation demultiplexing must be performed on a per wavelength basis, with the use of a polarisation insensitive wavelength demultiplexer.

 

Fig. 5. Channel isolation, function of wavelength for linear 300m (a) and circular 3km (b) input polarisation using a single PBS only optimised for the wavelength λ ₀ = 1545nm polarisation channels [equivalent to using Eqs. (9) and (10)].

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4. Transmission of polarisation- and wavelength-multiplexed data

4.1. Experimental setup

Figure 6 shows a schematic diagram of the two experiments. The transmission segment of the system (upper part of figure 6) was entirely singlemoded, and consisted of four tunable C-band DFB lasers, providing adjacent 100GHz or 200GHz ITU-grid-spaced consecutive wavelengths λ ₁, λ ₂, λ ₃, λ ₄ as necessary. The output of the first laser (λ ₁) was split and passed to two Mach-Zehnder intensity modulators (MZM’s) after alignment of the input polarisation states. Two separate channels at 2.5Gb/s and 2.6Gb/s, 2⁷ - 1, p.r.b.s. data were added. The slight bit-rate difference was used to distinguish between the two polarisation components. Subsequently, the MZM outputs were aligned to antipodal linear-polarisation states, and passed to a polarisation-preserving combiner; that is a PBS. Interference between the optical channels at the PBS was prevented by use of a dispersion-shifted fibre (DSF) delay line. An additional laser (λ ₃) was then added with its own polarisation controller to match the SOP at the inputs of the MZM’s. An EDFA was added at the output of the data modulation Mach-Zehnder to compensate for transmission losses, which amounted to about 19dB from the laser to the SMF-MMF coupling system (two 3dB couplers, typically 7dB per modulator, 2dB for the pigtailed PBS, and another 4dB for the AWG insertion loss). A second optical system, featuring another two lasers (λ ₂,λ ₄), identical in configuration to that just described, was also introduced. The outputs of the two data modulation Mach-Zehnders were amplified using EDFA’s to compensate for insertion losses. After passing through 3dB couplers (which are only required when all four wavelengths are used) and polarisation controllers, the convenient filtering, WDM multiplexing and polarisation-orthogonality-preserving properties [12] of an AWG were used to combine all eight channels into a single fibre, whilst the final EDFA compensated for MMF transmission loss and demultiplexing loss at the receiver side (up to 10dB depending on the experimental configuration). The polarisation states were measured at the end of the singlemode fibre and set to either linear or circular for each wavelength. Due to the polarisation orthogonality given by the PBS, the alignment of one polarisation per wavelength was sufficient, the other channel SOP being automatically aligned to the corresponding antipodal state. By this means, up to eight separate data channels could be transmitted in combined wavelength-polarisation space. The composite signal was then centre-launched into 50μm graded-index reeled MMF spans ranging from 300m to 3km. The bandwidth-distance product of these fibre spans were measured under centre-launch conditions and found to be 4.5GHz-km [13]. Other data, consistent with these results, suggest that centre-launching enhances the overfill launch bandwidth by at least a factor two [14, 15]. This restricted launch technique has been shown to be robust against MMF index profile variability [16]. Since the PWDM signal is also simply centre-launched, it is expected to be equally robust to index variability. At the MMF output, each set of two emergent orthogonal channels were transformed to horizontal and vertical linear polarisations [8].

 

Fig. 6. Schematic diagram of experimental set-up for combined WDM and polarisation-multiplexed MMF transmission.

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In a first experiment [Fig. 6(a), described more fully in 4.2] based on only two lasers with 100GHz spacing, the four resulting channels were passed to a Czerny-Turner monochromator, which either transmitted or extinguished the incident light depending on the well-known polarising properties of its metallic grating. The MMF pigtailed GRIN lenses used to couple light in and out of the monochromator provided a means of eye improvement via the spatial filtering selection of the less disturbed modes, but at the expense of some power loss [15]. Thus, each of the four channels could be recovered independently, after fine tuning of the MMF polarisation controller and proper selection of the wavelength. This demonstrated the principle of polarisation multiplexing, although only one polarisation channel could be recovered at a time.

In a second experiment (described more fully in Subsection 4.3), a polarisation insensitive, MMF pigtailed 200GHz-WDM demultiplexer became available. Unfortunately, the pigtail had a core diameter of 62.5μm in contrast to the 50μm MMF diameter, thus increasing mode coupling and reducing the transmission span. However, sufficient relative polarisation preservation allowed it to be used in the experimental demonstration of PWDM. Following wavelength demultiplexing, each wavelength was simultaneously polarisation demultiplexed using a PBS. Thus, each of the eight channels could be recovered, after fine tuning of its appropriate polarisation controller. The addition of MMF pigtailed GRIN lenses at the PBS also provided a means of eye improvement via spatial filtering.

4.2. Simultaneous transmission of 2P×2λ data channels over 300m and 3km of MMF

Two 100GHz-ITU adjacent wavelengths [namely λ ₁=1547nm and λ ₂=1547.8nm of Fig 6(a), without the 3dB couplers at the AWG entrance] were used for the first transmission experiments. Each wavelength carried a combination of two orthogonal circularly polarised data streams at 2.5 and 2.6Gb/s respectively.

 

Fig. 7. Eye diagrams for the 2.5Gb/s circularly left polarised (a) and 2.5Gb/s (b) circularly right polarised channels at λ = 1547.8nm after wavelength and polarisation demultiplexing at the end of a 300m sample of MMF.

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Figure 7 shows the typical open eye diagrams of two of the four transmitted channels at the end of 300m of MMF, following wavelength and polarisation demultiplexing. The clear opening resulted in an error-free transmission for all four channels, with a time stability between fine tuning as long as 60s in the laboratory environment.

Figure 8 shows a similar case after 3km of MMF. Though slightly less open, error-free transmission could still be measured. The decrease in amplitude of the eye was attributed to the extra degree of spatial filtering at the monochromator required to obtain an open eye. Due to the longer fibre length, the polarisation state was less stable, requiring fine tuning every 30s. Such behaviour was attributed to multimode polarisation mode dispersion (PMD) effects.

These open eye diagrams showed clear evidence of good channel selectivity, in terms of both wavelength and polarisation. This excellent performance is to be expected, as the AWG used for the wavelength multiplexing has approximately -30dB crosstalk, the monochromator polarisation selectivity is close to 20dB, and the 65GHz FWHM bandwidth selectivity resulting from the monochromator’s slit apertures and grating density provides at most -20dB crosstalk.

 

Fig. 8. Eye diagrams for the 2.5Gb/s (a) and 2.6Gb/s (b) channel circularly left polarised at λ = 1547.8nm after wavelength and polarisation demultiplexing at the end of a 3km sample of MMF.

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Fig. 9. Typical eye diagrams for the back-to-back experiment, including WDM and polarisation demultiplexing units- (right circ. pol., λ=1546.2nm, -5.1dBm on photodiode).

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4.3. Simultaneous transmission of 2P×4λ data channels over 300m MMF

In this second transmission experiment, shown in Fig. 6(b), the monochromator was replaced by a WDM-MMF-pigtailed demultiplexer. Four 200GHz-spacing ITU wavelengths (1544.5, 1546.4, 1547.7 and 1549.3nm) were used. Each wavelength carried a combination of two orthogonal circularly- (or linearly-) polarised data streams at 2.5 and 2.6Gb/s respectively. The back-to-back experiment, which includes both WDM and polarisation demultiplexing units [that is, all of Fig. 6(b) without the transmission fibre], already showed the effect of cross-talk due to coupling between the orthogonal polarisation multiplexed channels (Fig. 9).

Comparisons with the previous experiment indicated that the degradation of the transmission mainly occurs in the WDM-MMF demultiplexer. In fact, measurement of the SOP at the output of the WDM demultiplexer showed a degradation of the orthogonality, resulting in an increased cross-talk. However, combining a careful adjustment of the output polarisation with respect to the PBS axis, together with fine tuning of the spatial filtering still allowed the error-free recovery of the transmitted channels. The degradation of orthogonality incurred by the composite signal passing through the WDM demultiplexer is mainly attributed to its intrinsic free space propagation design. Thus, the launching condition into the output MMF does not retain the features of a SMF-into-MMF coupling-system as used at the beginning of the link, resulting in stronger polarisation mode coupling, as compared to wavelength demultiplexing using a monochromator. Moreover, the 62.5μm core diameter of its pigtailed fibres further contributes to polarisation mode coupling.

 

Fig. 10. Typical eye diagrams at the output of 300m MMF (right circ. pol. λ=1546.2nm, -5.7dBm on photodiode).

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Fig. 11. Typical eye diagrams at the output of 300m MMF (lin. vert. pol. λ=1546.2nm, -8.7dBm on photodiode).

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Figure 10 shows one of the eight circularly polarisation-multiplexed channels following wavelength and polarisation demultiplexing at the output of 300m of MMF. Though there was a significant eye closure, all eight channels were transmitted error-free. The presence of a pair of GRIN lenses in the PBS-based demultiplexing unit allowed for spatial filtering [see Fig. 6(b)], resulting in enhancement of some of the eyes, but to the detriment of the optical power available to the photodiodes (between -10 and -5dBm).

Results were similar for the linearly polarised cases, with error-free transmission of all eight channels as well (Fig. 11). The effect of spatial filtering is clearly visible in this case, resulting in a smaller amplitude of the detected signal.

4.4. BER measurements

BER curves have previously been measured in both 1P×1λ and 2P×1λ configurations [8], and indicated a power penalty of 1.9dB over 300m MMF, 3.9dB over 3km MMF at a BER of 10^-9 in the former case, and of 3.9db and 6.9dB over 300m and 3km of MMF respectively in the latter case, with a small 0.6dB degradation between the 2P×1λ and the 1P×1λ back-to-back experiments (see Fig 12). There is minimal cross-talk between wavelength channels, as isolation is given by the multiplexing AWG and either the monochromator (2P×2λ) or the demultiplexing AWG (2P×4λ), all of which have a spectral cross-talk better than -30dB. However, cross-talk between polarisation channels on a single wavelength is only -10dB. Hence, BER curves for the polarisation channels on a per wavelength basis indicate overall system performance, as shown in Fig. 12. These curves show that error-free transmission (BER = 10^-9) is achieved.

 

Fig. 12. BER curves measured at for a circular left polarised channel, with and without associated orthogonally-polarised multiplexed channel [8].

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5. Discussion

Using the MMF-WDM demultiplexer, transmission distance was limited to about 300m. This is mainly attributed to the free space propagation scheme of the MMF-WDM demultiplexer, together with its fibre core diameter mismatch with respect to the transmission fibre, resulting in strong polarisation mode coupling. When a monochromator was used for wavelength filtering instead, error-free transmission was achieved up to 3km of MMF. The absence of one of the two orthogonally polarisation multiplexed channels during detection in the latter case made it possible to achieve better filtering, as discussed in [8]. This is of course not compatible with the simultaneous monitoring of the two polarisation multiplexed channels, as used in the former case. However, providing that a WDM demultiplexer with 50μm core diameter graded-index MMF pigtails with a slightly modified design (taking into account the required SM launching condition in the output pigtail, probably at the expense of some increased insertion loss) is made available, the proof-of-principle experiment 2P×2λ indicates that 3km 2P×4λ MMF transmission should be possible as well.

As presented in this paper, the 2P×4λ is only a proof-of-principle of PWDM. Realistic deployment of our scheme will require an automated polarisation controller on a per wavelength basis, specially for legacy installed MMF fibres (rather than laboratory fibre reels) for which fluctuations of polarisation may be large. Thus, a polarisation tracking system similar to that done for PMD compensation and compatible with MMF fibres is required. Such a MMF-based device is the subject of further research, outside the scope of this paper.

Restricted launch techniques have been shown to be robust against index-profile variability [16] and always enhance the baseband bandwidth of MMF’s [13]. Since PWDM multiplexing is essentially a simple additional technology to the underlying launch condition, we expect it to be applicable to a wide selection of MMF’s, further enhancing the system bandwidth, regardless of the overfill launch bandwidth.

From a commercial point of view, WDM, polarisation multiplexing, PWDM or sub-carrier multiplexing can be applied according to the required bandwidth enhancement. However, WDM or sub-carrier multiplexing may be considered on their own, as their implementation is easier than that of full PWDM.

Ultimately, the only limit to the number of possible channels is the bandwidth of the optical amplifiers, and the channel spacing of the WDM mux-demux. Based on the assumption of an available 20GHz WDM-spacing [6], our results show that a possible bandwidth of 1Tb/s data can be transmitted up to 3km of MMF, every wavelength channel carrying two polarisation channels each at 2.5Gb/s. This greatly exceeds the conventional bandwidth-distance product normally attributed to MMF.

6. Conclusions

We have demonstrated that orthogonal SOP’s can be transmitted over up to 3km of graded-index 50μm MMF, keeping their relative orthogonal natures, and that polarisation orthogonality is available over the complete C-band. We have also shown that, for a potentially commercial PWDM system, a polarisation insensitive WDM demultiplexer is required, followed by polarisation demultiplexing, including an automated polarisation controller. We have performed an experiment to demonstrate 2P×4λ polarisation-multiplexing, achieving repeatable error-free data transmission of eight channels up to 300m of MMF, using a 200GHz ITU grid spacing. We have also demonstrated that extension of the MMF span length towards 3km is feasible for PWDM applications. We believe these results indicate the possibility of greatly enhancing the available bandwidth of legacy MMF in existing access networks.