Scalable mode division multiplexed transmission over a 10-km ring-core fiber using high-order orbital angular momentum modes.

We propose and demonstrate a scalable mode division multiplexing scheme based on orbital angular momentum modes in ring core fibers. In this scheme, the high-order mode groups of a ring core fiber are sufficiently de-coupled by the large differential effective refractive index so that multiple-input multiple-output (MIMO) equalization is only used for crosstalk equalization within each mode group. We design and fabricate a graded-index ring core fiber that supports 5 mode groups with low inter-mode-group coupling, small intra-mode-group differential group delay, and small group velocity dispersion slope over the C-band for the high-order mode groups. We implement a two-dimensional wavelength- and mode-division multiplexed transmission experiment involving 10 wavelengths and 2 mode groups each with 4 OAM modes, transmitting 32 GBaud Nyquist QPSK signals over all 80 channels. An aggregate capacity of 5.12 Tb/s and an overall spectral efficiency of 9 bit/s/Hz over 10 km are realized, only using modular 4x4 MIMO processing with 15 taps to recover signals from the intra-mode-group mode coupling. Given the fixed number of modes in each mode group and the low inter-mode-group coupling in ring core fibres, our scheme strikes a balance in the trade-off between system capacity and digital signal processing complexity, and therefore has good potential for capacity upscaling at an expense of only modularly increasing the number of mode-groups with fixed-size (4x4) MIMO blocks.


Introduction
Recently, multiplexing techniques utilizing the spatial or mode domain of light over multicore fibers (MCFs) or multi-mode fibers (MMFs) have been intensively investigated aiming at breaking the nonlinear Shannon limit of the single mode fiber (SMF) capacity [1,2]. Compared with the schemes implemented over MCFs where multiple single-mode cores must be sufficiently spaced to suppress crosstalk (XT) [3], techniques based on MMFs can increase the number of transmission channels within a limited aperture and thus increase the capacity density of optical fibers [4].
Conventional approaches based on MMFs are divided into two categories: the multi-input multi-output (MIMO) digital signal processing (DSP) based approaches and the MIMO-free approaches. MIMO-based approaches include both space division multiplexing (SDM) and mode division multiplexing (MDM) implemented using few-mode fibers (FMFs) or MMFs [4,5]. The main concern over their scalability is the complexity of MIMO DSP which increases with the square of the number of channels and with the differential group delay (DGD) among channels. For instance, in a 10-mode-multiplexed FMF transmission system, 20x20 MIMO signal processing at the receiver was required to compensate the mode coupling [5]. The ever-growing DSP complexity would be impractical in real-time implementations due to high hardware cost and power consumption, and would force frequent hardware upgrades to systems as channel count increases.
MIMO-free approaches mainly include mode-group multiplexing [6,7] and orbital angular momentum (OAM) mode multiplexing [8][9][10][11]. They aim to suppress crosstalk among all channels with large differential effective refractive indices (Δn eff ) between modes or mode groups (MGs). MG multiplexing [6,7] in graded index fibers (GIFs) typically employs all modes in each near-degenerate MG as one channel, therefore the capacity resource is underutilized. In addition, the intra-MG DGD would also cause performance degradation. OAM multiplexed communications are typically implemented over ring core fibers (RCFs). RCFs supporting single-radial-order modes were initially proposed in the 1970s [12]. The principal strategy in OAM RCF design is to increase Δn eff between OAM modes in the same MG to achieve MIMO-free transmission, typically using high contrast (such as air core [13]) fibers. To suppress modal XT over km-scale propagation, Δn eff > 1x10 -4 is typically required [9], and this requirement should become more critical when the distance is further increased. The most successful demonstrations of OAM-MDM based MIMO-free data transmission so far are realized over the distances of 1-2 km [9][10][11]. Recently, an air core fiber that supports good quality OAM mode transmission has been demonstrated, in which the intra-MG Δn eff of up to 1.7x10 -4 is achieved [14]. However, the coupling between spin-orbit aligned and anti-aligned modes in the same MG generally > -10 dB after 13.4 km transmission. To further increase the separation and consequently the MIMO-free transmission distance would be technically challenging.
Meanwhile, weakly-coupled FMF transmission incorporating partial MIMO processing has recently been proposed to decrease the DSP complexity, in which FMFs with large Δn eff between MGs (for graded-index FMFs) or non-degenerate modes (for step-index FMFs) are employed to ensure low inter-MG/mode coupling, so that only smaller MIMO blocks are required to equalize the XT between intra-MG/degenerate modes [15][16][17][18][19]. However, the DSP simplicity of such schemes is not sustainable in FMFs supporting high-order MGs, as the number of near-degenerate modes in each group of the graded-index FMFs and DGD between degenerate modes (e.g. LP31a/b, etc.) in the step-index FMFs increases with the mode order.
On the other hand, although MIMO-free transmission in RCFs over long distance is challenging, RCFs still have significant potential of increasing the capacity-distance product with low DSP complexity in fiber MDM systems [20]. In single-radial-mode RCFs, the number of degenerate modes in each high-order MG (and therefore the MIMO block size) is fixed at 4, reducing the DSP complexity significantly for high order modes. Furthermore, compared with the conventional MMFs that exhibit strong mode coupling among high order MGs [21], in RCF the coupling coefficient between adjacent MGs significantly decreases with the increasing azimuthal mode order due to increasing Δn eff [22]. Therefore, in this paper, we propose a scalable fiber MDM scheme (as shown in Fig. 1

Demonstration of proposed OAM-MDM scheme
With the GIRCF supporting low inter-MG XT and low intra-MG DGD for high-order MGs, the proposed OAM-MDM scheme shows more realistic DSP scalability: only a fixed-size (4x4) modular MIMO equalizer with relatively low memory length is needed for the signal recovery of each MG, and inter-MG coupling is suppressed due to the optical isolation of large inter-MG Δn eff . As a proof-of-principle demonstration, we show here an 8-mode OAM-MDM (using OAM modes in MGs |l| = 4 and 5) and 10-λ WDM data transmission system over the 10-km GIRCF, and the system implementation is shown in Fig. 4. 10 optical carriers from external cavity lasers with wavelengths ranging from 1547.71 nm to 1551.31 nm with a 0.4-nm/50-GHz channel spacing are combined by a wavelength multiplexer. Then the 10 WDM signals are obtained by modulating the carriers with 32-GBaud Nyquist-QPSK signals from an arbitrary waveform generator (AWG) with an I/Q modulator. The Nyquist filter is a square root raised cosine electrical filter with a 3-dB bandwidth of 0.6X symbol rate and a roll-off factor of 0.1. The sample rate of the digital-to-analog converter (DAC) is 64 GSa/s and the modulated electrical data sequence is pseudo-random binary sequence (PRBS) with pattern length of 2 18 -1. Here note that due to the device limitation, all the WDM channels are modulated by one electrical signal. Insufficient decorrelation between WDM channels will overestimates the performance of the practical WDM systems with individual optical carriers carrying different data patterns, considering the inter-WDM-channel XT. However, this performance overestimation can be significantly mitigated by keeping sufficient guard band intervals between adjacent WDM channels (normally no less than 20% optical signal bandwidth/wavelength channel) [27]. In our experiment, the WDM guard gap is more than 25% optical signal bandwidth/wavelength channel, as shown in Fig. 7(c). In addition, highly correlated bit patterns of optical waveforms in neighboring optical channels will also cause non-linear signal degradation of WDM optical signals [27], which can be neglected in relatively short-distance transmission system (~10km fiber length in our experiment). The WDM doped fiber a decorrelation) Each branch o After collima reflected by conversion to example the splitter (i.e., wave plate (H exhibit oppos of reflections (CPs) with a q a group of fou using PBS-2. reflections (i. QWP-2 is use the four deco group of |l| = by its specific Fig. 4 Fig. 6(a), c the 32-GBaud is less than 3 at the BER of mance of the mo group |l| = 4 m the relatively (see Table. Fig. 6(a). F transmission, and at wavelength of XT, the averag T after 10-km = 5 and |l| = ld). Compared BER of ~5×10 ission, which e groups for t d Nyquist QPSK in Fig. 6(b). nels, and those ion of the OAM rations of ps in each 6(a), the OSNR) for ding with figuration, nsmission, plemented the BER her. As a d f ge OSNR m GIRCF 4 group, d with the -3 for that might be the mode K signals Fig. 7(a) e of all 80 M-MDM-