The Gerchberg–Saxton (GS) algorithm, which retrieves phase information from the measured intensities on two related planes (the source plane and the target plane), has been widely adopted in a variety of applications when holographic methods are challenging to be implemented. In this work, we showed that the GS algorithm can be generalized to retrieve the unknown propagating function that connects these two planes. As a proof-of-concept, we employed the generalized GS (GGS) algorithm to retrieve the optical transmission matrix (TM) of a complex medium through the measured intensity distributions on the target plane. Numerical studies indicate that the GGS algorithm can efficiently retrieve the optical TM while maintaining accuracy. With the same training data set, the computational time cost by the GGS algorithm is orders of magnitude less than that consumed by other non-holographic methods reported in the literature. Besides numerical investigations, we also experimentally demonstrated retrieving the optical TMs of a stack of ground glasses and a 1-m-long multimode fiber using the GGS algorithm. The accuracy of the retrieved TM was evaluated by synthesizing high-quality single foci and multiple foci on the target plane through these complex media. These results indicate that the GGS algorithm can handle a large TM with high efficiency, showing great promise in a variety of applications in optics.

A novel topology multi-stage noise-shaping (MASH) delta-sigma modulator is proposed for 20-km digital mobile fronthaul (MFH) in this article. In the proposed MASH structure, a newly designed feedback unit is combined with a traditional fourth-order sturdy MASH structure to enhance the noise-shaping capacity. The detailed comparison between the conventional fourth-order single delta-sigma modulator (SDSM) and the proposed new topology MASH is presented in a 512/1024 quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) transmission system with the bandwidth of 1.125 GHz. The OFDM signal is quantized to two bits by SDSM/MASH analog-to-digital conversion (ADC), and this digitized signal is transmitted over 20-km single mode fiber (SMF) in 20-Gbaud 4-level pulse amplitude modulation (PAM4) intensity modulation direct detection (IM/DD) system. The signal to noise ratios (SNRs) of the retrieved OFDM signal utilizing the proposed new topology MASH and the fourth-order SDSM ADCs are 38.7dB and 34.5dB, respectively. In the case of 1024-QAM PAM4 system, the error vector magnitude (EVM) floors of the proposed new topology MASH and the conventional fourth-order SDSM schemes are 1.64% and 1.96% over 20-km SMF transmission at off-line digital signal processing (DSP) reception, and 1.2 dB receiver sensitivity improvement is achieved.

In this paper, we experimentally compared the performance of bit-loading discrete multi-tone (DMT) and pre-equalized discrete-Fourier-transform spread (DFT-Spread) DMT in intensity modulation with direct detection (IM/DD) system for 2-km optical interconnect for the first time. Pre-equalization is applied to compensate the high-frequency power fading in wideband communication system. However, it remains to be verified whether zero-forcing (ZF) channel estimation based complete pre-equalization can achieve the best performance for system with serious high frequency fading. In an IM/DD system with 120 Gbit/s data rate, we demonstrated that the bit error rate of DFT-Spread DMT signal with optimized quadratic curve fitting based partial pre-equalization outperforms ZF based complete pre-equalization after 2-km standard single mode fiber (SSMF) transmission. What's more, we experimentally compared the performance of pre-equalized DFT-Spread DMT and Chow-Cioffi-Bingham (CCB) algorithm-based bit loading DMT. The results show that the receiver sensitivity of pre-equalized DFT-Spread DMT is improved by 2.5 dB compared with CCB algorithm-based bit-loading DMT at hard decision forward error correction threshold of 3.8 × 10 ^-3 after 2-km SSMF transmission.

In this paper, we experimentally demonstrate the transmission of 100G PAM-6 and PAM-8 signals for 10-km intra-data center interconnects (intra-DCI) in C-band, which is enabled by pre-chirping technique utilizing a commercial dual-arm Mach-Zehnder modulator (MZM). At the transmitter side, the use of pre-chirping technology can overcome frequency selective fading (FSF) caused by fiber dispersion (CD) in intensity modulation and direct detection (IM/DD) systems. The pre-chirping is realized by adjusting the bias voltage of dual-arm MZM operating at single driven state. At the receiver, Volterra Non-Linear Equalizer (VNLE) is used to eliminate nonlinear impairments caused by pre-chirping. With the joint pre-chirping and nonlinear elimination in single driven dual-arm MZM based IM/DD system, 45-Gbaud PAM-6 and 40-Gbaud PAM-8 signals are successfully transmitted over 10-km single mode fiber (SMF) with a bit-error-ratio (BER) below 3.8 × 10 ^-3 . While in the chirp-free IM/DD system with dual-arm MZM operating at push-pull state, BERs of 45-Gbaud PAM-6 and 40-Gbaud PAM-8 signals over 10-km SMF transmission deteriorate dramatically to nearly 1 × 10 ^-1 . The experimental results show that our proposed pre-chirping scheme can effectively enhance the robustness of IM/DD systems against the CD-induced FSF, and this scheme is a promising candidate for 10-km 100G intra-DCI.

In this paper, we experimentally demonstrate the transmission of 56 Gbaud four-level pulse amplitude modulation (PAM4) signal over 2-km single mode fiber (SMF) with intensity modulation and direct detection (IM/DD) scheme, while the bit-error-ratio (BER) of the PAM4 signal is under hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10⁻³. Linear pre-equalization is implemented in the transmitter side with a 3-tap finite-impulse-response (FIR) filter to compensate for the intersymbol interference (ISI) induced by system bandwidth limitation. Receiver side equalization is realized with training sequence (TS) based feed-forward equalizer (FFE) with decision-feedback equalizer (DFE). Furthermore, an Adaptive Notch Filter (ANF) is proposed to suppress the digital-to-analog converter (DAC) clock leakage induced narrowband interference for the first time, and the bandwidth of the ANF is optimized to achieve the best BER performance.

A 60-GBaud intensity modulation and direct detection discrete Fourier transform spread (DFT-S) discrete multi-tone (DMT) transmission system employing low-density parity check- (LDPC-) encoded probabilistic shaping 16-ary quadrature amplitude modulation (PS-16QAM) is proposed and experimentally demonstrated. In contrast to classical probability-oriented PS schemes such as arithmetic distribution matching (ADM) and constant composition distribution matching (CCDM), the proposed one is performed based on a novel bit-weighted distribution matching (BWDM) algorithm having the advantage of simpler operations along with lower computation and hardware complexity, which merely relies on bit-class processing. As the key content of the BWDM, the bit weight intervention operation is utilized to enlarge the probability of bit `0' in the first two out of four serial binary sequences before PS-16QAM mapping. Different from the labels indicating probability distribution in ADM and CCDM, the end product of the BWDM is a group of bits mapped from input data source, which can be seamlessly compatible with the following LDPC-based forward error correction. In our experiments, system performance is respectively investigated with three LDPC code rates (3/4, 5/6, and 9/10) as well as three PS parameter values (k = 4, 5, and 7), which leads to various symbol probability distribution. Compared with standard uniformly-distributed 16QAM, up to 0.407-dB shaping gain can be achieved to approach Shannon limit in the low signal-to-noise ratio region. Moreover, the experimental results show that appreciable receiver power sensitivity improvement can be obtained by the PS-16QAM DMT based on BWDM over 2-km standard single-mode fiber for short-reach optical interconnection. Additionally, the reference-based pre-equalization is equipped to compensate for the high frequency loss by ultra-wide signal bandwidth.