Exabit optical communication explored using 3M scheme

The capacity of the optical communication infrastructure in backbone networks has increased 1000-fold over the last 20 years, and this has been made possible by the development of the erbium-doped fiber amplifier (EDFA) and wavelength division multiplexing (WDM).¹⁾ Despite such rapid progress, information capacity is still growing at an annual rate of 40%, which means that in 20 years we will need petabit/s or even exabit/s optical communication. However, it is widely recognized that the maximum transmission capacity of a single strand of fiber is rapidly approaching its limit at ∼100 Tbit/s owing to optical power limitations imposed by the fiber fuse phenomenon²⁾ and the finite transmission bandwidth determined by EDFAs. This situation is depicted in Fig. 1.

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To explore breakthrough technologies that will enable us to exceed these limits and achieve a giant leap, we launched a collaborative study group called EXtremely Advanced Transmission (EXAT) in Japan in 2008, and advocated the promotion of the three "M technologies" as shown in Fig. 2.³⁾ The first "M technology" is a multi-level modulation format, which enables us to achieve a high spectral efficiency comparable to that of wireless communication. The second "M technology" is multi-core fiber (MCF), which employs space division multiplexing (SDM). The third "M technology" is mode division multiplexing in which multi-input and multi-output (MIMO) technology, which originated from wireless communication, will be useful for handling multi-modes in multi-core/multi-mode fibers. These "multi" technologies have attracted considerable interest from researchers worldwide, and intensive efforts have been made to pursue these goals. As a result, a number of studies on the three M technologies have been reported simultaneously at recent conferences, and rapid and substantial progress has been made in these fields.^4–33)

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In this paper, we describe recent challenges and the efforts we have made towards a hardware paradigm shift in the optical communication infrastructure by employing the "multi" technologies. This includes ultra multilevel coherent transmission including 1024 quadrature amplitude modulation (QAM) and an ultrahigh-speed and spectrally efficient transmission using optical Nyquist pulses, ultralow-crosstalk MCF and its application to SDM transmission, and mode division multiplexing with MIMO technology.

Achieving an ultrahigh spectral efficiency (SE) toward the Shannon limit is one of the targets of our three-M breakthrough technologies, which allows us to expand the total WDM capacity within a finite optical amplification bandwidth. Of the various available formats, M-ary QAM is capable of approaching the Shannon limit most closely by increasing the multiplicity M. QAM is a modulation format that combines two carriers whose amplitudes are modulated independently with the same optical frequency and whose phases are 90 degrees apart. A 2^N QAM signal represents N bits, so it has N times the spectral efficiency compared with OOK.

The challenge with respect to a higher QAM multiplicity is to meet higher SNR and phase noise tolerance requirements. Figure 3 shows the relationship between E_b/N₀ and the theoretical bit error rate (BER) for M-ary QAM. For a BER of 2 × 10⁻³, the required E_b/N₀ values are 21 and 24 dB for 512 and 1024 QAM, which corresponds to SNRs of 30.5 and 34 dB, respectively. To realize a better BER performance with a lower E_b/N₀, the forward error correction (FEC) technique has been developed. Figure 4 shows the BER after applying FEC vs the input Q value without FEC, Q_in.³⁴⁾ Q_in is the SNR given by

$$\begin{equation} Q_{\text{in}} = \frac{I_{1} - I_{0}}{\sigma_{1} + \sigma_{0}} \end{equation} \tag{ 1 }$$

where I₁ and I₀ are the mean values and σ₁ and σ₀ are the standard deviations of the bits corresponding to 1 and 0, respectively. Here, the Shannon limit describes the lowest Q_in value needed to achieve an infinitely low BER by employing FEC under a certain code rate R:

$$\begin{align} &R = 1 + \mathrm{BER}_{\text{in}}\log_{2}\mathrm{BER}_{\text{in}} + (1 - \mathrm{BER}_{\text{in}})\log_{2}(1 - \mathrm{BER}_{\text{in}})\\ &\mathrm{BER}_{\text{in}} = \frac{1}{2}\text{erf}c\left(\frac{Q_{\text{in}}}{\sqrt{2}}\right) \end{align} \tag{ 2 }$$

which is known as Shannon's second theorem or the noisy-channel coding theorem.^35,36) This provides the ultimate limit for the minimum Q value needed to achieve an infinitely low BER. Recently, third generation FEC, namely a turbo block code with a soft decision, has been developed that enables us to realize BER performance very close to the Shannon limit. This indicates the possibility of realizing ultrahigh spectral efficiency by combining QAM and FEC.

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Here we describe our recent demonstration of a 1024 QAM transmission, in which a polarization-multiplexed 60 Gbit/s signal was transmitted over 150 km.⁴⁾ Figure 5 shows the experimental setup. As a coherent light source, we used a 1.5 µm acetylene frequency-stabilized fiber ring laser with a linewidth of 4 kHz.³⁷⁾ The output of the laser was modulated at an IQ modulator with a 3 Gsymbol/s 1024 QAM baseband signal produced by an arbitrary waveform generator (AWG) operating at 12 Gsample/s. We employed a raised-cosine Nyquist filter at the AWG using a software program to reduce the bandwidth of the QAM signal. It is well known in the microwave communication field that a Nyquist filter is very useful for reducing the bandwidth of a data signal without introducing intersymbol interference.³⁸⁾ Figure 6 shows the transfer function and impulse response of the raised-cosine Nyquist filter. The transfer function is given by

$$\begin{equation} H(f) = \begin{cases} \frac{1}{2} \left\{1 - \sin \frac{\pi (f - 0.5)}{\alpha}\right\} & 0.5 - \frac{\alpha}{2} \leq |f| < 0.5 + \frac{\alpha}{2} \\ 1 & |f| < 0.5 - \frac{\alpha}{2} \\ 0 & |f| \geq 0.5 + \frac{\alpha}{2} \end{cases} , \end{equation} \tag{ 3 }$$

where α is called a roll-off factor. As shown in Fig. 6(b), the impulse response becomes zero at the location of neighboring symbols. This indicates that the bandwidth can be reduced with the Nyquist filter while avoiding intersymbol interference (ISI). We employed a root raised-cosine Nyquist filter with a roll-off factor α = 0.35 at the AWG as well as in the digital signal processor (DSP) at the receiver using software, so that the bandwidth of the QAM signal was reduced to 4.05 GHz. In addition, a pre-equalization process based on frequency domain equalization (FDE)³⁹⁾ was adopted to provide high-resolution compensation for the distortions caused by individual components such as the AWG and the IQ modulator.

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The optical QAM signal was then orthogonally polarization-multiplexed and launched into a 150 km fiber link. At the receiver, the QAM signal was homodyne-detected at a 90° optical hybrid. As a local oscillator (LO), we used a frequency-tunable fiber laser whose phase was locked to the pilot tone transmitted with the data signal via the optical phase-locked loop (OPLL), which enables low phase-noise coherent detection. After detection with balanced photodiodes, the QAM data were A/D converted and processed with a DSP in an off-line condition. In the DSP, a digital back-propagation method was adopted to compensate for fiber nonlinearities and dispersion simultaneously.⁴⁰⁾ Here, we employed a split-step Fourier analysis of the Manakov equation, which describes the pulse propagation in a fiber with dispersion, SPM, and XPM between the two orthogonal polarizations under a randomly varying birefringence.⁴¹⁾ Finally, the compensated QAM signal was demodulated into binary data, and the bit error rate was evaluated.

The experimental results are shown in Fig. 7. In this experiment, 60 Gbit/s data were transmitted within an optical bandwidth of only 4.05 GHz. This indicates a net spectral efficiency as high as 13.6 bit/s/Hz in a multi-channel transmission, even when accounting for the 7% FEC overhead.

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Along with the aim of higher multiplicity, it is very important to explore ways of increasing the symbol rate, which are currently limited by the speed and bandwidth of analog-to-digital (A/D) and digital-to-analog (D/A) converters. To overcome these limitations, coherent optical time division multiplexing (OTDM) has been demonstrated that employs multi-level QAM modulation for ultrashort optical pulses.^5–7) However, typical pulse waveforms such as Gaussian or sech profiles generally occupy a large bandwidth in the frequency domain and thus may not be an appropriate waveform in terms of SE. We recently proposed a new type of optical pulse, which we call an "optical Nyquist pulse", whose shape is given by the sinc-function-like impulse response of the Nyquist filter shown in Fig. 6(b).⁸⁾ The fundamental configuration of the ultrahigh-speed Nyquist TDM transmission is shown in Fig. 8. The optical Nyquist pulse trains are bit interleaved to a higher symbol rate by OTDM. Here, in spite of a strong overlap, no ISI occurs due to the zero crossing property of the Nyquist pulse at every symbol interval. The OTDM demultiplexing from this continuous data sequence can be realized with ultrafast optical sampling, so that only data at the ISI-free point could be extracted. In this way, it is possible to reduce the signal bandwidth without ISI during transmission, and therefore, the SE can be significantly improved.

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Here we present the 1.28 Tbit/s (640 Gbaud) polarization-multiplexed transmission of Nyquist OTDM signals over 525 km.⁹⁾ Figure 9 shows the experimental setup. In the transmitter, we first generated an optical Nyquist pulse train from a mode-locked fiber laser (MLFL) that emits Gaussian pulses. The Gaussian pulses were transformed into a Nyquist profile by using a spectrum manipulation technique based on the spatial intensity and phase modulation of spectral components with a liquid crystal spatial modulator.⁴²⁾ The generated waveform is shown in Fig. 10(a), where the periodic zero crossing in the tail can be clearly seen. The optical Nyquist pulses were then DPSK modulated at 40 Gbit/s and multiplexed to 640 Gbit/s using a delay-line bit interleaver. An eye diagram of the obtained Nyquist OTDM signal is shown in Fig. 10(b). The OTDM signal becomes an analog-like continuous data stream, and the eye diagram appears greatly distorted due to the interference. However, as indicated by the blue line, no ISI occurs and a constant level is maintained at every symbol interval. The 640 Gbit/s Nyquist pulses were polarization multiplexed to 1.28 Tbit/s and transmitted over a 525 km dispersion-managed transmission link. In the receiver, the transmitted Nyquist pulse was first demultiplexed to 40 Gbit/s. Here, unlike conventional OTDM demultiplexing, we adopted an optical sampling technique so that only data at the ISI-free point could be extracted from the continuous data stream. As an ultrashort optical sampler, we employed a nonlinear optical loop mirror (NOLM) switch with a gate width of 830 fs.

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Figures 11(a) and 11(b) show the BER characteristics for 1.28 Tbit/s-525 km Gaussian and Nyquist pulse transmission. As shown in Fig. 11(a), with a Gaussian pulse, the BER for a 1.28 Tbit/s polarization-multiplexed transmission was greatly degraded compared with the single-polarization result as a result of the depolarization-induced crosstalk⁴³⁾ as shown in the inset of Fig. 11(a). On the other hand, the BER degradation associated with polarization multiplexing was much smaller with a Nyquist pulse as shown in Fig. 11(b), and a BER of ∼10⁻⁷ was achieved after a 525 km transmission with a much lower power penalty and a reduced error floor. These results indicate that the use of Nyquist pulses is very promising for ultrahigh-speed transmission. This scheme is scalable to a higher symbol rate per channel of for example 1 Tbaud,¹⁰⁾ and simultaneously enables ultrahigh SE by employing coherent QAM.¹¹⁾

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One of the strongest motivations for developing new fiber technologies is the huge increase in optical power. As the optical power reaches a certain level, serious damage called a "fiber fuse" occurs. A fiber fuse is a phenomenon whereby a fiber core is partially melted as a result of high optical power, and holes propagate through the core until the optical source is shut down.¹⁹⁾ The fiber fuse propagation threshold is around 1 W, and it is especially disadvantageous for single-mode fibers with small MFDs. The optical power for WDM signals and the pump power for Raman amplification has now reached of the order of a few Watts, which is very close to the threshold power for fiber fuse propagation. This means that the allowable optical power input into an optical fiber is approaching its limit.

The basic parameters for optical fibers have remained almost unchanged for more than 20 years, but if we are to overcome the power limitation, a paradigm shift from single core to multiple cores is indispensable. One of the most important factors in multi-core design is to minimize the crosstalk between any pair of cores. It has been found that the crosstalk in MCF is described by coupled-power theory more accurately than coupled-mode theory.^12,13) This indicates that the dominant factor as regards the crosstalk is stochastic mode coupling along the MCF caused by longitudinal perturbations. The crosstalk is also significantly affected by fiber bending.¹⁴⁾ From this perspective, heterogeneous MCF has been proposed, which is composed of cores with different propagation constants.¹⁵⁾ It has also been found that even a very small fluctuation of the structural parameters results in crosstalk reduction. Trench-assisted MCF, which is composed of cores with depressed cladding, has been proposed as another way of suppressing crosstalk without adversely affecting core density. Several groups have reported MCF with ultra-low crosstalk,^16–18) including a 17.4 km MCF with crosstalk as low as −77.6 dB.¹⁶⁾ The details of these MCFs are shown in Table I. Recently, by using a low-crosstalk 12-core MCF, a record 1.01 Pbit/s capacity has been demonstrated with the SDM of 222 WDM channels of 456 Gbit/s PDM-32QAM signals.¹⁸⁾

Table I. MCFs for SDM transmission.

Number of cores	19	7	12
Core pitch (µm)	35	45	37
Cladding diameter (µm)	200	150	225
Loss (dB/km)	0.23	0.18	0.199
Aeff (µm2)	72	80	88
Crosstalk (dB/km)	−42	−90	−55 to −49
Reference	16	17	18

If we can obtain the mode-coupling coefficient in the propagation direction, we can analyze the optical power distribution along each core, which will give us useful knowledge about SDM transmission using MCF. Recently, we proposed a novel technique for measuring the mode coupling along an MCF using synchronous multi-channel optical time domain reflectometry (OTDR).¹⁹⁾ This technique clarifies the nonuniformity of the mode-coupling coefficient along the fiber caused by the structural irregularity of the fiber. A schematic diagram of the MCF mode-coupling measurement and the experimental results are shown in Fig. 12. As shown in Fig. 12(a), an optical pulse is coupled to the core 1, and the backscattered light in the core n, P_bsn, is detected by multi-channel synchronous OTDR. Example backscattered OTDR measurements from each core are shown in Fig. 12(b), when a 1 µs optical pulse was coupled into core 1 (center core) of a 2.9 km-long 7-core MCF with a core pitch of 46 µm and a cladding diameter of 217 µm. The mode coupling between core 1 and n along the fiber under a condition of small mode coupling can be then obtained from the power ratio between P_bs1 and P_bsn:

$$\begin{equation} \eta_{n,1}(L) = \frac{P_{\text{bs}n}}{P_{\text{bs1}}} = 2h_{n,1}L + K\quad\text{for $h_{n,1}L \ll 1$}, \end{equation} \tag{ 4 }$$

where h_n,1 is the mode coupling coefficient between core 1 and n, L is the fiber length, and K is a constant determined by the Fourier transformation of the autocorrelation function of the mode-coupling coefficient.^44,45) This indicates that η_n,1 is proportional to the fiber length, with the slope given by twice the mode-coupling coefficient. Figure 12(c) shows the power ratio η_n,1 (n = 2–7) obtained from Fig. 12(b). We can therefore obtain the mode-coupling coefficient by using the derivative of the power ratio, which is shown in Fig. 12(d). These results indicate that the mode-coupling coefficient varies with position, and there is a structural irregularity that must be eliminated.

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For long-haul SDM transmission, it is essential to develop optical amplifiers for multi-cores^20–22) as well as other active or passive components and splicing technologies. Figure 13 shows the basic configuration of a multi-core optical amplifier. As in conventional EDF, multiple erbium-doped cores are used as a gain medium. The EDF is pumped either with an individual core pumping scheme using a multi-core coupler as shown in (a),^20,21) or with uniform clad pumping as shown in (b),²²⁾ which has been adopted in high power fiber lasers, namely the double clad pumping scheme. In Ref. 20 a net gain of about 30 dB was obtained for seven cores with a crosstalk of less than −30 dB with individual core pumping. With a cladding-pumped seven-core EDFA, a gain of >15 dB, a noise figure of <5.5 dB and a crosstalk of <−30 dB have been achieved.²²⁾ A cladding-pumped MC-EDFA may have a lower pump efficiency than individual core pumping, but the power consumption is expected to be lower because only a single multi-mode pumping source is used. The MC-EDFA has been successfully applied to long-haul MCF transmission such as a 140.7 Tbit/s, 7326 km seven-core transmission, demonstrating a capacity-distance product of more than 1 Exabit/s·km.²³⁾

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As regards fusion splicing, the existing fusion splice technology developed for polarization-maintaining fibers can be extended to the core alignment of multiple cores using a triangular mirror and side-view observation. In addition, by swinging the electrodes, the temperature is uniform for the inner and outer cores.²⁴⁾ Figure 14 shows the basic configuration of an MCF fusion splicer. Along with splicing, the multi-core connector is a key element from a practical point of view, where precise control of the central axis as well as the axial angles will be very important. An MU-type seven-core connector has been developed by employing Oldham's coupling mechanism inside the connector plug housing for precise alignment.²⁵⁾

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In addition to multi-cores, multiple modes can also offer additional spatial degrees of freedom and are expected to offer another potential way of overcoming the capacity limitation. In particular, MIMO technology, which was originally developed in wireless communications to cope with multi-path interference, is expected to be a key element for realizing mode multiplexing and demultiplexing capable of handling inter-modal crosstalk and differential group delay.

In the field of wireless communications, MIMO technologies have been developed for high-speed transmission.⁴⁶⁾ In a wireless system, a signal is transmitted through multiple paths between multiple antennas at the transmitter and receiver. By representing multiple paths as channel matrix H, the receiver can separate the channels based on signal processing. It is important to incorporate such technologies from the viewpoint of mode division multiplexing using multi-modes.

The MIMO technique was first applied to optical communication for polarization demultiplexing, which enables the separation of two orthogonal polarizations at the receiver without any manual adjustment of the polarization axis.⁴⁷⁾ Recently, a number of studies have reported the application of MIMO to mode-division-multiplexed transmission. MIMO-based multi-mode transmission is shown schematically in Fig. 15. For a single input signal x(t), the received signal y(t) is represented by

$$\begin{equation} y(t) = \sum_{k = 1}^{Q}h_{k}x(t) + n(t) \end{equation} \tag{ 5 }$$

where n(t) is noise and Q is the number of modes. The first term has Q contributions representing the distortion in a certain mode k. The distortion includes the loss, group delay, and coupling ratio with mode k. By extending this representation to multiple inputs and outputs, the received signal at the ith receiver is given by

$$\begin{align} y_{i}(t) &= \sum_{j = 1}^{M}\sum_{k = 1}^{Q}h_{ijk}x_{j}(t) + n_{i}(t) = \sum_{j = 1}^{M}H_{ij}x_{j}(t) + n_{i}(t),\\ i& = 1, \ldots, N \end{align} \tag{ 6 }$$

where h_ijk is the distortion when the signal is transmitted from the jth transmitter to the ith receiver via mode k, which is estimated from the input and received training symbols. Equation (6) can be represented in a matrix form:

$$\begin{equation} \boldsymbol{{y}}(t) = \boldsymbol{{Hx}}(t) + \boldsymbol{{n}}(t). \end{equation} \tag{ 7 }$$

By estimating the channel matrix H from x(t) and y(t) using signal processing, and multiplying the inverse matrix of H, we can recover the input signal x(t). In general, to avoid increasing the noise term through the multiplication of H⁻¹ by n(t), we diagonalize H in the form D = V^†HU using unitary matrices U and V. Then, x(t) can be obtained by receiving y(t) by multiplying U and V^† by x and y respectively as follows:

$$\begin{equation} \boldsymbol{{V}}^{\dagger}\boldsymbol{{y}}(t) = \boldsymbol{{V}}^{\dagger}\boldsymbol{{H}}(\boldsymbol{{Ux}}(t)) + \boldsymbol{{V}}^{\dagger}\boldsymbol{{n}} = \boldsymbol{{Dx}} + \boldsymbol{{V}}^{\dagger}\boldsymbol{{n}}. \end{equation} \tag{ 8 }$$

Each component of x(t) can be extracted by dividing the right-hand side of Eq. (8) with diagonal components of D. It should be noted here that the noise increase does not occur in the term V^†n, as the magnitude of this term is |V^†n| = |n| due to the property of a unitary matrix.

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Several groups have demonstrated MIMO-based multi-mode transmission over a few-mode fiber using fundamental and higher-order LP modes. Figure 16 shows examples of mode multiplexers and demultiplexers. Higher-order modes are excited and separated using free-space optics with phase plates for phase inversion [Fig. 16(a)],²⁶⁾ long-period fiber Bragg gratings for fundamental to higher-order mode conversion [Fig. 16(b)],²⁷⁾ or a liquid crystal on silicon (LCOS)-type spatial intensity and phase modulator for beam profiling [Fig. 16(c)].²⁸⁾ Recent demonstrations of mode-division-multiplexed transmission are summarized in Table II.^29–33) For example, the 5-mode transmission of 100 Gbit/s PDM-QPSK signals has been realized using the LP₀₁, LP_11a, LP_11b, LP_21a, and LP_21b modes by using 4 × 4 MIMO (used to separate degenerate modes, e.g., LP_11a,x, LP_11a,y, LP_11b,x, and LP_11b,y).³¹⁾ A 6-mode transmission including the LP₀₂ mode has also been achieved with 12 × 12 MIMO.³³⁾ These reports potentially demonstrate the capability of spatial and polarization mode discrimination with MIMO.

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We reviewed recent progress on the 3M scheme, which consists of multi-level modulation, multi-core fibers, and multi-mode technologies. These innovative technologies are expected to overcome the power and capacity limitations of today's optical communication, and ultimately lead to a thousand-fold giant leap toward the Exabit optical communication infrastructure in the coming 20 to 30 years.