Advanced nonlinear digital signal processing technologies, which bring significant performance gain for high-speed optical interconnects, are highly constrained by huge complexity in the actual deployment. Fully connected neural network based equalizer has shown powerful efficacy to deal with the complex linear and nonlinear impairments for VCSEL-enabled multimode optical interconnects, but it also contains a number of redundancies with little impact on performance improvement. In this work, we experimentally demonstrate a compressed neural network equalization using the iterative pruning algorithm for 112-Gbps VCSEL-enabled PAM-4 and PAM-8 transmissions over 100-m MMF. We also study the impact of threshold and pruning span on the performance of proposed algorithms. The results show up to 71% connection compression by use of the iterative pruning algorithms and maximum 28.4% improvement compared with the one-shot pruning algorithm.

The high speed multimode optical interconnects based on vertical-cavity surface-emitting laser (VCSEL) and multimode fiber (MMF) are severely constrained by the band-limited devices, modulation nonlinearity as well as laser induced noises such as relative intensity noise (RIN), mode partition noise (MPN) and fiber induced noises such as chromatic dispersion and mode dispersion. The advanced digital signal processing (DSP) technologies have been viewed as the inevitable tool to mitigate the physical limitations of electrical and optical components, and the noise interactions during the transmission. In order to achieve multimode 100 Gbps/lane over 100 m transmission with the existing devices, Volterra equalizer (VE) has been proven as a very effective equalization solution to deal with the nonlinear impairments. However, the practical implementation of this nonlinear equalizer has been constrained by its tremendously high computation complexity. In this paper, we propose the threshold based pruned retraining Volterra equalization (TRVE) to reduce the computation complexity while maintaining the transmission performance. Multimode 100 Gbps/lane transmission over 100 m OM3 MMF has been experimentally demonstrated with up to 70.7% computation complexity reduction while keeping the BER under the 7% HD FEC limit. In addition, the TRVE with $\ell_1$ -regularization ( $\ell_1$ -TRVE) is also proposed and experimentally verified to optimize the threshold selection.

Ultra-low-loss all-fiber mode selective couplers (MSCs) have been designed and fabricated using fused biconical taper technique with precise control on phase matching condition. An LP01 MSC with minimum insertion loss about 0.1 dB is fabricated. It is promising for single-mode excitation in large-mode-area few-mode fibers. The insertion loss of the demonstrated LP11 MSC is 0.3 dB at 1540 nm with mode extinction ratio higher than 28 dB. It has a broad operation wavelength from 1480 nm to 1640 nm with wavelength dependent loss about 0.3 dB. To the best of our knowledge, it shows the lowest loss in the reported broadband LP11 mode converters with high mode purity. The fabrication process is reliable and repeatable with smooth power curves, which is of great importance to the practical fabrication of these components. MIMO-less 2×25-Gb/s OOK signal and 2×20-Gb/s PAM-4 signal transmission over 15-km few-mode fiber have been demonstrated using the fabricated components. The low loss, large bandwidth and the high fabrication repeatability of the mode selective couplers make them promising for low-cost MIMO-less WDM-MDM transmission.

In this work, dyadic probabilistic shaping (PS) for PAM has been investigated and experimentally demonstrated for intensity-modulation and direct-detection (IM-DD) optical interconnection systems. Improved achievable information rate can be obtained under the condition of limited bandwidth and SNR. Theoretical investigations of generalized mutual information have been performed. 0.61- and 1.74-dB SNR gains by dyadic PS can be obtained for PAM-4 and PAM-8 respectively, to achieve error free assuming optimal 20% FEC. Meanwhile, such fixed distributions can offer a considerably broad SNR range (10.3∼16.7 dB for PAM-4 and 13.4∼24.6 dB for PAM-8) with positive gain. Moreover, experimental investigations have been carried out over optical multimode fiber (MMF) links at 850 nm using a commercial-product-level vertical-cavity surface-emitting laser (VCSEL) chip. PAM-8 signaling by PS at the net rate of 75 Gbps has been realized with 100-m OM3 fiber transmission. Energy efficient signaling can be achieved with up to 46% theoretical power reduction by PS. Experimentally, we obtained 16% reduction of optical power for the VCSEL-MMF optical link. The dyadic distribution of PS, due to its simplicity of coding, as well as considerable shaping gain and energy efficiency, is expected to be an opportune solution for the cost-sensitive short-reach scenarios.

In this paper, we propose a new method to mitigate the mode partition noise (MPN) in VCSEL-MMF based links by using wavefront shaping technique. The noise characteristic of the VCSEL-MMF links is theoretically studied and the impacts of coupling coefficients between VCSEL and MMF on the MPN and the system performance are investigated via simulation and experiment. The simulation results show that for 25-Gb/s OOK signal after 300-m MMF transmission, five orders of magnitude improvement of BER can be observed and the standard deviation of the received signal, which is the characterization of the MPN, is reduced for about an order when wavefront shaping is applied. With the help of wavefront shaping, we show that the DSP complexity has been profoundly reduced in order to achieve reliable 56-Gb/s and 112-Gb/s PAM-4 transmission by simulation. We perform experiment for 25-Gb/s OOK signal transmission over 300-m OM3 MMF with the launching optical power of −4 dBm to the fiber. About 1-dB power penalty improvement has been achieved at 7% FEC threshold after 300-m MMF transmission and the noise in the eye diagram is mitigated. The results of our simulation and experiment show the effectiveness of wavefront shaping to mitigate the MPN, therefore reduce the DSP complexity and improve transmission performance for the VCSEL and MMF based high speed short reach optical interconnects.

Low-complexity nonlinear equalization is critical for reliable high-speed short-reach optical interconnects. In this paper, we compare the complexity, efficiency and stability performance of pruned Volterra series-based equalization (VE) and neural network-based equalization (NNE) for 112 Gbps vertical cavity surface emitting laser (VCSEL) enabled optical interconnects. The design space of nonlinear equalizers and their pruning algorithms are carefully investigated to reveal fundamental reasons of powerful nonlinear compensation capability and restriction factors of efficiency and stability. The experimental results show that NNE has more than one order of magnitude bit error rate (BER) advantage over VE at the same computation complexity and pruned NNE has around 50% lower computation complexity compared to VE at the same BER level. Moreover, VE shows serious performance instability due to its intricate structure when communication channel conditions become tough. Moreover, pruned VE presents more consistent equalization performance within varying bias values than NNE.