We use a neural network to inversely design a four-ring few-mode fiber for weak-coupling optimization so as to support MIMO-less MDM optical communication. This method provides high-accuracy, high-efficiency and low-complexity for complexed fiber design.

Few-mode fiber (FMF) supporting many modes with weak-coupling is highly desired in mode division multiplexing (MDM) systems. The multi-parameter design of FMF becomes comparably difficult, inaccurate and time-consuming when it comes for complex fiber structures and many high order modes. In this work, we demonstrate a machine learning method using neural network to inversely design the desired FMF based on multiple-ring structure. By using the minimum index difference between adjacent modes as the weak-coupling optimization aim, we realize the inverse design of 4-ring step-index FMFs for supporting 4, 6 and 10 -mode operation, and 6-ring step-index FMF for supporting 20-mode operation. This method provides high-accuracy, high-efficiency and low-complexity for fast and reusable design of optical fibers, including particularly weak-coupling FMF in this work. It can be widely extended to a lot of fibers and has great potential for instantaneous applications in the optical fiber industry. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Few-mode fiber (FMF) supporting many modes with weak-coupling is highly desired in mode division multiplexing (MDM) systems. The multi-parameter design of FMF becomes comparably difficult, inaccurate and time-consuming when it comes for complex fiber structures and many high order modes. In this work, we demonstrate a machine learning method using neural network to inversely design the desired FMF based on multiple-ring structure. By using the minimum index difference between adjacent modes as the weak-coupling optimization aim, we realize the inverse design of 4-ring step-index FMFs for supporting 4, 6 and 10 -mode operation, and 6-ring step-index FMF for supporting 20-mode operation. This method provides high-accuracy, high-efficiency and low-complexity for fast and reusable design of optical fibers, including particularly weak-coupling FMF in this work. It can be widely extended to a lot of fibers and has great potential for instantaneous applications in the optical fiber industry.

2-Micron waveband optical interconnection at record-high-speed of 100 Gbps/lane with 100-m hollow-core photonic bandgap fiber transmission is achieved. Mode-dependent bandwidth restriction is well optimized by probabilistically shaped discrete multi-tone (PS-DMT) modulation.

Hollow-core fiber (HCF) has been attracting broad interests in recent decades, and has extended the communication window to longer wavelength, 2 micron. In this article, we present a demonstration of low-latency HCF short-reach optical interconnection at 2 micron, achieving a high single-lane speed of 100 Gbps. High physical speed (near vacuum-light-speed) and high information speed (100-Gbps) optical interconnection with 100-m transmission distance is experimentally achieved with error-free performance. Probabilistically shaped discrete multi-tone (PS-DMT) modulation with entropy loading is employed to accommodate the deteriorated frequency response caused by the mode dispersion in HCF. Compared with conventional solid-core fiber (SCF), HCF contributes 30.95% (1.5-μs per kilometer) latency reduction for the physical link. The system level latency reduction is 28% for 1-km interconnection distance (11% for 100-m), with respect to a microsecond-scale switching network for typical datacenter applications. This work substantially leaps over the 100G milestone of 2-micron HCF optical interconnection, and shows the potentiality with lower latency and further higher capacity.

For decades, advanced modulation techniques have been proposed to increase the capacity for intensity-modulation and direct-detection (IM-DD) optical fiber interconnection systems. Typically, the frequency-resolved discrete multi-tone (DMT) modulation was proposed by loading modulations with different bit numbers to fit the channel's frequency response. Capacity can thus be better improved through finer use of the signal-to-noise-ratio (SNR) distribution in the frequency domain. For conventional DMT, the constellations loaded on individual subcarriers are all equip probability distributed. In this work, we propose a probabilistically shaped DMT (PS-DMT) modulation with adaptively loaded entropies referring to channel frequency response for short-reach optical interconnects. Achievable information rate (AIR) improvements of PS-DMT with both Maxwell-Boltzmann and dyadic distribution are investigated based on generalized mutual information (GMI). Moreover, the proposed PS-DMT has been realized experimentally over a multimode optical link using vertical-cavity surface-emitting lasers (VCSELs) with 100-m-long multimode fiber (MMF) transmission. This method can significantly improve the signaling capacity since two significant benefits are simultaneously utilized: 1) the shaping gain of PS at limited SNR condition and 2) the frequency-resolved continuous entropy loading for better fitting to the channel frequency response. Improved capacity, in terms of AIR, can thus be expected for a practical channel when using PS-DMT. This method can potentially be extended to a wide range of application scenarios, including both multimode and single-mode IM-DD fiber-optic communications.

We experimentally achieved the highest single-lane optical interconnection speed of 90 Gbps at 2-micron waveband, based on external modulation of discrete multi-tone (DMT), with BER under the FEC limit after 100-m fiber transmission.

In this paper, 112-Gbps low latency and nonlinearity-free optical interconnection at vacuum-light-speed is experimentally demonstrated through 50-m HC-PBGF by using SSB PAM-4 modulation with Kramers-Kronig receiver.

High-order quadrature amplitude modulation (QAM) formats are very effective for increasing the transmission capacity due to the highly increased spectral efficiency. However, the signal-to-noise-ratio (SNR) hungry and dense constellation of QAM make it very sensitive to nonlinear distortion. The nonlinear decision boundary adaptively generated by machine learning method of support vector machine (SVM) can be effectively used for the classification of the symbols. The different classification methods have different performance in terms of classification complexity. We experimentally investigated five SVM multi-classification methods for machine learning assisted adaptive nonlinear mitigation, including the one versus rest (OvR), the symbol encoding (SE), the binary encoding (BE), the constellation rows and columns (RC), and the in-phase and quadrature components (IQC). The comprehensive results with comparisons are demonstrated, indicating significant nonlinear mitigation with BER reductions. The SVM multi-classifier based on the in-phase and quadrature components is relatively optimal, considering the calculation and storage.

In this paper, dyadic probabilistic shaping (PS) for pulse amplitude modulation (PAM) has been investigated and experimentally demonstrated for intensity-modulation and direct-detection optical interconnection systems. Improved achievable information rate can be obtained under the condition of limited bandwidth and signal-to-noise ratio (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 Gb/s 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.

We experimentally investigated four SVM multi-classification methods for machine learning nonlinearity mitigation. The comparison results indicate very close BER performance with significant improvement. Meanwhile, the SVM multi-classifier based on the in-phase and quadrature component has the lowest complexity.

112-Gbps VCSEL-MMF optical interconnection has been experimentally demonstrated in this paper, based on DMT modulation assisted by machine learning signal processing. The results indicate an effective nonlinearity mitigation by machine learning detection of SVM with improved BER.

Summary form only given. We reviewed our recent progresses regarding probabilistic shaping for signaling and machine-learning for detection in short reach optical interconnection systems, regarding VCSEL based MMF link and silicon MRM based SMF link. Software defined optical interconnection of optical signaling and adaptive detection have been realized. Firstly, probabilistic shaping (PS) for PAM-4 and PAM-8 signaling over vertical cavity surface emitting laser (VCSEL) has been proposed and demonstrated experimentally for short-reach optical interconnection applications. With the use of prefix-free dyadic matcher, the proposed PS-PAM signals have shown improved signal-to-noise ratio (SNR) tolerance and energy efficiency. To evaluate the performance of dyadic PMF shaping, theoretical comparisons of achievable information rates (AIRs) between uniformly-distributed PAM-N and PS-PAM-N are carried out under the constrained signal-to-ratios (SNRs) and channel bandwidths condition. 0.18-bit AIR improvement of PAM-8 is achieved by using dyadic shaping, at SNR of 7 dB. The experiment verifications are presented on VCSEL&OM3 fiber links with 16.6-GHz 10-dB back-to-bck bandwidth. Secondly, we employ a machine learning algorithm for detection of PAM-4 modulated signals. Our approach is based on the support vector machine (SVM) method and we applied it to mitigate the distortion of a silicon micro-ring modulator (Si-MRM). We characterize the nonlinearity distortion in terms of level deviation (LD) of PAM-4 arising from wavelength drift. Up to 2.7-dB receiver sensitivity gain is obtained at about 26% LD by using the proposed SVM machine learning method. The receiver sensitivity-float range can be squeezed to be within 0.3 dB even with up to 30% LD. Up to 3.63-dB receiver sensitivity improvement has been achieved at 50 Gbps for a Si-MRM after 2-km standard single mode fiber (SSMF) transmission.