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Ultra-dense spatial-division multiplexing (SDM) is achieved by mode multiplexed technique with multiple cores in a single fiber, namely few-mode multi-core fiber. Using a 9.8-km six-mode nineteen-core fiber, we demonstrate an ultra-dense SDM transmission of 16-channels wavelength-division-multiplexed (WDM) dual-polarization quadrature phase shift keying signals, achieving a record spatial multiplicity of 114. With the help of ultra-dense Super-Nyquist WDM techniques in the 4.5-THz bandwidth of the full C-band, we demonstrate 2.05 Pbit/s transmission over 9.8-km six-mode nineteen-core fibers. In this experiment, the highest aggregate spectral efficiency of 456 bit/s/Hz is achieved.
© 2016 Optical Society of America
1. Introduction
Ultra-dense wavelength-division multiplexed (WDM) techniques with digital coherent reception have drastically increased the transmission capacity over optical fiber. Single-mode fiber (SMF) transmission experiments with a capacity over 100 Tbit/s have been reported [1, 2]. In the transmission experiments, ultra-dense WDM techniques in C and extended L bands with high-order quadrature-amplitude-modulation (QAM) were introduced, while total input powers over 1 Watt were required in order to maintain the optical signal-to-noise ratio (OSNR). The required power launched into a fiber rapidly approaches a fundamental limitation due to light-induced catastrophic damage in a fiber (fiber fuse) [3] and fiber nonlinearity [4], resulting in a capacity crunch in SMF transmission.
Space division multiplexing (SDM) based on multi-core fibers (MCFs) and/or few-mode fibers (FMFs) [5] is a technique for overcoming the limits in SMF transmission. The fiber capacity and aggregate spectral efficiency in the MCF and FMF transmission experiments reported recently are plotted by red and blue open triangles in Fig. 1, respectively [6–16]. For comparison, the open triangles indicate those in SMF transmission. The spectral efficiency based on SDM techniques is improved, whereas the fiber capacity of the SMF transmission experiments stays around 100 Tbit/s. In particular, the use of MCF is capable of drastically increasing the fiber capacity, while the maximum fiber capacity in the FMF transmission has remained at 115.2 Tbit/s [16]. Fiber capacity over 1 Pbit/s has been demonstrated by using a 52-km twelve-core fiber [9]. Eventually, the record capacity of 2.15 Pbit/s was achieved by using a 31-km twenty-two-core fiber [10].
Fig. 1 The relationship between the fiber capacity and the aggregate spectral efficiency in the transmission experiment reported so far. Open triangles: standard single-mode fibers (SMFs), red open triangles: multi-core fibers (MCFs), blue open triangles: few-mode fibers (FMFs), and red closed circles: few-mode multi-core fibers (FM-MCFs).
In order to further improve the aggregate spectral efficiency, hybrid approaches with a combination of few-mode and multi-core fibers, namely few-mode multi-core fibers, have recently been developed [17–22]. Closed red circles in Fig. 1 show the fiber capacity and the aggregate spectral efficiency. Using hybrid MCF with twelve single-mode cores and two three-mode cores, a 1.05-Pbit/s transmission experiment was achieved [17], and dense SDM transmission over 527-km three-mode twelve-core fibers was demonstrated [20]. Eventually, transmission experiments with a spatial multiplicity over 100 have been achieved using a three-mode thirty-six-core fiber or a six-mode nineteen-core fiber [19, 21].
In this paper, we show ultra-dense SDM transmission using a 9.8-km six-mode nineteen-core fiber (6M-19CF), achieving the record spatial multiplicity of 114. We show measured mode dependent loss and the core-to-core crosstalk of the 9.8-km 6M-19CF including fan-in and fan-out devices. We demonstrate ultra-dense SDM Nyquist-WDM transmission using 9.8-km 6M-19CF with low-crosstalk mode multiplexers and demultiplexers, in which the coupling between the lower three modes and the higher three modes is maintained to be smaller than −15 dB, reducing the computational complexity of multiple-input multiple-output (MIMO) processing. In order to investigate the feasibility of the ultra-high capacity transmission with 6M-19CF, we demonstrate 2.05 Pbit/s ultra-dense SDM Super-Nyquist WDM transmission in full C-band. In this experiment, the record spectral efficiency of 456 bit/s/Hz is achieved.
2. Characteristics of a 6-mode 19-core fiber span
In SDM transmission, it is essential to suppress crosstalk between SDM channels. In principle, such SDM crosstalk can be compensated for by MIMO processing in the receiver as long as the mode dependent loss is maintained to be negligibly small. In order to reduce MIMO complexity, it is preferable that the SDM crosstalk is suppressed to the extent possible. The SDM crosstalk in the MCF case would occur between cores, which is called core-to-core crosstalk, and it increases as the distance between cores is closer. A large cladding diameter is expected to suppress core-to-core crosstalk efficiently in MCF having many cores. The SDM crosstalk in the FMF case would be originated from the coupling between modes, and it can be suppressed by enlarging the effective refractive index difference between modes because the phase mismatch between coupled modes becomes lager. For the large effective refractive index difference, the high refractive index ratio of the core and the clad, Δ, is required. Here, our fabricated 6M-19CF was designed so that the core-to-core crosstalk and mode coupling were suppressed as much as possible, resulting in the relatively large cladding diameter over 300 µm and high Δ over 1%.
Figure 2(a) shows the configuration of the 6M-19CF span used in our transmission experiments. It was composed of 9.8-km 6M-19CF for the transmission line, fan-in and fan out devices. The fan-in and fan-out devices were equipped with 19 10-m-long six-mode fibers and 10-m-long 6M-19CF as the fiber ports. The input and output edges of 9.8-km 6M-19CF were fusion-spliced to the 6M-19CF ports of fan-in and fan-out devices, respectively. A photograph of the cross-section of 6M-19CF is shown in Fig. 2(b). The core alignment was based on a hexagonal close-packed structure with twelve outer cores, six inner cores, and a center core. The core diameter and the core pitch of 6M-19CF were 17 µm and 62 µm, respectively. The core pitch was maintained to be relatively large in order to suppress the core-to-core crosstalk. Although the cladding diameter was 318 µm, the bending loss was negligible even when it was coiled with a diameter of 150 mm. In this experiment, the 6M-19CF was coiled around a fiber bobbin with a diameter of 280 mm. The index profile is shown in Fig. 2(c). The graded-index profile with a profile parameter α ~2 was adopted, and Δ was designed to be over 1.1%. Based on the designed index profile, four types of linear-polarized (LP) modes with degenerated modes, namely LP01, LP11a, LP11b, LP21a, LP21b, and LP02, can be sustained. In the center core, the differential mode delay (DMD) between LP01 and LP11 was measured to be 0.65 ns/km at the wavelength of 1550 nm, and that between LP01 and LP21/LP02 was 2.03 ns/km.
Fig. 2 (a) Configuration, (b) cross-section, and (c) refractive index profile of a fabricated 6-mode 19-core fiber.
In order to launch 19 six-mode-multiplexed signals into 19 cores of 6M-19CF, we used a lens-coupling-type fan-in device [23], which was fusion-spliced to the input edge of 6M-19CF. Figure 3(a) shows the configuration of the fan-in device. Using a single lens, collimated mode-multiplexed signals from single-core six-mode fibers with collimators were focused on the input edges of 19 cores of 6M-19CF. The alignment of free-space optics was optimized so that the mode coupling was minimized. A photograph of the fan-in device is shown in Fig. 3(b), and the length is about 300 mm. For the output of 6M-19CF, a fan-out device was used in the same manner as the fan-in device.
The measured total loss of 6M-19CF including the fan-in and fan-out devices is shown in Fig. 4. In this experiment, the output power after the fan-out device was measured when each mode was excited in the measured core through the fan-in device and same mode multiplexer as that used in the transmission experiments, as described below. The total losses of LP01, LP11a, LP11b, LP21a, LP21b and LP02 are plotted by closed circles, closed triangles, open triangles, closed squares, open squares, and open circles, respectively. The loss of the lower three modes (LP01, LP11a, and LP11b) was maintained to be smaller than 5 dB. For the higher three modes (LP21a, LP21b, and LP02), the loss was increased by 1 ~4 dB compared with the lower three modes. The mode dependent loss and the variation originated from the fan-in and fan-out devices rather than 6M-19CF.
Fig. 4 The measured loss of 6M-19CF including fan-in and fan-out devices for each mode input. Closed circles: LP01, closed triangles: LP11a, open triangles: LP11b, closed squares: LP21a, open squares: LP21b, and open circles: LP02.
We measured the core-to-core crosstalk when each mode was input. The experimental setup is shown in Fig. 5(a). Here, we consider to measure the crosstalk from the core B to the core C for the mode A. The mode A is launched into the core B through the mode multiplexer and the fan-in device, and then, we measure the output powers of the core B and C after the fan-out device. We define core-to-core crosstalk for mode A to be the ratio of output powers from the core B and C. Figure 5(b) shows the measured core-to-core crosstalk of the typical outer core (the core number of 1), the typical inner core (13), and the center core (19). The horizontal axis indicates the distance between cores normalized by the core pitch. The measured core-to-core crosstalk of the remaining 16 cores are shown in Fig. 6. With the smaller distance between cores, the core-to-core crosstalk was increased. The crosstalk from the adjacent core was suppressed to be smaller than −50 dB. Even for the center core, the total core-to-core crosstalk from all 18 cores was maintained to be smaller than −40 dB. The results suggest that the core-to-core crosstalk of 6M-19CF is negligible for this transmission experiment.
Fig. 5 (a) Configuration of the experimental setup for measuring core-to-core crosstalk of 6M-19CF. (b) The measured core-to-core crosstalk in the outer core (the core number of 1), the inner core (13), and the center core (19), as a function of the distance between cores normalized by the core pitch.
Fig. 6 The measured core-to-core crosstalk as a function of core-to-core distance normalized by the core pitch.
3. Ultra-dense SDM transmission experiment using 6M-19CF
Using 6M-19CF as mentioned in the previous section, we demonstrated ultra-dense SDM transmission of 16-channnl Nyquist-WDM dual-polarization (DP) quadrature phase shift keying (QPSK) signals. It is expected that the mode coupling between the lower three modes of LP01/LP11a/LP11b and the higher three modes of LP21a/LP21b/LP02 is suppressed because the effective refractive index difference between the mode groups is large. It would be possible to divide into two sets of small size MIMO for the lower three modes and the higher three modes, independently. By dividing large-size MIMO into two sets of small-size MIMO, the computational complexity is reduced.
The experimental setup is shown in Fig. 7. In the transmitter, eight even and odd channels aligned with frequency spacing of 22 GHz were independently modulated by an optical IQ modulator (IQM) driven by 10-Gbaud electrical Nyquist-shaped binary signals based on pseudo random sequences (PRBSs) with the length of 215 – 1, which were generated from an arbitrary waveform generator (AWG) with a sampling rate of 50 GSample/sec. In this experiment, the electrical signal generated from AWG was divided into two streams corresponding to I and Q components. The delay between two streams was about 100 symbols, and it was not sufficient for the decorrelation. The influence due to the short IQ delay will be discussed later. By using a polarization multiplexing emulator composed of a 3-dB coupler, a polarization beam combiner, and an optical delay line with length of 20 m for decorrelation, even and odd channels were combined with polarization multiplexing, and then, we obtained 16-channel Nyquist-WDM DP-QPSK signals. The frequency spacing was fixed to 11 GHz. The frequencies of the WDM channels ranged from 193.353 THz to 193.518 THz.
Fig. 7 The experimental setup for 16-channel Nyquist-WDM DP-QPSK signals. IQM: optical IQ modulator, AWG: arbitrary waveform generator, mode MUX: mode multiplexer, mode DMUX: mode demultiplexer, BPD: balanced photodetector, Pol OH: polarization-diversity optical hybrid, and LO: local oscillator.
The WDM signals were split into three branches. One was used for a measured SDM channel, and others were used for dummy SDM channels. For the measured channel, the WDM signals were amplified and split into six paths with optical fiber lines having lengths of longer than 40 m, 80 m, 160 m, 200 m, and 240 m for mode decorrelation. The six delayed signals were multiplexed by a six-mode multiplexer based on multi-plane light conversion (MPLC) [24]. A photograph of the mode multiplexer is shown in Fig. 8(a). The size is 250 mm × 220 mm × 50 mm. The measured spatial patterns of LP01, LP11, LP21 and LP02 after the mode multiplexer are shown in Fig. 8(b). We obtained the patterns similar to those of the ideal LP modes. The crosstalk from other modes after the demultiplexer following the multiplexer was maintained to be smaller than −15 dB for all modes, while the worst coupling was between LP11 and LP21. The mode coupling characteristics will be experimentally evaluated in detail later.
Fig. 8 (a) A photograph of the six-mode multiplexer. (b) The measured spatial intensity distribution of LP01, LP11, LP21, and LP02 modes after mode multiplexer.
The mode-multiplexed signal was launched into the measurement core of 6M-19CF through the fan-in device. For the dummy channels, two sets of WDM signals were divided into two sets of six paths. After amplification and decorrelation delay, they were mode-multiplexed by another two sets of a six-mode multiplexer, obtaining two sets of six-mode-multiplexed WDM signals. The mode-multiplexed signals were separated by two sets of a 1:16 six-mode splitter, which was composed of a tree structure of five 1:4 splitters based on free-space optics. The insertion loss of the 1:16 splitter was 13.8 ~14.3 dB for the lower three modes, while that was 15.1 ~16.1 dB for the higher three modes. The 18 SDM dummy channels out of 32 splitter outputs were launched into the remaining 18 cores through the fan-in device. The optical components were connected by fusion-splicing for the measured SDM channel, while connectors of six-mode fibers were used for dummy SDM channels. The input powers of all SDM channels before 19 cores were adjusted to be −11 dBm/wavelength/mode.
After the SDM transmission over a spool of 9.8-km 6M-19CF, the measured SDM channels were spatial demultiplexed by the fan-out device and a six-mode demultiplexer. When the measured SDM signal was switched to the measured core in each bit-error rate (BER) measurement, the mode multiplexer and demultiplexer for measured SDM channels were re-spliced to input/output ports of the fan-in and fan-out devices in turn. The six demultiplexed signals passed through optical bandpass filters (BPFs). The edge gradient and the full width at half maximum of BPF were over 4 dB/GHz and 15 GHz, respectively. After that, the six demultiplexed signals were simultaneously detected by six synchronized coherent detectors based on heterodyne reception, as shown in Fig. 9. A free-running laser was used as a local oscillator (LO). The frequency offset between LO and the received signal was set to be 10 GHz. In this experiment, we used a polarization-diversity optical hybrid in order to combine the signal and LO, whereas Q components of x polarization and y polarization were not required for heterodyne detection. The I components of both polarizations were balanced-detected, and then, the detected signals were digitized at 50 GSample/sec by using three synchronized real-time oscilloscopes. The stored size was 500k samples for one mode with single polarization.
Fig. 9 The configuration of heterodyne detection in the experiment. BPF: optical bandpass filter, BPD: balanced photodetector
The stored data were processed offline as shown in Fig. 10. The stored samples corresponding to the IF signals were frequency-converted to baseband. The baseband samples were down-sampled to two sample/symbol, and then, the rectangle-shaped Nyquist filtering was performed. After that, the set of stored samples were processed by a half-symbol-spaced adaptive MIMO equalization, achieving polarization demultiplexing, mode demultiplexing, and signal equalization [25]. The matrix elements of MIMO were composed of finite impulse response (FIR) filters. The tap coefficients of the FIR filters were adaptively controlled based on a decision-directed least-mean-square (DD-LMS) algorithm [26]. After the symbols were decoded, bit errors were counted.
Fig. 10 Procedure of digital signal processing in the receiver. MIMO: multi-input multi-output, LMS: least mean square algorithm.
In order to compensate for the crosstalk due to the mode coupling in the SDM transmission based on six-mode multiplexing, 12 × 12 MIMO is usually required. In our transmission experiment, the coupling between the lower three modes and the higher three modes was efficiently reduced, while the core-to-core crosstalk was maintained to be smaller than −40 dB as mentioned in the previous section. In this case, it is possible to divide into two sets of 6 × 6 MIMO for the three modes (LP01, LP11a, and LP11b) and the higher three modes (LP21a, LP21b, and LP02). In this experiment, the tap size was fixed to be 500.
Here, we consider the temporal delay between modes, polarization, and cores for the decorrelation of SDM channels. As mentioned above, the fiber length difference between polarization components was fixed to be 20 m, and that between modes was 40 m. Using the fibers, the relative delay between modes including polarizations was maintained to be about 1,000 symbols at 10 Gbaud. It is sufficient for signal decorrelation, even when we use a half-symbol-spaced MIMO equalizer with 1,000 taps. The fiber delay difference between cores was limited to be shorter than 10 m. Although it is not enough for the signal decorrelation, the crosstalk from all other cores was maintained to be −40 dB even for the center core having the largest number of neighborhood cores. In this case, the signal decorrelation between cores has little influence over experimental results.
We experimentally evaluated the BER performance of six-mode-multiplexed Nyquist-WDM DP-QPSK signals in back-to-back configuration without 6M-19CF. Figure 11(a) shows measured BER characteristics of single-channel six-mode-multiplexed Nyquist-shaped DP-QPSK signals. For the horizontal axis, averaged OSNR of six modes is shown. Dots indicate the averaged BER of six modes as a function of averaged OSNR in the case of using full 12 × 12 MIMO with 40 taps. In the case of using partial 6 × 6 MIMO with 40 taps, closed and open triangles show the averaged BERs of the lower three modes (LP01, LP11a, and LP11b) and the higher three modes (LP21a, LP21b, and LP02), respectively. Dashed line indicates the calculated curve determined from OSNR. Compared with the results of full 12 × 12 MIMO, the penalty due to dividing into two sets of 6 × 6 MIMO is less than 1 dB. By dividing into partial MIMO, it is expected that the computational complexity is reduced for demodulation of mode-multiplexed signals. Figure 11(b) shows the measured BERs of the center channel of 16-channel Nyquist-WDM DP-QPSK signals. The penalty due to the use of the partial 6 × 6 MIMO did not increase from the 12 × 12 MIMO results even in the WDM case, although BER performance was slightly degraded from single-channel case due to adjacent WDM channels in the image band of heterodyne detection.
Fig. 11 Measured averaged bit-error rate (BER) characteristics of (a) single-channel and (b) 16-channel WDM Nyquist-shaped six-mode-multiplexed DP-QPSK signals as a function of averaged OSNR. Dots, closed triangles, and open triangles indicate averaged BERs of six modes with 12 × 12 MIMO, the lower three modes with 6 × 6 MIMO, and the higher three modes with 6 × 6 MIMO, respectively.
By calculating magnitude of the tap coefficients of the 12 × 12 MIMO matrix, we investigated the mode coupling characteristic of the mode multiplexer and demultiplexer with the transmission line. Figure 12 shows the squared magnitude of tap coefficients of the MIMO matrix when the six-mode-multiplexed signals were demodulated by 12 × 12 MIMO in back-to-back configuration without 6M-19CF. Solid lines and red lines indicate the results of x and y polarization components, respectively. The matrix elements of 12 × 12 MIMO correspond to the mode coupling between input and output modes. The coupling between the lower three modes and the higher three modes, which are shown by the gray areas in Fig. 12, cannot be compensated for by partial 6 × 6 MIMO, and the components were efficiently suppressed, compared with the diagonal components of the matrix. The crosstalk ratio between the lower three modes and the higher three modes was smaller than −20 dB, and the performance degradation due to the crosstalk was negligible for the QPSK format even when the partial 6 × 6 MIMO was used, as shown in Figs. 11. We found the peak components in the diagonal components as indicated by the arrows in Fig. 12. This is because the IQ delay is shorter than the tap size of MIMO in these experiments [27], resulting in improvement of the Q value or the required SNR by around 1.5 dB. We have to evaluate the BER performance in consideration of the artificial improvement, as investigated below.
Fig. 12 Squared magnitude of tap coefficients of 12 × 12 MIMO of six-mode-multiplexed signals in back-to-back configuration without 6M-19CF. Solid: x polarization. Red: y polarization.
In addition, we also investigated the squared magnitude of the tap coefficients of 12 × 12 MIMO after 9.8-km 6M-19CF transmission. The worst case of mode coupling is shown in Fig. 13. The coupling components between the lower three modes and the higher three modes were enhanced by 6M-19CF transmission, compared with those in the case without 6M-19CF shown in Fig. 12. Nevertheless, the crosstalk between the lower three modes and the higher three modes was maintained to be smaller than −15 dB. The results suggest that the coupling between the mode groups is suppressed even in the SDM transmission over 9.8-km 6M-19CF.
Fig. 13 Squared magnitude of tap coefficients of 12 × 12 MIMO of six-mode-multiplexed signals after 6M-19CF transmission. Solid: x polarization. Red: y polarization.
We measured the BERs of all SDM and WDM channels. The results are shown in Fig. 14. In the horizontal axis, the number of SDM channels is defined by order of core number and mode. For instance, LP01, LP11a, LP11b, LP21a, LP21b and LP02 in Core 1 are SDM channels from 1 to 6, respectively. After transmission, OSNR was maintained to be over 25 dB. In this case, the expected BER with the 1M demodulated bits in each I or Q component of single polarization of the SDM channel was smaller than 1 × 10−6. For around half of all SDM channels, error free operation corresponding to smaller than 1 × 10−6 was achieved in all WDM channels. Some bit errors due to coupling between mode groups were measured for other channels, while the worst Q value calculated from the worst measured BER was 9.5 dB. Even after subtracting the artificial improvement of 1.5 dB due to shorter IQ delay into consideration, it did not exceed the Q threshold of 5.7 dB of the LDPC convolutional codes with 20% overhead [28]. The aggregate spectral efficiency was achieved to be over 345 bit/s/Hz (6 modes × 19 cores × 3.03 bit/s/Hz).
4. 2.05 Pbit/s SDM transmission over 6M-19CF
As mentioned above, we confirmed the feasibility of ultra-dense SDM transmission over 100 with 6M-19CF. Next, in order to investigate the applicability of 6M-19CF to ultra-large capacity transmission, we conducted transmission experiments with a higher spectral efficient scheme and the expanded signal bandwidth to the full C band, achieving 2.05 Pbit/s ultra-dense SDM transmission. In this experiment, we applied Super-Nyquist WDM technique based on the duobinary shaping with maximum likelihood sequence estimation (MLSE) in order to achieve higher spectral efficiency than that of conventional Nyquist-shaped signals [29–31]. The duobinary shaping reduces the signal bandwidth to smaller than the signal baudrate, suppressing WDM crosstalk even for WDM spacing of smaller than the baudrate. Although inter-symbol interference (ISI) due to the duobinary shaping is inevitable, it is compensated for by MLSE at the receiver. In this experiment, 15-Gbaud duobinary-shaped DP-QPSK signals were aligned with WDM spacing of 12.5 GHz, as shown in Fig. 15(a), achieving the spectral efficiency of 4 bit/s/Hz for single SDM channel even with the use of LDPC-based FEC with 20% overhead.
Fig. 15 (a) Spectral alignment of Super-Nyquist WDM signals in our experiment. (b) Measured optical spectra of Super-Nyquist WDM channels.
The experimental setup is shown in Fig. 16. The transmitter was based on three rail configuration. Two rails were used for measured even and odd WDM channels, and the other rail was used for dummy WDM channels in order to maintain not only OSNR but also nonlinear effects. For measured WDM channels, eight even and odd channels aligned with a frequency spacing of 25 GHz were independently modulated by IQM driven by 15-Gbaud electrical duobinary-shaped signals. Using two AWGs with a sampling rate of 50 GSample/sec, the electrical signals for I and Q components were independently generated based on the following off-line processing. After up-sampling of PRBSs with the length of 215 – 1 to two sample/symbol, square-root duobinary shaping was performed in the frequency domain. The obtained samples were rate-converted and sent to digital-to-analog converters embedded in AWGs. In this experiment, the delay between I and Q components was set to be more than 10,000 symbols, and it was enough for signal decorrelation. In the third rail for dummy WDM channels, 180 lasers aligned with the frequency spacing of 25 GHz were combined. Modulating them at 6.25 GHz with the carrier-suppressed condition, we obtained 360 tones with 12.5 GHz spacing, ranging from 191.69375 THz to 196.18125 THz. All tones were signal-modulated and polarization-multiplexed in the same manner as the measured WDM channels. Combining measured and dummy WDM channels, we obtained 360-channel Super-Nyquist-WDM DP-QPSK signals with line rates of 60 Gbit/s. Assuming the use of 20%-overhead FEC, the net bit rate was calculated to be 50 Gbit/s. In the experiment, we disabled 16 consecutive channels on the dummy-channel rail, and the measured 16 channels were tuned to the corresponding frequencies. All powers of the WDM channels were simultaneously controlled by using a wavelength selective switch (WSS) so that optical spectra became flat. The measured optical spectra of Super-Nyquist-WDM channels are shown in Fig. 15(b).
Fig. 16 Experimental setup for 2.05 Pbit/s SDM transmission. IQM: optical IQ modulator, AWG: arbitrary waveform generator, MZM: Mach-Zehnder modulator, Pol. MUX: polarization multiplexing: WSS: wavelength selective switch, OSA: optical spectrum analyzer, PC: personal computer, six-mode MUX: six-mode multiplexer, mode DMUX: mode demultiplexer, Pol OH: polarization-diversity optical hybrid, BPD: balanced photodetector, and LO: local oscillator.
For spatial multiplexing, the measured SDM channel and 18 dummy SDM channels were generated and launched into 9.8-km 6M-19CF in the same manner as in the previous experiment as mentioned in Section 3. After SDM transmission, the measured SDM channel was spatial-demultiplexed by using the fan-out device and the mode multiplexer, and then the six-mode demultiplexed signals were simultaneously detected by six synchronized coherent detectors based on heterodyne reception in the same manner as those in the previous experiment. In this experiment, the offset frequency between the received signal and LO was experimentally optimized for the signal baudrate of 15 Gbaud and the 20-GHz bandwidth of the oscilloscopes, and then, it was fixed to be 9.5 GHz. The detected signals were digitized and stored by three synchronized oscilloscopes with a sampling rate of 50 GSample/sec. The stored samples were off-line processed as shown in Fig. 17. After down-sampling to two sample/symbol followed by rectangular-shaped Nyquist filtering, the samples of all six modes were processed not by parallel 6 × 6 MIMO equalization but full 12 × 12 MIMO in order to avoid degradation of the required OSNR to the extent possible. The tap size was 1,000, and the tap coefficients were updated by LMS algorithm so that the equalized samples became duobinary-shaped symbols. After that, MLSEs were independently performed for I and Q components of equalized samples, and then bit errors were counted.
We experimentally evaluated the BER performance of Super-Nyquist WDM DP-QPSK signals in the back-to-back configuration without any 6M-19CF. The measured results are shown in Fig. 18. In this figure, the horizontal axis represents averaged OSNR of six modes. Open triangles and closed triangles indicate the averaged BER of the single-channel case and Super-Nyquist WDM case, respectively. For comparison, the results of single-channel Nyquist-shaped signals are plotted by open circles. We found that the OSNR penalty at BER of 1 × 10−2 was maintained to be smaller than 3 dB in the Super-Nyquist WDM case even with the 12.5 GHz WDM spacing for 15 Gbaud signals.
Fig. 18 Measured averaged bit-error rates (BERs) of six-mode-multiplexed duobinary-shaped DP-QPSK signals in the back-to-back configuration without 6M-19CF. Open triangles: single-channel duobinary-shaped signal, closed triangles: Super-Nyquist WDM signals, and open circles: single-channel Nyquist-shaped signals.
In the SDM transmission in full C band, DMD of 9.8-km 6M-19CF could depend on the optical carrier frequencies of WDM channels. We measured the dependence of the equalizer response of six modes after 9.8-km 6M-19CF on the WDM channel in the C band. Figures 19(a), 19(b) and 19(c) show superimposed tap coefficients of the diagonal components of 12 × 12 MIMO for the six-mode-multiplexed WDM channel of the lowest, the center, and the highest carrier frequencies in C band used in this experiment, respectively. We found three clear peak components. The slowest peak corresponded to LP11, and the second peak was LP01. The third peak was LP21/LP02, while it was difficult to distinguish the peaks of LP21 and LP02 because they are closely located each other. At the lowest frequency as shown in Fig. 19(a), the DMD values between LP01 and LP11, and between LP01 and LP21/LP02 were 5.8 ns and 21.2 ns, respectively. At the highest frequency as shown in Fig. 19(c), DMD between LP01 and LP21/LP02 was reduced to 15.6 ns, while we did not observe large difference of DMD between LP01 and LP11. The results suggest that the dependency of DMD on the optical frequency is larger at the higher-order mode. In this experiment, we used MIMO with rather long taps of 1,000 to compensate for the frequency-dependent DMD.
Fig. 19 The tap coefficients of the diagonal components of 12 × 12 MIMO for (a) the lowest, (b) the center, and (c) the highest carrier frequencies of six-mode-multiplexed WDM channels.
We measured BERs of all 41,040 WDM/SDM channels after SDM transmission. Figure 20 shows measured BERs of the six-mode-multiplexed WDM channels of the typical outer core with the core number of 1, the typical inner core (13), and the center core (19). For the remaining 16 cores, the measured results are shown in Fig. 21. They were maintained to be smaller than 2.3 × 10−2, which did not exceed the threshold BER of 2.7 × 10−2 of SD-FEC with 20% overhead [28]. The transmission capacity of 2.05 Pbit/s (360 WDM × 114 SDM × 50 Gbit/s) was achieved in the full C band with the record aggregate spectral efficiency of 456 bit/s/Hz.
Fig. 20 The measured BERs of six-mode-multiplexed WDM channels in the outer core with the core number of 1, the inner core with the core number 13, and the center core with the core number 19. The insets show the core number in the cross-section of the 6M-19CF and the constellation maps of demodulated signals of six modes for the center carrier frequency in Core 1.
In this experiment, the transmission length was limited to 9.8 km. For longer transmission, a longer tap length of the MIMO equalizer is required to compensate for the large DMD. Instead of the long tap MIMO equalizer, the combination of two types of FMFs with negative and positive DMD values would be more effective for DMD compensation in the optical domain [32].
4. Conclusion
We presented ultra-dense SDM transmission techniques based on 9.8-km 6M-19CF, achieving the record spatial multiplicity of 114. The core-to-core crosstalk of 6M-19CF was sufficiently suppressed to be smaller than −50 dB. We demonstrated ultra-dense SDM transmission of 16-Nyquist-WDM DP-QPSK signals using 9.8-km 6M-19CF with low-crosstalk mode multiplexers and demultiplexers. The coupling between the lower three modes and the higher three modes was maintained to be smaller than −15 dB, allowing division of 12 × 12 MIMO into two sets of partial 6 × 6 MIMO, in which the lower and higher three modes were independently processed even for the six-mode-multiplexed signals. Next, we demonstrated ultra-dense SDM Super-Nyquist WDM transmission using 9.8-km 6M-19CF. In this experiment, we achieved the transmission capacity of 2.05 Pbit/s and the record aggregate spectral efficiency of 456 bit/s/Hz.
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