Ultra-low-complexity weight-sharing trigonometric nonlinear equalizer for beyond net-200-Gb/s/λ short-reach optical interconnects.

An ultra-low-complexity third-order weight-sharing trigonometric nonlinear equalizer (WS-TNLE) is proposed to eliminate nonlinear signal distortions in short-reach optical interconnects exceeding net 200 Gb/s/λ. By replacing the second- and third-order nonlinear terms in a third-order weight-sharing diagonally pruned Volterra nonlinear equalizer (WS-DP-VNLE) with cosine and sine terms, respectively, the required number of real-valued multiplications per symbol of the proposed third-order WS-TNLE is significantly reduced to the same value as the number of weight-sharing kernels. When transmitting probabilistically shaped 16-level pulse amplitude modulation (PS-PAM-16) signals at net rates ranging from 200.4 Gb/s to 300.4 Gb/s over a 1-km standard single-mode fiber (SSMF), the proposed third-order WS-TNLE requires the lowest number of real-valued multiplications per symbol, ranging from 10 to 44, which reduces the computational complexity by up to 96.2% and 52.4% compared to the third-order WS-DP-VNLE and WS-DP-absolute-term nonlinear equalizer (WS-DP-ATNLE), respectively.

C-band 100-GBaud PS-PAM-4 transmission over 50-km SSMF enabled by FIR-filter-based pre-electronic dispersion compensation.

Chromatic dispersion (CD) is always an obstacle to C-band high-speed intensity modulation and direct detection (IM/DD) transmissions, especially with a fiber reach of > 20 km. To reach beyond net-100-Gb/s IM/DD transmission over 50-km standard single mode fiber (SSMF), we for the first time present a CD-aware probabilistically shaped four-ary pulse amplitude modulation (PS-PAM-4) signal transmission scheme with a FIR-filter-based pre-electronic dispersion compensation (FIR-EDC) for C-band IM/DD transmission system. With the help of the FIR-EDC at the transmitter, 100-GBaud PS-PAM-4 signal transmission at 150-Gb/s line rate and 115.2-Gb/s net rate over 50-km SSMF is realized with only feed-forward equalization (FFE) at the receiver side. The superiority of the CD-aware PS-PAM-4 signal transmission scheme over other benchmark schemes has been successfully verified by experiments. Experimental results show that 24.5% improvement of system capacity is obtained by the FIR-EDC-based PS-PAM-4 signal transmission scheme in comparison to the FIR-EDC-based on-off keying (OOK) signal transmission scheme. Compared with the FIR-EDC-based uniform PAM-4 signal transmission scheme or the PS-PAM-4 signal transmission scheme without EDC, the capacity improvement obtained by the FIR-EDC-based PS-PAM-4 signal transmission scheme becomes more profound. The results show the potential and feasibility of such CD-aware PS-PAM-4 signal transmission scheme applied in CD-constrained IM/DD datacenter interconnects.

Signal processing integrated with fiber-optic Vernier effect for the simultaneous measurement of relative humidity and temperature.

A novel inline Fabry-Perot interferometer (FPI) for simultaneous relative humidity (RH) and temperature monitoring is proposed. The sensing probe consists of a section of hollow core Bragg fiber (HCBF) spliced with a single-mode fiber pigtail. The end-face of the HCBF is coated with Chitosan and ultraviolet optical adhesive (UVOA), forming two polymer layers using a well-designed fabrication process. The surfaces of the layers and splicing point will generate multiple-beam interference and form Vernier-effect (VE) related envelopes in the reflection spectrum. A signal processing (SP) method is proposed to demodulate the VE envelopes from a complicated superimposed raw spectrum. The principle of the SP algorithm is analyzed theoretically and verified experimentally. The sensor's RH and temperature response are studied, exhibiting a high sensitivity of about 0.437 nm/%RH and 0.29 nm/ ∘C, respectively. Using a matrix obtained from experiment results, the simultaneous RH and temperature measurement is achieved. Meanwhile, the simple fabrication process, compact size and potential for higher sensitivity makes our proposed structure integrated with the SP algorithm a promising sensor for practical RH and temperature monitoring.

Dynamic analysis of PAM-4 IM/DD OAM-based MGDM transmission enabled by mode-group filter approach.

Mode-group-division multiplexing (MGDM)-based intensity modulation direct detection (IM/DD) transmission is an attractive approach to increase the capacity for short-reach optical communication. In this Letter, a simple but versatile scheme of mode group (MG) filtering for MGDM IM/DD transmission is proposed. The scheme is applicable to any mode basis in the fiber, and it satisfies the needs of low complexity, low power consumption, and high system performance. By employing the proposed MG filter scheme, a total raw bit rate of a 152-Gb/s multiple-input-multiple-output (MIMO)-free IM/DD co-channel simultaneous transmit and receive system based on two orbital angular momentum (OAM) MGs, each carrying a 38-GBaud four-level pulse amplitude modulation (PAM-4) signal, is experimentally demonstrated over a 5-km few-mode fiber (FMF). The bit error ratios (BERs) of the two MGs are below the 7% hard-decision forward error correction (HD-FEC) BER threshold at 3.8×10-3, using simple feedforward equalization (FFE). Furthermore, the dependability and robustness of such MGDM links are of great significance. Thus, the dynamic evaluation of BER and signal-to-noise ratio (SNR) for each MG is tested over 210 minutes under different conditions. In the dynamic cases, all the BER results using the proposed scheme can be below 1×10-3, which further confirms the stability and feasibility of our proposed MGDM transmission scheme.

Efficient 330-Gb/s PAM-8 modulation using silicon microring modulators.

We propose and demonstrate a high-efficiency silicon microring modulator for next-generation optical transmitters operating at line rates above 300 Gb/s. The modulator supports high-order PAM-8 modulation up to 110 Gbaud (330 Gb/s), with a driving voltage of 1.8 Vpp. The small driving voltage and device capacitance yields a dynamic energy consumption of 3.1 fJ/bit. Using the modulator, we compare PAM-8 with ultrahigh baud rate PAM-4 of up to 130 Gbaud (260 Gb/s) and show PAM-8 is better suited for 300-Gb/s lane rate operation in bandwidth-constrained short-reach systems.

Fabry-Perot interferometers for highly-sensitive multi-point relative humidity sensing based on Vernier effect and digital signal processing.

A highly sensitive relative humidity (RH) sensor based on Fabry-Perot interferometers (FPI) is proposed and experimentally demonstrated. The sensor is fabricated by splicing a segment of hollow core Bragg fiber (HCBF) with single mode fiber (SMF) and functionalized with chitosan and ultraviolet optical adhesive (UVOA) composite at the end of HCBF to form a hygroscopic polymer film. The reflection beams from the splicing point and the two surfaces of the polymer film generate the Vernier effect in the reflection spectrum, which significantly improves the humidity sensitivity of the sensor. To demodulate the envelope based on the Vernier effect and realize multi-point sensing, a digital signal processing (DSP) algorithm is proposed to process the reflection spectrum. The performance of the DSP algorithm is theoretically analyzed and experimentally verified. The proposed sensor demonstrates a high sensitivity of 1.45 nm/% RH for RH ranging from 45% RH to 90% RH. The compact size, high sensitivity and multiplexing capability make this sensor a promising candidate for RH monitoring. Furthermore, the proposed DSP can potentially be applied to other sensors based on the Vernier effect to analyze and extract valuable information from the interference spectrum.

Simple amplifier configuration algorithm for dynamic C + L-band systems in the presence of stimulated Raman scattering.

We propose a simple two-step amplifier configuration algorithm based on signal power across different channels to improve the generalized signal-to-noise ratio (GSNR) performance of dynamic C + L-band links in the presence of amplifier spontaneous emission (ASE) noise, Kerr nonlinearity, and stimulated Raman scattering (SRS) using erbium-doped fiber amplifiers (EDFA). In step 1, ASE noise and Kerr nonlinearity are taken into account to derive sub-optimal signal power profiles at the beginning of each span using the local optimization global optimization (LOGO) strategy. The effect of SRS is compensated through amplifier gain pre-tilt in step 2. Simulations for links with homogeneous/heterogeneous spans, static full-channel loading, and dynamic loading due to gradual channel additions for C + L-band upgrades show that the proposed algorithm can achieve similar GSNR performance, but requires much less execution time, compared to other iterative methods that target for improving the GSNR across the C + L band, thus making it a fast and efficient GSNR management strategy for future dynamic C + L-band networks.

Low-complexity absolute-term based nonlinear equalizer with weight sharing for C-band 85-GBaud OOK transmission over a 100-km SSMF.

A low-complexity absolute-term based nonlinear feed-forward equalizer (FFE) combined with a decision-feedback equalizer (DFE) with weight sharing (AT-NLE-WS) is proposed and experimentally performed in a C-band 85-GBaud on-off keying (OOK) transmission system over a 100-km standard single-mode fiber (SSMF). By applying the k-means clustering algorithm to reduce weight redundancy, the required number of real-valued multiplications per symbol (RNRM) of the proposed AT-NLE-WS is only 14 for a bit error ratio (BER) under a KP4-forward error correction (FEC) threshold of 2.4 × 10-4. Compared with FFE-DFE, polynomial based nonlinear FFE-DFE (P-NLE), and AT-NLE, the proposed AT-NLE-WS saves >93% real-valued multiplications under the KP4-FEC threshold. In addition, compared with FFE-DFE, the proposed AT-NLE-WS can simultaneously achieve an approximately 2-dB improvement of receiver sensitivity and reduce the complexity by >80%. All experimental results show that AT-NLE-WS is a very attractive approach for practical implementation of low-cost optical interconnections with a data rate beyond 50 Gb/s and transmission distance up to 100 km.

C-band 67†GHz silicon photonic microring modulator for dispersion-uncompensated 100 Gbaud PAM-4.

A very-high-bandwidth integrated silicon microring modulator (MRM) designed on a commercial silicon photonics (SiP) platform for C-band operation is presented. The MRM has a 3 dB electro-optic (EO) bandwidth of over 67 GHz and features a small footprint of 24 µm × 70 µm. Using the MRM, we demonstrate intensity modulation-direct detection (IM-DD) transmission with 4-level pulse amplitude modulation (PAM-4)  signaling of over 100 Gbaud. By utilizing the optical peaking effect and negative chirp in the MRM, we extend the transmission distance, which is limited by the fiber-dispersion-induced frequency fading. Using a standard single-mode fiber (SSMF) for transmission across distances of up to 2 km, we measured the data transmission of 100 Gbaud PAM-4 signals with a bit error rate (BER) under the general 7% hard-decision forward-error correction (HD-FEC) threshold. The MRM enables an extended transmission distance for 100 Gbaud signaling in the C-band without dispersion compensation.

Nonlinearity-aware PS-PAM-16 transmission for C-band net-300-Gbit/s/λ short-reach optical interconnects with a single DAC.

A nonlinearity-aware signal transmission scheme based on a low-complexity 3rd-order diagonally pruned absolute-term nonlinear equalizer (NLE) with weight sharing (DP-AT-NLE-WS) and rate-adaptable probabilistically shaped 16-level pulse amplitude modulation (PS-PAM-16) signal is proposed and experimentally demonstrated for C-band net-300-Gbit/s/λ short-reach optical interconnects. By replacing the multiplication operation with the absolute operation and applying weight sharing to reduce the kernel redundancy, the computational complexity of the proposed 3rd-order DP-AT-NLE-WS is reduced by >40% compared with the 3rd-order DP-Volterra NLE (DP-VNLE), DP-AT-NLE, and DP-VNLE-WS, with the achieved normalized general mutual information (NGMI) above a threshold of 0.857. Employing a commercial 32-GHz Mach-Zehnder modulator (MZM) and a single digital-to-analog converter (DAC), we demonstrate the single-lane transmission of 100-GBaud PS-PAM-16 signal using DP-AT-NLE-WS in the C band at record 370-Gbit/s line rate and 300.4-Gbit/s net rate over 1-km standard single-mode fiber (SSMF), achieving 21.2% (15.5%) capacity improvement over 100 (105)-GBaud PAM-8 transmission. To the best of our knowledge, this is the first net-300-Gbit/s intensity modulation and direct detection (IM/DD) short-reach transmission in the C band using commercially available components.

Experimental demonstration of pre-electronic dispersion compensation in IM/DD systems using an iterative algorithm.

To combat chromatic dispersion (CD) in intensity modulation and direct detection (IM/DD) systems, three chirp-free demonstrations are experimentally performed with an iterative pre-electronic dispersion compensation (pre-EDC) algorithm at the transmitter end, for 28 GBaud non-return-to-zero on-off keying (NRZ-OOK), 56 GBaud NRZ-OOK and 28 GBaud four-level pulse-amplitude-modulation (PAM-4) signals, over distances of 100 km, 50 km and 40 km of single mode fiber (SMF), respectively. The iterative pre-EDC algorithm is based on the Gerchberg-Saxton (GS) algorithm, which treats the unconstrained phase at the direct detection receiver as a degree of freedom. At the receiver side, only a linear fractionally-spaced (T/2) post-feed-forward equalizer (post-FFE) is employed to combat the residual inter-symbol interference (ISI). Experimental results show that the aforementioned three demonstrations can approach the forward error correction (FEC) bit error rate (BER) threshold of 3.8 × 10-3 with (15 pre-EDC iterations and 5-tap post-FFE), (30 pre-EDC iterations and 15-tap post-FFE), and (10 pre-EDC iterations and 25-tap post-FFE), respectively. The results indicate the applicability of the pre-EDC algorithm in high-capacity IM/DD systems for transmission distances below 100 km of SMF.

Two-dimensional grating coupler on an X-cut lithium niobate thin-film.

A two-dimensional grating coupler for coupling light between a standard single-mode fiber and ridge waveguides on an X-cut lithium niobate thin-film is designed and demonstrated. Using circular holes for grating cells, simulated coupling losses reach -3.88 dB at 1550 nm and -5.78 dB at 1563 nm with 1-dB bandwidths of 49 nm and 45 nm for P-polarized and S-polarized light inputs, respectively. Experimentally, peak coupling losses of -5.13 dB at 1561 nm and -7.6 dB at 1568 nm are obtained for P-polarized and S-polarized light inputs, respectively, and corresponding 1 dB bandwidths are about 30 nm. An approach to improve the coupling performance of the grating coupler is also proposed using two crossing ellipses as grating cells as well as a bottom metal reflector. The coupling loss and the polarization dependent loss are decreased to around -3.4 dB and 0.44 dB, respectively.

Folded thin-film lithium niobate modulator based on a poled Mach-Zehnder interferometer structure.

The thin-film lithium niobate structure has been used recently to construct compact and high-performance electro-optical modulators. Due to the moderate electro-optical coefficient of the lithium niobate material, the device length of such a modulator is still long, a few centimeters usually. Here, a folded Mach-Zehnder interferometer based modulator on x-cut thin-film lithium niobate is demonstrated. An effective poling procedure is developed to activate the device. The proposed modulator structure can shorten the device length without affecting its performance. The measured VπL product of a fabricated and completely poled folded modulator is about 2.74V⋅cm, and the 3 dB electro-optical bandwidth is about 55 GHz. They are close to those of a conventional Mach-Zehnder modulator with a straight modulation section.

Modulation format identification assisted by sparse-fast-Fourier-transform for hitless flexible coherent transceivers.

For hitless flexible coherent transceivers based next-generation agile optical network, efficient modulation format identification (MFI) is an essential element in digital signal processing (DSP) flow at the receiver-side (Rx). In this paper, we propose a blind and fast MFI scheme with high identification accuracy at low optical signal-to-noise ratio (OSNR) regime. This is achieved by first raising the signal to the 4th power and calculate the peak-to-average power ratio (PAPR) of the corresponding spectra to distinguish 32 quadrature amplitude modulation (QAM) from quadrature phase shift keying (QPSK), 16 and 64QAM signals. Then, followed by iterative partition schemes to remove signals with phase ±π4,±3π4 (or QPSK-like phases) based on the signal amplitudes, the PAPR of the remaining signals is calculated to distinguish the other three formats. Additionally, by frequency offset (FO) pre-compensation, the spectrum can be obtained using sparse-fast-Fourier-transform (S-FFT), which greatly reduces the total complexity. The MFI performance is numerically and experimentally investigated by 28 Gbaud dual-polarization (DP) coherent optical back-to-back (B2B) and up to 1500 km standard single mode fiber (SSMF) transmission system using QPSK, 16QAM, 32QAM, and 64QAM. Results show that high identification accuracy can be achieved, even when OSNR is lower than that required for the 20% forward error correction (FEC) threshold of BER=2×10-2 for each format. Furthermore, fast format switching between 64QAM-32QAM and 32QAM-16QAM are demonstrated experimentally for B2B scenario and 900 km SSMF with the proposed MFI technique, respectively.

Memory-controlled deep LSTM neural network post-equalizer used in high-speed PAM VLC system.

Linear and nonlinear impairments severely limit the transmission performance of high-speed visible light communication systems. Neural network-based equalizers have been applied to optical communication systems, which enables significantly improved system performance, such as transmission data rate and distance. In this paper, a memory-controlled deep long short-term memory (LSTM) neural network post-equalizer is proposed to mitigate both linear and nonlinear impairments in pulse amplitude modulation (PAM) based visible light communication (VLC) systems. Both 1.15-Gbps PAM4 and 0.9Gbps PAM8 VLC systems are successfully demonstrated, based on a single red-LED with bit error ratio (BER) below the hard decision forward error correction (HD-FEC) limit of 3.8 x 10-3. Compared with the traditional finite impulse response (FIR) based equalizer, the Q factor performance is improved by 1.2dB and the transmission distance is increased by one-third in the same experimental hardware setups. Compared with traditional nonlinear hybrid Volterra equalizers, the significant complexity and system performance advantages of using a LSTM-based equalizer is demonstrated. To the best of our knowledge, this is the first demonstration of using deep LSTM in VLC systems.

Chromatic dispersion mitigation using a SEFDM-based diversity technique for IM/DD long reach optical links.

Spectral efficient frequency division multiplexing (SEFDM) can offer a higher spectral efficiency (SE) than orthogonal frequency division multiplexing (OFDM). In this work, we propose a diversity technique based on SEFDM for beyond 100-Gb/s optical intensity modulation and direct detection (IM/DD) long reach (LR) applications. We mathematically demonstrate that the self-created inter-carrier interference of SEFDM signals can be reused to achieve a diversity gain on each sub-carrier and, in turn, improve the tolerance to power fading induced by chromatic dispersion (CD) in IM/DD LR links. Based on the proposed diversity technique, we further demonstrated a 112-Gb/s SEFDM transmission over 80-km standard single-mode fiber, using only 28-GHz bandwidth and modulation format of up to 16-QAM. Experimental results show that SEFDM with the proposed diversity technique performs robust against CD effects and outperforms the conventional OFDM with adaptive bit and power loading of the same bandwidth and data rate, which validates the superiority of the proposed SEFDM in optical IM/DD LR transmissions.

Low-complexity carrier phase recovery based on principal component analysis for square-QAM modulation formats.

We propose, numerically analyze and experimentally demonstrate a low-complexity, modulation-order independent, non-data-aided (NDA), feed-forward carrier phase recovery (CPR) algorithm. The proposed algorithm enables synchronous decoding of arbitrary square-quadrature amplitude modulation (QAM) constellations and it is suitable for a realistic hardware implementation based on block-wise parallel processing. The proposed method is based on principal component analysis (PCA) and it outperforms the well-known and widely used blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) values, showing much lower cycle slip rate (CSR) both numerically and experimentally. For operation at higher SNR values, a hybrid two-stage implementation combining the proposed method and BPS is also proposed and their performance are investigated benchmarking them against the two-stage BPS (2S-BPS). The complexity of the proposed simple and hybrid methods are evaluated against 2S-BPS and computational complexity savings of 92% and 40% are expected for the simple and hybrid methods, respectively.

Modulation-format-transparent IQ imbalance estimation of dual-polarization optical transmitter based on maximum likelihood independent component analysis.

We propose and experimentally demonstrate a modulation-format-transparent dual-polarization (DP) transmitter (Tx) in-phase/quadrature (IQ) imbalance estimation scheme based on maximum likelihood independent component analysis (ML-ICA). The proposed scheme can separate Tx IQ imbalance from polarization crosstalk and phase noise and achieve accurate IQ imbalance estimation without training data and the information of modulation format. Firstly, the complex-ML-ICA is used to implement format-transparent polarization de-multiplexing to remove polarization crosstalk; then the real-ML-ICA is employed to estimate inverse IQ mixing matrix and compensate Tx IQ imbalance/phase noise on each polarization channel. Inverse IQ mixing matrix contains the information of phase noise and Tx IQ imbalance; Finally, Tx IQ imbalance is derived from the inverse matrix by analytic method. The impact of Tx IQ imbalance on polarization demultiplexing and carrier phase recovery (CPE) is investigated by numerical simulation from three aspects of Jones space, Stokes space, and Kurtosis. The simulation results demonstrate the proposed scheme has strong robustness to phase noise, quantization noise, and amplified spontaneous emission (ASE) noise. The proposed ML-ICA algorithm is verified experimentally in polarization division multiplexing (PDM) quadrature phase-shift keying (QPSK)/8 quadrature amplitude modulation (QAM)/16QAM/64QAM systems. The experimental results show the scheme can accurately estimate Tx IQ imbalance within wide range in a format transparent manner.

120 Gbaud PAM-4 transmission over 80-km SSMF using optical band interleaving and Kramers-Kronig detection.

We demonstrate generation and detection of 120-Gbaud PAM-4 signals using an I/Q modulator based on optical band interleaving (OBI) technique. The spectral components of target PAM signals are split and pre-processed before being sent to two digital-to-analog convertors (sub-DACs) whose outputs are imprinted to an optical carrier by an optical I/Q modulator forming a carrier-suppressed tandem single side-band (SSB) signal. The PAM signals can be recovered after photo-detection provided that an optical beating tone is added at the edge of the signal spectrum along with the modulator output. The proposed method requires only half of the Nyquist bandwidth of the target PAM signal for the transmitter and has the advantage of a simple implementation. Using Kramers-Kronig (K-K) detection, a 120 Gbaud PAM-4 transmission over 80-km standard single mode fiber (SSMF) is successfully demonstrated. The proposed scheme entails a simple implementation and a much lower bandwidth requirement at the transmitter compared with conventional all-electronic high baud rate signal generation schemes.

Nonlinear frequency division multiplexing with b-modulation: shifting the energy barrier.

The recently proposed b-modulation method for nonlinear Fourier transform-based fiber-optic transmission offers explicit control over the duration of the generated pulses and therewith solves a longstanding practical problem. The currently used b-modulation however suffers from a fundamental energy barrier. There is a limit to the energy of the pulses, in normalized units, that can be generated. In this paper, we discuss how the energy barrier can be shifted by proper design of the carrier waveform and the modulation alphabet. In an experiment, it is found that the improved b-modulator achieves both a higher Q-factor and a further reach than a comparable conventional b-modulator. Furthermore, it performs significantly better than conventional approaches that modulate the reflection coefficient.