Single-etched fiber-chip coupler with a metal mirror on a 220-nm silicon-on-insulator platform for perfectly vertical coupling.

Vertical couplers play a pivotal role as essential components supporting interconnections between fibers and photonic integrated circuits (PICs). In this study, we propose and demonstrate a high-performance perfectly vertical coupler based on a three-stage inverse design method, realized through a single full etching process on a 220-nm silicon-on-insulator (SOI) platform with a backside metal mirror. Under surface-normal fiber placement, experimental results indicate a remarkable 3-dB bandwidth of 99 nm with a peak coupling efficiency of -1.44 dB at the wavelength of 1549 nm. This achievement represents the best record to date, to the best of our knowledge, for a perfectly vertical coupler fabricated under similar process conditions.

Real-time FPGA prototyping of Doppler frequency shift compensation using DSP-assisted automatic frequency control.

This Letter presents a real-time coherent receiver using digital signal processing (DSP)-assisted automatic frequency control (AFC) to compensate for the Doppler frequency shift (DFS). DFS compensation range of ±8 GHz and the frequency shifting rate of 33 MHz/s are demonstrated in an FPGA-based 2.5 Gbaud QPSK coherent optical system. The experimental results indicate that the scheme achieves a sensitivity of -47 dBm at a bit error rate (BER) of 2E-4. The power penalty induced by the DFS compensation is less than 1 dB.

Photonic integrated coherent beam combiner based on MMI and the SPGD algorithm.

Atmospheric turbulence severely degrades the optical wavefront of a propagating beam, which greatly reduces the coupling efficiency of free-space optical (FSO) receivers. Among the various methods to mitigate the effects, the use of a multi-channel receiver is more convenient and economical. After passing through the multi-channel receiver, multiple single-mode fibers (SMFs) are output and need to be combined. In this paper, we propose photonic integrated coherent beam combiners based on multimode interference (MMI) and the stochastic parallel gradient descent (SPGD) algorithm, which avoids detecting the light out of each channel and adding the data signal in the electrical domain. First, we propose a 4-channel coherent beam combiner based on a 4×1 MM, and about 21 iterations of the SPGD algorithm are required to enhance the combined optical power to a maximum of 96%. Furthermore, we demonstrate a combination of 16 beams using five 4×1 MMIs, which requires 140 iterations to enhance the combined power to 89%. This study offers theoretical insights to enhance the integration of FSO communication systems.

Digitization method for a photonic analog-to-digital converter with phase-shifted optical quantization.

This Letter proposes a novel, to the best of our knowledge, matrix digitization method for a photonic analog-to-digital converter with phase-shifted optical quantization (PSOQ-ADC). This method overcomes the issues of excessive bit width of the output code and the generation of invalid codes encountered by the traditional direct digitization method. A PSOQ-ADC was fabricated on a lithium niobate on insulator (LNOI) platform, and an experimental platform was built. The results show that RF signals at 1/2/5 GHz, which were sampled by a 50GS/s optical pulse train, were digitized successfully with the matrix digitization method, producing 5-bit codes without invalid codes. In comparison, the direct digitization method yields 10-bit codes, and as the optical signal-to-noise ratio (OSNR) decreases, the ratio of invalid codes increases in the direct digitization method; even with Hamming distance correction, its effective number of bits (ENOB) remains smaller than that of the matrix digitization.

The Effects of VR-assisted and Overground Gait Adaptation Training on Balance and Walking Ability in Stroke Patients.

OBJECTIVE: This study compared the effects of virtual reality(VR)-assisted gait adaptation training with the overground gait adaptation training on balance and walking in patients with stroke. METHODS: Fifty-four eligible patients were enrolled. All patients were randomly divided into a VR and control group, with 27 patients in each group. The VR group received VR-assisted training on the treadmill, whereas the control group received overground training in a physical therapy room. After the intervention, patients were assessed using walking speed, obstacle avoidance ability, timed up and go (TUG) test, postural stability, and the Barthel Index (BI). RESULTS: Significant improvements in walking speed, obstacle avoidance ability, TUG test and eye-opening center of pressure (COP) speed were observed after the intervention (P < 0.05). No statistically significant differences were found in eye-closing COP speed, tandem COP speed, single-leg COP speed, and BI (P > 0.05). CONCLUSIONS: Stroke patients may benefit from VR-assisted gait adaptation training in improving walking and static balance function and reducing the risk of falls.

Real-time low-complexity diversity combining algorithm for free space coherent optical communication systems over atmospheric turbulence channel.

A novel diversity combining scheme, in conjunction with the complex-valued decision-directed least mean square (CV-DD-LMS) algorithm, is evaluated, and a real-time experimental validation is presented. This proposed scheme employs the CV-DD-LMS algorithm to concurrently perform beam combination and carrier phase recovery (CPR), thereby effectively reducing the overall complexity of digital signal processing. Furthermore, in the numerical simulation, under a low signal-to-noise ratio (SNR), a scheme utilizing the CV-DD-LMS algorithm effectively avoids cycle slips (CS) and outperforms schemes employing independent CPR modules. We experimentally validate this novel scheme by implementing it on an FPGA in a real-time 2.5Gb/s QPSK diversity-receiving system with three inputs. The back-to-back sensitivity is assessed using static received optical power, while the dynamic performance is evaluated by employing variable optical attenuators (VOAs) to simulate a power fluctuation at a frequency of 100kHz. The result proves that the implementation of the CV-DD-LMS algorithm yields stable performance while effectively reducing computational complexity.

Experimental demonstration of a dynamic range enhancement method for a phase-shifted PADC by using a modulo operation.

We propose what we believe to be a novel approach to enhance the dynamic range of a photonic analog-to-digital converter (PADC) without the need of additional custom-designed circuits or components. The method utilizes the unique characteristic of our previously reported multimode interference (MMI) coupler-based optical quantizer that exploits the periodicity of the optical phase to realize a modulo operation. Experiments were carried out to verify the effectiveness of the proposed method on our phase-shifted optical quantization ADC (PSOQ-ADC) chip. Experimental results show that our proposed method enhance the dynamic range from [-V π, V π] to [-2V π, 2V π] and has the potential to be further extended. Additionally, we successfully reconstructed radio frequency (RF) signals at a sampling rate of 30 Gs/s. Our work provides a promising solution for achieving a high dynamic range in on-chip PSOQ-ADC.

Integrated spatial light receivers based on inverse design.

Photonic integrated spatial light receivers play a crucial role in free space optical (FSO) communication systems. In this paper, we propose a 4-channel and 6-channel spatial light receiver based on a silicon-on-insulator (SOI) using an inverse design method, respectively. The 4-channel receiver has a square receiving area of 4.4 µm × 4.4 µm, which enables receiving four Hermite-Gaussian modes (HG00, HG01, HG10, and HG02) and converting them into fundamental transverse electric (TE00) modes with insertion losses (ILs) within 1.6∼2.1 dB and mean cross talks (MCTs) less than -16 dB, at a wavelength of 1550 nm. The 3 dB bandwidths of the four HG modes range from 28 nm to 46 nm. Moreover, we explore the impact of fabrication errors, including under/over etching and oxide thickness errors, on the performance of the designed device. Simulation results show that the 4-channel receiver is robust against fabrication errors. The designed 6-channel receiver, featuring a regular hexagon receiving area, is capable of receiving six modes (HG00, HG01, HG10, HG02, HG20, and HG11) with ILs within 2.3∼4.1 dB and MCTs less than -15 dB, at a wavelength of 1550 nm. Additionally, the receiver offers a minimum optical bandwidth of 26 nm.

Satellite-to-ground optical downlink model using mode mismatching multi-mode photonic lanterns.

Photonics lanterns (PLs) provide an effective mode diversity solution to mitigate atmospheric turbulence interference in free-space optical communications (FSOC). This paper presents mode-mismatching multimode photonic lanterns (MM-PLs) for diversity receiver in satellite-to-ground downlink scenarios. Our study evaluates the coupling characteristics of the mode-selective PLs (MSPLs) and non-mode-selective PLs (NSPLs) for the influence of strong-to-weak turbulence and confirms that MSPLs outperform NSPLs under weak turbulence conditions. The research further explores the impact of fiber position error (FPE) on the spatial light-to-fiber coupling, including the optimal focal length deviation and lateral offset of receiving fiber devices. We have calculated and compared the coupling power and signal-to-noise ratio (SNR) of few-mode PLs (FM-PLs) and MM-PLs for various turbulence intensities. The results indicate that the optimal focal length tolerance, which corresponds to a decrease of approximately 1 dB in the average coupling power, is 2-3 m and 5-6 m for FM-PLs and MM-PLs, respectively. Furthermore, regardless of whether it is strong or weak turbulence, MM-PL exhibits a lateral offset tolerance exceeding 12 µm for a 0.5 dB drop in the mean coupled power, whereas the lateral offset tolerance of FM-PL is only 3 µm under weak turbulence. Additionally, the decrease in the average SNR of MM-PLs is gentle, only 0.67-1.16 dB at a 12 µm offset under weak turbulence, whereas there is a significant reduction of 6.50-8.49 dB in the average SNR of FM-PLs. These findings demonstrate the superiority of MM-PLs over FM-PLs in turbulence resistance and fiber position tolerance in the satellite-ground downlink.

Nonlinear transmission performance comparison employing 60 × 416.7-Gb/s TPS-64QAM and UD-16QAM systems with limited bandwidth.

The impacts of limited bandwidth on the nonlinear transmission performance are investigated by employing a truncated probabilistic shaped 64-ary quadrature amplitude modulation (TPS-64QAM) and a uniformly distributed 16-ary quadrature amplitude modulation (UD-16QAM) over a bandwidth-limited 75-GHz spaced 25-Tb/s (60 × 416.7 Gb/s) 6300-km transmission system. In terms of nonlinear performance measured by optimal launch power, theoretical analyses show that a 0.4-dB improvement could be introduced by UD-16QAM with respect to TPS-64QAM over a 6300-km transmission without limited bandwidth. However, contrary results would be observed that TPS-64QAM would outperform UD-16QAM by about 0.8 dB in terms of optimal launch power when the impacts of limited bandwidth are considered. Besides, numerical simulations and experimental results could both validate that about 1.0-dB optimal launch power improvement could be obtained by TPS-64QAM under bandwidth-limited cases, which is roughly similar to the results of theoretical analyses. Additionally, WDM experimental results show that all 60 tested channels could agree with the BER requirements by employing TPS-64QAM, further validating the superiority of TPS-64QAM compared to UD-16QAM under bandwidth-limited cases.

Real-time FPGA prototyping of a 15GBaud SP-16QAM coherent optical receiver with optimal interpolating for clock recovery and equalization.

We demonstrate a real-time coherent optical receiver based on a single field programmable gate array (FPGA) chip. To strike the balance between the performance and hardware resources, we use a clock recovery scheme using the optimal interpolation (OI). The performance and complexity of the OI-based scheme and the traditional schemes are compared and discussed via offline digital signal processing. And a real-time 15GBaud single-polarization 16QAM transmission experiment under different received optical power using the FPGA-based receiver is carried out to demonstrate the overall performance of different clock recovery and equalization schemes. The result proves that, compared to the traditional scheme with a cubic interpolator and a 7-tap equalizer, the optimal interpolator significantly lowers the utilization of LUT, CARRY8, and DSP48 by 35%, 50%, and 11%, respectively, and can work properly under a received optical power of -40dBm.

[Jiao's scalp acupuncture combined with virtual reality rehabilitation training for motor dysfunction in patients with Parkinson's disease: a randomized controlled trial].

OBJECTIVE: To compare the clinical efficacy between Jiao's scalp acupuncture combined with virtual reality (VR) rehabilitation training and VR rehabilitation training alone for motor dysfunction in patients with Parkinson's disease (PD). METHODS: A total of 52 patients with PD were randomly divided into an observation group and a control group, 26 cases in each group. The patients in both groups were treated with routine basic treatment, and the patients in the control group were treated with VR rehabilitation training. The patients in the observation group were treated with Jiao's scalp acupuncture on the basis of the control group. The scalp points included the movement area, balance area and dance tremor control area. Both groups were treated once a day, 5 times a week for a total of 8 weeks. Before treatment and 4 and 8 weeks into treatment, the gait parameters (step distance, step width, step speed and step frequency), timed "up and go" test (TUGT) time and unified Parkinson's disease rating scale part Ⅲ (UPDRS-Ⅲ) score were compared between the two groups, and the clinical efficacy was evaluated. RESULTS: Four weeks into treatment, except for the step width in the control group, the gait parameters of the two groups were improved, the TUGT time was shortened, and the UPDRS-Ⅲ scores were reduced (P<0.01, P<0.05); the step distance in the observation group was better than that in the control group, and the UPDRS-Ⅲ score in the observation group was lower than that in the control group (P<0.05). Eight weeks into treatment, the gait parameters of the two groups were improved, the TUGT time was shortened, and the UPDRS-Ⅲ scores were reduced (P<0.01); the step distance and step speed in the observation group were better than those in the control group, the TUGT time in the observation group was shorter than that in the control group, and the UPDRS-Ⅲ score in the observation group was lower than that in the control group (P<0.05, P<0.01). The total effective rate was 92.3% (24/26) in the observation group, which was higher than 69.2% (18/26) in the control group (P<0.05). CONCLUSION: Jiao's scalp acupuncture combined with VR rehabilitation training could improve the gait parameters, walking ability and motor function in patients with PD. The clinical effect is better than VR rehabilitation training alone.

Ultracompact and ultralow-loss S-bends with easy fabrication by numerical optimization.

Ultra-longitudinal-compact S-bends with flexible latitudinal distances (d) are proposed and experimentally demonstrated with ultralow loss and fabrication-friendly structures by three steps based on numerical optimization. During the first step (curve optimization), insertion losses (ILs) of S-bends are significantly reduced by optimizing transition curves based on Bézier curves. During the second step (shape optimization), the ILs are further minimized by varying the widths of S-bends to increase optical confinement. In the third step (curvature optimization), considering ease of fabrication, an optimization of curvature radius is used to ensure that all feature sizes for the S-bends are larger than 200 nm. Simulation results show that for S-bends with footprints of 2.5× d µm2, the ILs are less than (0.19, 0.045, 0.18, 0.27) dB in a wavelength range of 1400-1700 nm when d is set as (3, 6, 9, 12) µm, respectively. Then, the S-bends of 2.5× 3 µm2 and 2.5× 12 µm2 are fabricated on a commercial 220-nm silicon-on-insulator (SOI) platform. Experimental results show that the ILs of both are less than 0.16 dB in a wavelength range of 1420-1630 nm. The lowest ILs are 0.074 dB and 0.070 dB, respectively. Moreover, in addition to the ultralow ILs and ease of fabrication, our design is flexible for designing S-bends with a flexible value of d, which makes our approach practical in large-scale photonic integrated circuits.

Performance investigation of the probability-aided maximum likelihood sequence detector for a probabilistic shaped 16-QAM system.

In this paper, for the first time, a probability-aided maximum-likelihood sequence detector (PMLSD) is experimentally investigated through a 64-GBaud probabilistic shaped 16-ary quadrature amplitude modulation (PS-16QAM) transmission experiment. In order to relax the impacts of PS technology on the decision module, a PMLSD decision scheme is investigated by modifying the decision criterion of maximum-likelihood sequence detector (MLSD) correctly. Meanwhile, a symbol-wise probability-aided maximum a posteriori probability (PMAP) scheme is also demonstrated for comparison. The results show that the PMLSD scheme outperforms the direct decision scheme about 1.0-dB optical signal to noise ratio (OSNR) sensitivity. Compared with symbol-wise PMAP scheme, PMLSD scheme can effectively relax the impacts of PS technology on the decision module and a more than 0.8-dB improvement in terms of OSNR sensitivity in back-to-back (B2B) case is obtained. Finally, we successfully transmit the PS-16QAM signals over a 2400-km fiber link with a bit error ratio (BER) lower than 1.00×10-3 by adopting the PMLSD scheme.

Investigation of the low-complexity Hilbert FIR filter enhanced 112-Gbit/s SSB 16-QAM transmission with parallelized Kramers-Kronig reception over 1440-km SSMF.

The Hilbert transform links the log-magnitude and the phase of the field modulated signals as long as the minimum phase condition is satisfied in the Kramer-Kronig (KK) receiver. In discrete-time signal processing, the Hilbert transform is generally replaced by a finite impulse response (FIR) filter to reduce the computational complexity, that is the so-called Hilbert transform FIR (HT-FIR) filter. The performance of the HT-FIR filter is extremely important, as the in-band flatness, the ripple, the group delay, the Gibbs phenomenon, and the edge effect, which indeed impair the phase retrieval. Hence, we investigate four different HT-FIR filter schemes that are in the form of type III and type IV based on the frequency-domain (FD) sampling approach and the time-domain (TD) windowing function approach. Also, we analyze the performance for each filter under different digital upsampling scenarios and conclude that a trade-off between the reduced inter-symbol-interference (ISI) and the Gibbs phenomenon is essential to obtain an optimal sampling rate and an improved KK performance when the HT-FIR filter with a short length is adopted. The results show that the FD-based HT-FIR filter can relax the upsampling requirement while having a better in-band flatness and a lower edge effect. The experiment is conducted in the parallelized block-wise KK reception-based 112-Gbit/s SSB 16-QAM optical transmission system over a 1920-km cascaded Raman fiber amplifier (RFA) link to investigate the limit transmission performance of the practical KK receiver. The experimental results show that when the transmission distance is up to 1440-km, the BER of the FD-based HT-FIR filter can be lower than the soft decision-forward error correction (SD-FEC) threshold of 2 × 10-2 with only 3 samples per symbol (3-SPS) upsampling rate and 8 non-integer tap coefficients are used, while other TD-based HT-FIR filter schemes with a BER lower than the SD-FEC threshold require at least 4-SPS upsampling rate.

Ultra-compact X-shaped waveguide crossings with flexible angles based on inverse design.

When photonics integrated circuits (PICs) become more massive in scale, the area of chip can't be taken full advantage of with 2×2 waveguide crossings with a 90° intersection angle. Crossings with small angles would be a better idea to further improve the area utilization, but few works have researched 2×2 crossings with different angles. In this paper, in order to have an ultra-compact footprint and a flexible intersection angle while keeping a high performance, we report a series of compact X-shaped waveguide crossings in silicon-on-insulator (SOI) waveguides for fundamental transverse electric (TE0) mode, designed by using finite-difference frequency-domain (FDFD) numerical analysis method and a global optimization method. Thanks to inverse design, a compact footprint as small as 4.5 µm2 and various angles between two input/output waveguides of 30°, 45°, 60°, 80° and 90° are achieved. Simulation results show that all crossings have good performance of insertion losses (ILs) within 0.1∼0.3 dB and crosstalks (CTs) within -20∼-50 dB in the wavelength range of 1525∼1582 nm. Moreover, the designed crossings were fabricated on a commercially available 220-nm SOI platform. The measured results show that the ILs of all crossings are around 0.2∼0.4 dB and the CTs are around -20 dB∼-32 dB; especially for the 30° intersection angle, the crossing has IL around 0.2 dB and CT around -31 dB in C band. Besides, we theoretically propose an approach of a primary structure processing technique to enhance the device performance with a more compact footprint. This technique is to remove the redundant structures in conjunction with the electric field distribution during the optimization procedure of inverse design. For the new 90° crossing structure produced by it, simulation results show that ILs of 0.29 ± 0.03 dB and CTs of -37 ± 2.5 dB in the wavelength range of 1500∼1600 nm are achieved and the footprint is shrunk by 25.5%.

Polar coded probabilistic shaping PAM8 based on many-to-one mapping for short-reach optical interconnection.

In this paper, a polar coded probabilistic shaping (PS) 8-ary pulse amplitude modulation (PAM8) based on many-to-one (MTO) mapping is investigated for short-reach optical interconnection. By ingeniously assigning parity bits to ambiguities positions, no extra PS redundancy and no complex distribution matcher are required in the scheme comparing to traditional probabilistic amplitude shaping (PAS). The noise distributions after different transmission distances are studied and an optimal clock recovery method for PS signal is proposed to degrade the impact of severe eye skew effect on BER performance. The experimental results show that up to 1.2 dB and 0.8 dB shaping gains are respectively achieved over back-to-back (BTB) and 2-km standard single mode fiber (SSMF) transmission. With the help of the proposed optimal clock recovery method in the PS scheme, the shaping gain is improved from 0.15 dB to 0.4 dB after 10-km transmission. Moreover, compared to low-density parity-check (LDPC) code, the polar coded PS-PAM8 can provide an additional coding gain of 2.2 dB with code length of 256, which proves the performance superiority of polar code in short code length. Therefore, the proposed polar coded PS-PAM8 with low complexity and satisfactory BER performance is believed to be an alternative solution for the cost-sensitive short-reach optical interconnection.

Transmission of a 112-Gbit/s 16-QAM over a 1440-km SSMF with parallel Kramers-Kronig receivers enabled by an overlap approach and bandwidth compensation.

We investigate the parallelized performance of the conventional Kramers-Kronig (KK) and without the digital up-sampling KK (WDU-KK) receivers in a 112-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) system over a 1440-km standard single-mode fiber (SSMF). A joint overlap approach and bandwidth compensation filter (OLA-BC) architecture is presented to mitigate the edge effect caused by the Hilbert transform and the Gibbs phenomenon induced by the FIR filter, respectively. Moreover, the computational complexity of the OLA-BC based parallelized KK/WDU-KK receiver is also discussed. Parallelized KK/WDU-KK receivers based on the presented OLA-BC architecture can effectively mitigate the edge effect and the Gibbs phenomenon together with more than two orders of magnitude improvement in terms of bit-error-ratio (BER) compared with parallelized KK/WDU-KK receivers without OLA-BC receivers in back-to-back (B2B) case. Finally, we successfully transmit the 16-QAM signals over 960-km SSMF with a BER lower than 7% hard-decision forward error correction (HD-FEC) threshold (3.8 × 10-3) and 1440-km SSMF with a BER lower than 20% soft-decision FEC (SD-FEC) threshold (2 × 10-2).

Experimental demonstration of an optical quantizer with ENOB of 3.31 bit by using a cascaded step-size MMI.

We experimentally demonstrated an optical phase shifted quantizer using a cascade step-size MMI (CS-MMI), which was fabricated on a commercially available 220-nm SOI platform via multi-project wafer (MPW) process. An experimental setup was built to test the ability of the CS-MMI acting as a quantizer. The experimental results show that the proposed CS-MMI-based quantizer has an effective number of bit (ENOB) of 3.31bit, which is a little slighter than the ideal ENOB of 3.32bit. The operation range is 12 nm for ENOB≥3 bit. Moreover, the insertion loss of the CS-MMI is -1.26 dB at 1560 nm, the performance of the fabricated device agrees well with simulation results.

Improved polar decoding for optical PAM transmission via non-identical Gaussian distribution based LLR estimation.

In this paper, an improved polar decoder based on non-identical Gaussian distributions is proposed and experimentally demonstrated for optical pulse amplitude modulation (PAM) interconnection. The principle of the polar coded PAM system is illustrated theoretically and the non-identical Gaussian distributions based log-likelihood ratio (LLR) estimation is introduced in the polar decoder to mitigate nonlinearity. Transmission systems of 28-Gbaud 4-level pulse amplitude modulation (PAM-4) and 8-level pulse amplitude modulation (PAM-8) based on commercial 10-GHz directly modulated laser (DML) are both demonstrated over 10-km standard single-mode fiber (SSMF) in C-band without dispersion compensation. Experimental results show that, aided by the improved polar decoder, the channel nonlinearity can be taken into consideration and additional sensitivity gains of 0.7 dB and 1 dB are respectively achieved compared with traditional polar decoder for PAM-4 and PAM-8 systems.