# Real-Time Spatial-Division Multiplexing Transmission with Commercial 400 Gb/s Transponders
## 1 Introduction  
With the rapid development of cloud computing, 5G mobile communications and virtual reality applications and services, single-mode optical fiber (SMF) transmission systems and networks are facing great challenges on overcoming the capacity crunch. Recently, spatial-division multiplexing (SDM) fibers are widely studied as a new type of transmission media which could easily duplicate the system capacity and meet the demands of the next few decades [1; 2]. From the perspective of dimensionalities, SDM fibers mainly include few-mode fibers (FMFs) and multicore fibers (MCFs). According to the crosstalk among spatial channels, SDM techniques have strongly coupled and weakly coupled transmission approaches [3; 4; 5; 6]. The strongly coupled SDM systems usually adopt coupled-core MCFs or graded-index FMFs [7; 8]. When there are \(N\) (\(N=1,2,3\ldots\)) spatial channels in the strongly coupled SDM transmission link, \(2\)\(N\times 2\)\(N\) multiple input multiple output (MIMO) digital signal processing (DSP) and coherent detection are required at the receiver side to combat crosstalk among \(N\) spatial channels with dual polarizations. There has been a lot of research in this area using dozens of spatial channels. These workssuccessfully prove that SDM combined with wavelength-division multiplexing (WDM) techniques have great advantages in capacity expansion [9; 10]. So far, most strongly coupled SDM experiments are based on offline DSP due to the huge computational load of MIMO processing. However, current 100 G to 400 G commercial single-mode coherent optical transponders only equip 2 \(\times\) 2 real-time MIMO DSP hardware for polarization diversity. The incompatibility with commercial equipment greatly hinders the near-term deployment of the SDM techniques compared to other economic and technical factors. SDM transmission using single-mode weakly coupled MCF (WC-MCF) can effectively suppress the crosstalk among spatial channels [11; 12]. Since there is no need for mode-division multiplexing (MDM), single-mode WC-MCF systems have the most straightforward migration path from SMF transmission systems. In order to suppress the inter-core crosstalk, single-mode WC-MCF usually adopts a low-index trench outside each fiber core and the core-to-core pitch is generally larger than 30 \(\upmu\)m [13]. An increase in the number of cores means an increase in fiber diameter. For an MCF with large cladding diameter, the mechanical reliability, splice loss and production cost should be concerned at the same time, which places a limit on the number of spatial channels. Therefore, there is renewed interest in smaller diameter WC-MCFs. In particular, MCFs with the same 245 \(\upmu\)m coating diameter as standard SMF, which are compatible with current cabling technology, have been widely explored recently. Weakly coupled MDM approaches utilizing weakly coupled FMFs (WC-FMF) and highly selective mode multiplexer/demultiplexer (MUX/DEMUX) have also been studied to achieve practical application [14; 15; 16]. In circular-core WC-FMFs, all linear polarized (LP) modes can be divided into non-degenerate \(\mathrm{LP}_{\mathrm{0m}}\) modes and degenerate \(\mathrm{LP}_{\mathrm{1m}}\) (\(l\geq 1\)) modes. The \(\mathrm{LP}_{\mathrm{1m}}\) modes have two-fold spatial degenerate modes with the same propagation constant, labeled as \(\mathrm{LP}_{\mathrm{1m}}\) and \(\mathrm{LP}_{\mathrm{1m}}\) modes. According to coupled-mode theory, the modal crosstalk between two LP modes is inversely related to the modal effective refractive index difference (\(\mathrm{min}\,|\,\Delta\mathrm{r}_{\mathrm{eff}}\,|\) ), and the overall performance is determined by the \(\mathrm{min}\,|\,\Delta\mathrm{r}_{\mathrm{eff}}\,|\) among all the modes [17]. Owing to a relatively large \(\mathrm{min}\,|\,\Delta\mathrm{r}_{\mathrm{eff}}\,|\), different LP modes can be well separated in WC-FMF and the inter-LP mode crosstalk can be suppressed.