Joint equalization of RSOP and PMD fused probability-aware with square-root cubature Kalman filter for the PDM PCS-64QAM system under extreme scenarios.

Extreme scenario of lightning strikes would generate ultra-fast rotation of state-of-polarization (RSOP) up to 5.1 Mrad/s and large polarization mode dispersion (PMD) in optical ground wire (OPGW). Unfortunately, the conventional multiple modulus algorithm (MMA) cannot equalize these polarization impairments in polarization division multiplexing (PDM) probabilistic constellation shaping (PCS)-64QAM system. Moreover, due to unavoidable linearization errors and higher modulation order, the extended Kalman filter based on measurement equations of concatenated multiplication (EKF-CM) is highly unstable and fails under such scenarios. To address the above issues, we have proposed a joint equalization scheme of PMD and RSOP, which fuses probability-aware with square-root cubature Kalman filter (PA-SCKF). Firstly, according to the characteristic that the amplitude of PCS signals obeys mixed Rician distribution, the scheme combines maximum a posteriori criterion to obtain the optimal radius of constellation ring which the received symbol belongs to, for the sake of calculating the innovations of SCKF. Secondly, it performs joint equalization of PMD and RSOP impairments based on SCKF and time-frequency conversion architecture. 28GBaud PDM PCS-64QAM simulation results demonstrate that our scheme can jointly equalize maximum impairments of 8.34 Mrad/s RSOP and 90ps DGD under entropy of 4.5bits/symbol. Additionally, only 0.9 dB OSNR penalty is obtained after joint equalization of 6 Mrad/s RSOP with 70ps DGD impairments. Even under entropy of 5.5bit/symbol, it can still jointly equalize impairments of 6.05 Mrad/s RSOP with 60ps DGD. Furthermore, 16GBaud PCS-64QAM experimental results indicate that the maximum joint equalization performances of PA-SCKF scheme under entropy of 4.5bit/symbol and 5bit/symbol are 17 Mrad/s RSOP with 52ps DGD, and 9 Mrad/s RSOP with 52ps DGD, respectively. These results manifest that our PA-SCKF scheme outperforms both MMA and EKF-CM schemes. Importantly, its complexity is on an order of O(Llog2 L), which is comparable to that of EKF-CM scheme.

Joint intra and inter-channel nonlinear compensation scheme based on improved learned digital back propagation for WDM systems.

In this paper, we improve the learned digital back propagation (LDBP) and propose a novel joint intra and inter-channel nonlinearity compensation scheme for polarization division multiplexing wavelength-division multiplexed (PDM-WDM) systems. From the perspective of interpretable neural network, the scheme realizes the alternating compensation of chromatic dispersion (CD) and nonlinearity based on physical models. The chromatic dispersion compensation (CDC) adopts one-dimensional convolution operation in the time domain. Moreover, the pulse-broadening effect is introduced into the overlap-and-save method. For nonlinear compensation, the improved joint model is applied, and the impact of the intra-channel pulse broadening and the walk-off effect between different channels caused by CD on the nonlinear effect is considered. To validate the effectiveness of the proposed scheme, we construct an 11-channel simulation system of 36 GBaud PDM uniform 16 quadrature amplitude modulation (PDM-16QAM) 1600 km and 64 GBaud PDM-64QAM 400 km, as well as a 5-channel experimental system of 28 GBaud PDM-16QAM 806.4 km. The simulation results show that the performance of PDM-16QAM with 0.5 steps per span and PDM-64QAM with 2 steps per span improve the Q-factor by approximately 0.75 dB and 0.54 dB at the optimal launch power, compared with the linear compensation scheme. The transmission performance of PDM-16QAM is higher than that of digital back propagation with 5 steps per span (DBP-5StPS), and the complexity is only 31.36% of that of DBP-5StPS. The performance of PDM-64QAM is higher than that of DBP-10StPS, with a complexity of 62.72%. The experimental results show that the performance of PDM-16QAM with 0.5 steps per span is improved with 0.86 dB Q-factor improvement compared with the linear compensation scheme at the optimal launch power, and the performance of the proposed scheme is higher than that of DBP-5StPS with a complexity of only 23.68%.

Joint equalization of frequency offset and phase noise using two-stage cascaded extended Kalman filter for discrete spectrum 16/64APSK NFDM systems.

For the discrete spectrum nonlinear frequency division multiplexing (DS-NFDM) 16/64 amplitude phase shift keying (APSK) system, the inevitable laser impairments including frequency offset (FO) and carrier phase noise (CPN) would cause different rotations of the received signal constellations. In addition, the combined effect of FO and amplifier spontaneous emission (ASE) noise induces the eigenvalue shift, accordingly the residual channel impairment (RCI) is inevitably yielded. To address the above problems, we deduce the joint impairment model of FO, CPN and RCI, and then propose a joint equalization scheme using two-stage cascaded extended Kalman filter (TSC-EKF) for these impairments. It performs frequency offset compensation in the first stage, subsequently carries out joint equalization of CPN and RCI in the second stage. Meanwhile, the minimum Euclidean distance and phase difference between the received symbols and the ideal 16/64APSK constellations are ingeniously fused to calculate the innovations of TSC-EKF. The effectiveness has been verified by 2 GBaud DS-NFDM 16/64 APSK simulations and DS-NFDM 16APSK transmission experiments. The results demonstrate that when performing the joint equalization of FO, CPN and RCI, the maximum FOE range of TSC-EKF scheme achieves 1.2 and 9.6 times as that of nonlinear frequency domain (NFD) scheme and fast Fourier transform -Like (FFT-Like) scheme, respectively. Furthermore, its maximum LW tolerance reaches 3.3 times as that of the M-th power scheme. Importantly, the complexity of TSC-EKF is 63.4% as that of NFD scheme and on an order of O(N).

Optimized equalization based on MAP detection for C-band bandwidth-limited IM/DD systems.

Entangled dynamic and deterministic inter-symbol interferences (ISIs) induced by complicated channel impairments, limit the transmission capacity of intensity modulation and direct detection (IM/DD) systems. This Letter proposes a colored noise-suppressed channel shortening filter (CNS-CSF)-enabled maximum a posteriori (MAP) estimation (CNS-CSF-MAP) scheme to disentangle and mitigate deterministic and dynamic ISIs, where the CNS-CSF is deployed to perform the optimized dynamic ISI equalization with equalization-enhanced noise suppression, and the subsequent MAP algorithm is used to eliminate the residual deterministic ISI. The performance of the CNS-CSF-MAP scheme is evaluated and demonstrated in a C-band 61-Gb/s 100-km optical on-off keying (OOK) IM/DD system. The experimental results show that the proposed CNS-CSF-MAP scheme reaches the 20% and 7% forward error correction (FEC) thresholds at received optical powers (ROPs) of -6.6 dBm and -4 dBm, achieving 0.5- and 1.5-dB gains over a conventional post-filter-enabled MAP (PF-MAP) scheme.

Single wavelength MDM-PDM 800-Gb/s net data rate transmission over a standard multimode fiber employing a Kramers-Kronig receiver.

We propose a high-speed multimode fiber short-reach optical interconnect system based on a Kramers-Kronig (KK) field reconstruction with the mode division multiplexing (MDM) and polarization division multiplexing (PDM) technology. In this work, the LP01, LP21a, LP21b, and LP02 modes are selected as independent channels to carry information. The demonstration achieved the 800 Gb/s net data rate per wavelength with a bit-rate-distance-product (BDP) of 8 Tb/s·km. To the best of our knowledge, this is the highest experimental record of a single wavelength BDP over the SMMF with KK detection. In addition, we discuss the system performance after all multiple-input multiple-output (MIMO) and partial MIMO processing and give guidance on the trade-off between system performance and computational resource.

Physical layer encryption for coherent PDM system based on polarization perturbations using a digital optical polarization scrambler.

In this paper, a security enhanced physical layer encryption scheme is proposed for coherent optical polarization division multiplexing (PDM) systems. The concept of a digital optical polarization scrambler (DOPS) is introduced to apply high speed rotation of state of polarization (RSOP) to the transmitted signal, which enables encryption based on polarization perturbations and offers superior flexibility in polarization management. By utilizing different combinations of digital polarization device matrices and adjusting their key parameters, four encryption modes are designed. The proposed encryption scheme is successfully implemented in a PDM-QPSK system at the data rate of 32 Gbps. Experimental results demonstrate that authorized users can successfully decrypt the received signal, while the eavesdroppers cannot derive useful information with a bit error rate (BER) at approximately 0.5. To enhance system security, a 5-D chaotic system is introduced with superior properties of high sensitivity to initial values and improved uniform distribution, which guarantees the large entropy and further the system's security. This scheme can effectively prevent against brute attacks with the expanded key space of 1060.

Excitation of multiple Fano resonances on all-dielectric nanoparticle arrays.

In this paper, an all-dielectric metasurface consisting of a unit cell containing a nanocube array and organized periodically on a silicon dioxide substrate is designed and analyzed. By introducing asymmetric parameters that can excite the quasi-bound states in the continuum, three Fano resonances with high Q-factor and high modulation depth may be produced in the near-infrared range. Three Fano resonance peaks are excited by magnetic dipole and toroidal dipole, respectively, in conjunction with the distributive features of electromagnetism. The simulation results indicate that the discussed structure can be utilized as a refractive index sensor with a sensitivity of around 434 nm/RIU, a maximum Q factor of 3327, and a modulation depth equal to 100%. The proposed structure has been designed and experimentally investigated, and its maximum sensitivity is 227 nm/RIU. At the same time, the modulation depth of the resonance peak at λ = 1185.81 nm is nearly 100% when the polarization angle of the incident light is 0 °. Therefore, the suggested metasurface has applications in optical switches, nonlinear optics, and biological sensors.

ASE noise mitigation with digital frequency offset loading for discrete spectrum nonlinear frequency division multiplexing systems.

We propose an amplified spontaneous emission (ASE) noise mitigation scheme utilizing digital frequency offset loading (DFO-loading) for discrete spectrum nonlinear frequency division multiplexing (DS-NFDM) systems. Firstly, based on the one-to-one mapping relationship between frequency offsets and eigenvalue positions, the transmitter side encodes 4-bit information onto 16 kinds of different digital frequency offsets. Then, a sliding window-assisted eigenvalue position (SWA-EP) decoding technology is further proposed to substitute the classical channel equalization and carrier phase recovery processes, with the purpose of recovering the original information. The numerical and experimental results demonstrate that, compared with b-coefficient 16 quadrature amplitude modulation (QAM) scheme, Q-factor gains are 2.1 dB under 15 dB optical signal-to-noise ratio (OSNR) and 1.8 dB after 800 km fiber transmission, respectively. Moreover, its complexity is only 0.6% of the b-coefficient scheme. The DFO-loading scheme offers an effective and low-complexity way to mitigate ASE noise of DS-NFDM system.

High Q-factor Fano resonances based on a permittivity-asymmetric dielectric pea-shaped cylinder.

We numerically investigate two Fano resonances with high Q-factors based on a permittivity-asymmetric metastructure composed of two pea-shaped cylinders. By employing different materials to break the permittivity-asymmetry, the quasi-bound state of the continuum spectrum (BIC) resonance at 982.87 nm is excited, showing the Q-factor as high as 8183.7. The electromagnetic fields and vectors are analyzed by using the finite-difference time-domain (FDTD) method, and the resonance modes are identified as magnetic dipole (MD) responses and MDs by multipole decomposition in Cartesian coordinates, displaying that the light is confined within a pea-shaped cylinder to achieve localized field enhancement. In addition, the sensing performances of the metastructure are evaluated, and an optical refractive index sensor can be obtained with the sensitivity of 152 nm/RIU and maximum figure of merit (FOM) of 832.6. This proposed structure offers a new, to the best of our knowledge, way to achieve Fano resonant excitation on all-dielectric metastructures and can be used in nonlinear optics, biosensing, optical switches, and lasers.

Joint equalization of EEPN, RSOP, and CD with the sliding window assisted extended Kalman filter for a high baud rate Stokes vector direct detection system.

Equalization-enhanced phase noise (EEPN) has emerged as one of the major impairments that cannot be ignored for a high baud rate Stokes vector direct detection (SVDD) system. When EEPN interacts with the rotation of state-of-polarization (RSOP) and chromatic dispersion (CD), the joint impairment effects become even more complicated. To achieve the joint equalization of EEPN, RSOP, and CD impairments of a high baud rate SVDD system, this paper first derives a joint impairment model of these three kinds of impairments, and then proposes a joint equalization scheme of EEPN, RSOP, and CD with a sliding window assisted extended Kalman filter (SWA-EKF). The SWA-EKF scheme first tracks RSOP in the time domain, subsequently compensates CD in the frequency domain, and finally performs EEPN mitigation in the time domain again. The effectiveness of the proposed scheme has been verified by a 60 GBaud SVDD-16QAM simulation system. The results show that when these three impairments are jointly equalized, the SWA-EKF scheme can track RSOP as fast as 3 Mrad/s, cumulative dispersion up to 1600 ps/nm, and EEPN caused by laser linewidth up to 3 MHz. In addition, with an optical signal-to-noise ratio penalty of 0.3 dB, it could increase 35 G baud rate under 3 MHz laser linewidth for the SVDD system. More importantly, its total complexity can be reduced to an order of O(N log N).

Offset double sideband carrier assisted differential detection with field recovery at low carrier-to-signal power ratio.

Four system frameworks based on carrier assisted differential detection (CADD) receivers for offset double sideband (DSB) signal transmission, including offset DSB asymmetric CADD (offset DSB A-CADD), offset DSB symmetric CADD (offset DSB S-CADD), offset DSB parallel double delay asymmetric CADD (offset DSB PDD-A-CADD), and offset DSB parallel double delay symmetric CADD (offset DSB PDD-S-CADD) are proposed to reduce the requirement for carrier-to-signal power ratio (CSPR) and improve the spectral efficiency (SE) of the self-coherent detection. These frameworks accommodate signal-signal beat interference (SSBI) and efficiently solve the noise enhancement by placing a frequency gap as wide as the signal bandwidth in the middle of the left and right sideband signal. Massive theoretical derivation and simulation verification illustrated that compared with previous interleaved A-CADD, our system achieve field recovery under the condition of 0 dB CSPR with the improvement of SE by 5%, and the OSNR sensitivity is improved by 4.5 dB with 20% forward error correction (FEC) threshold. In addition, due to the devices' limited bandwidth (BW), the information-bearing signal is attenuated at the high-frequency region. And since SSBI has less influence on the signal in the high-frequency region, the frequency gap of the four offset DSB CADD schemes are compressed to utilize as much low-frequency resource as possible and improve the SE. Efficient compression of the frequency gap from 50% to 32.3% with 20% FEC threshold and 50% to 37.7% with 7% FEC threshold at 0 dB CSPR is achieved, and only a slight performance degradation is observed. At this time, the SE is improved by 22.7% and 17.3% with different FEC thresholds, respectively, compared with the 5% frequency gap interleaved A-CADD.

Blind frequency offset estimation using the optimal decision threshold-assisted QPSK-partition method for probabilistically shaped MQAM systems.

Moderate or strong shaping conditions reduce the occurrence probability of the outermost ring constellation points of probabilistically shaped (PS)-M quadrature amplitude modulation (QAM) signals, which easily causes the peaks in the 4th power periodogram of received signals be submerged, accordingly the classical frequency offset estimation (FOE) scheme using 4th power fast Fourier transform (FFT) cannot be applied in PS-MQAM system. To solve this issue, we have proposed an optimal decision threshold assisted quadrature phase shift keying (QPSK)-partition blind FOE scheme. Firstly, the proposed scheme utilizes an optimal decision threshold assisted method for the symbol decision of received symbols, then chooses the symbols on multiple specific QPSK-shape rings. Secondly, the amplitude of each symbol selected above is normalized and uniformly augmented to 18. Finally, it carries out FOE using an improved time-domain 4th power feedforward method that eliminates the time interval. The effectiveness of the proposed scheme has been verified by 28 GBaud polarization division multiplexing (PDM) PS-16/64QAM simulations and 28/8 GBaud PS-16/64QAM experiments. The results obtained by this scheme present that under moderate or strong shaping conditions, the generalized mutual information (GMI) increases with optical signal-to-noise ratio (OSNR) and eventually exceeds the corresponding GMI threshold. Besides that, the FOE range can reach [-Rs/8, Rs/8], where Rs denotes the baud rate. When OSNRs are higher than 16 dB and 19.5 dB, the NMSEs of PS-16QAM-3/3.6 are lower than 1e-7, respectively. For PS-64QAM-4.4/5, the NMSEs achieve lower than 1e-6 after OSNR increases to 20.3 dB and 23.4 dB, respectively. More importantly, the overall complexity can be reduced to O(N), which is at most as 26.5% as that of FFT FOE scheme.

Joint multi-parameter optical performance monitoring scheme based on trajectory information for a Stokes vector direct detection system.

In this study, we propose and verify a joint multi-parameter optical performance monitoring (OPM) scheme based on trajectory information for the Stokes vector direct detection (SVDD) system, for the first time, to the best of our knowledge. Here, the proposed scheme first performs quantification of the trajectory to construct trajectory information, which not only presents diversity of the received symbols in spatial dimension, but also records the jump pattern among symbols in time dimension. Subsequently, eigenanalysis is introduced to extract critical features hidden in trajectory information and simultaneously achieve the purpose of dimensionality reduction. The effectiveness of the scheme is verified through 14/28 GBaud SVDD binary phase shift keying/quadrature phase shift keying/-8 quadrature amplitude modulation (QAM)/-16QAM/-32QAM/-64QAM simulation systems. Under the scenario of joint modulation format (MF) identification and optical signal to noise ratio (OSNR) monitoring, the identification rates of all six kinds of MFs achieve 100% within their corresponding reasonable OSNR ranges. Besides that, the average mean absolute error (MAE) of the monitored OSNRs are obtained as 0.03 dB, 0.22 dB, 0.36 dB, 0.41 dB, 0.46 dB, and 0.49 dB for those six kinds of MFs, respectively. Under the scenario of multi-parameter OPM, SVDD-8QAM/-16QAM/-32QAM signals are 100% successfully identified when residual chromatic dispersion (RCD) is located in the ranges of 0-200 ps/nm, 0-190 ps/nm, and 0-160 ps/nm, respectively. The average MAE of OSNR monitoring and RCD estimation for these three commonly used MFs are 1.08 dB and 3.23 ps/nm, respectively. Moreover, the study also demonstrates the robustness for baud rates and a relatively simpler calculation complexity about the proposed OPM scheme.

Joint nonlinear optical signal-to-noise ratio estimation and modulation format identification based on constellation-points trajectory information and multitask 1DCNN for WDM systems.

We propose a joint monitoring scheme of nonlinear optical signal-to-noise ratio (O S N R N L ) estimation and modulation format identification (MFI) in wavelength division multiplexing (WDM) systems. Based on the abundant information of both nonlinear noise (NLN) and modulation format (MF) in received signals, this scheme first counts the trajectory information of all adjacent constellation points, and then quantifies them into the adjacent matrix. Subsequently, the eigenvectors corresponding to the largest eigenvalues are extracted via eigen-decomposition of the adjacent matrix, which characterize the information of NLN and MF effectively. Finally, the eigenvectors are fed into multitask one-dimensional convolutional neural network to perform O S N R N L estimation and MFI simultaneously. To verify the effectiveness of the scheme, five-channel 28 GBaud polarization division multiplexing (PDM) -16/32/64 quadrature amplitude modulation (QAM) WDM simulation systems are built by VPI. The simulation results demonstrate that, for PDM-16/32/64QAM signals, the mean absolute errors of O S N R N L estimation are 0.18, 0.17, and 0.20 dB, respectively. At the same time, the identification accuracy rates of these three MFs have achieved 100% within the ranges of estimated O S N R N L . Furthermore, a three-channel 28 GBaud WDM experimental system is constructed to further investigate the effectiveness of trajectory information for O S N R N L estimation. The experimental results show that the O S N R N L estimation errors of PDM-16QAM are less than 0.5 dB. In addition, our analysis of complexity from two aspects of trajectory information extraction and neural network model shows that the overall complexity scale of this scheme is O(K i,3 M C i,3 C o,3).

Noise equalization scheme based on complex-valued ANN for multiple-eigenvalue modulated nonlinear frequency division multiplexing systems.

In multiple-eigenvalue modulated nonlinear frequency division multiplexing (NFDM) systems, the noise degrades the accuracy of the nonlinear Fourier transform (NFT) algorithm, resulting in perturbations in the received eigenvalues and the corresponding discrete spectrum. Moreover, with the increase in the number of eigenvalues and the order of the modulation formats, the impact of noise on the performance of the system is even more. A noise equalization scheme based on complex-valued artificial neural network (c-ANN) for multiple-eigenvalue modulated NFDM systems is proposed. This sceheme inputs the eigenvalues perturbation and the impaired discrete spectrum corresponding to the eigenvalues into the c-ANN in complex form. The scheme constructs a complex-valued logic structure with both amplitude and phase information, overlapping reuse input features and, thereby, effectively reducing the effect of noise on the multiple-eigenvalue NFDM system. The effectiveness of the scheme is verified in long-haul seven-eigenvalue modulated single-polarization NFDM simulation systems with 1 GBaud 16APSK/16QAM/64APSK/64QAM modulation formats, and the results show that the scheme outperforms the NFT receiving without equalization by 1 to 2 orders of magnitude in terms of bit error rate (BER). Among them, the transmission distance of the 64APSK signal after equalization exceeds 800 km while the BER meets 7% forward error correction (FEC) threshold, which is 600 km longer than that of the disequilibrium case, and the spectral efficiency (SE) can reach 1.85 bit/s/Hz. Compared with other schemes, the proposed scheme has better equalization performance under the same complexity, and the complexity can be reduced by half or even under the same performance.

Blind modulation format identification based on improved PSO clustering in a 2D Stokes plane.

Blind modulation format identification (MFI) is indispensable for correct signal demodulation and optical performance monitoring in future elastic optical networks (EON). Existing MFI schemes based on a clustering algorithm in Stokes space have gained good performance, while only limited types of modulation formats could be correctly identified, and the complexities are relatively high. In this work, we have proposed an MFI scheme with a low computational complexity, which combines an improved particle swarm optimization (I-PSO) clustering algorithm with a 2D Stokes plane. The main idea of I-PSO is to add a new field of view on each particle and limit each particle to only communicate with its neighbor particles, so as to realize the correct judgment of the number of multiple clusters (local extrema) on the density images of the s2-s3 plane. The effectiveness has been verified by 28 GBaud polarization division multiplexing (PDM)-BPSK/PDM-QPSK/PDM-8QAM/PDM-16QAM/PDM-32QAM/PDM-64QAM simulation EON systems and 28 GBaud PDM-QPSK/PDM-8QAM/PDM-16QAM/PDM-32QAM proof-of-concept transmission experiments. The results show that, using this MFI scheme, the minimum optical signal-to-noise ratio (OSNR) values to achieve 100% MFI success rate are all equal to or lower than those of the corresponding 7% forward error correction (FEC) thresholds. At the same time, the MFI scheme also obtains good tolerance to residual chromatic dispersion and differential group delay. Besides that, the proposed scheme achieves 100% MFI success rate within a maximum launch power range of -2∼+6 dBm. More importantly, its computational complexity can be denoted as O(N).

Density-matrix formalism for modal coupling and dispersion in mode-division multiplexing communications systems.

Borrowing methodology from quantum mechanics, we propose and develop a density-matrix formalism for modal coupling and dispersion in mode-division multiplexing communications systems. The central concept in our formalism is the density matrix, from which all observable information of an optical field can be handily accessed. In the formalism, we derive fundamental evolution equations and concatenation rules for the key elements that characterize essential modal properties, and construct a statistical model ready for the numerical analysis of stochastic light propagation in randomly perturbed fibers. Unlike the Stokes-vector formalism that requires J2 - 1 auxiliary Gell-Mann matrices, the density-matrix formalism can be directly formulated for arbitrary modal-space dimension J. Based on the density-matrix formalism, the statistical modal properties of a 4-mode fiber under random perturbation are numerically investigated, which raises an interesting possibility of optimizing the modal dispersion by manipulation of the random perturbation.

Blind and low-complexity modulation format identification scheme using principal component analysis of Stokes parameters for elastic optical networks.

We propose a blind and low-complexity modulation format identification (MFI) scheme for elastic optical networks (EONs). Since the square operation reduces half the number of the clusters in Stokes space, the scheme directly performs principal component analysis (PCA) on Stokes parameters after square operation. This greatly reduces the dimensionality of received signals from 3 × N to 3 × 3. Subsequently, three obtained principal components (PCs) are employed synthetically to identify the modulation formats. The effectiveness is first verified through 28 GBaud polarization division multiplexing (PDM)-BPSK/-QPSK/-8QAM/-16QAM/-32QAM/-64QAM simulation systems. Only using 2048 symbols, the required minimum optical signal-to-noise ratio (OSNR) values to achieve 100% MFI success rate are all equal to or lower than their corresponding 7% forward error correction (FEC) thresholds. Besides that, the scheme also obtains significant tolerances to residual chromatic dispersion (CD) and differential group delay (DGD). Finally, the proposed scheme is further verified by 20 GBaud PDM-QPSK/-16QAM/-32QAM long-haul transmission experiments. The results demonstrate that the scheme exhibits good resilience towards fiber nonlinear impairments. More importantly, compared with other four kinds of MFI schemes, the used symbol number to achieve 100% MFI success rate notably equals to at most 2/5 as that of other schemes, and its time complexity can be reduced to O(N).

Nondiffracting light beams carrying fractional orbital angular momentum.

We investigate a new class of nondiffracting optical beams carrying fractional orbital angular momentum (FOAM Bessel beams), which can be constructed by modifying the phase step of the spiral phase plate in a setup originally for the generation of traditional Bessel beams. The FOAM Bessel beams have entirely stable vortex structures, and form an infinite number of orthogonal and complete subsets for monochromatic scalar light in free space. With the advantages of structural stability and orthogonality-completeness, the FOAM Bessel beams are expected to be useful for study and application in various fields of modern optics.

Construction of a novel nomogram for predicting overall survival in patients with Siewert type II AEG based on LODDS: a study based on the seer database and external validation.

Background: In recent years, the incidence of adenocarcinoma of the esophagogastric junction (AEG) has been rapidly increasing globally. Despite advances in the diagnosis and treatment of AEG, the overall prognosis for AEG patients remains concerning. Therefore, analyzing prognostic factors for AEG patients of Siewert type II and constructing a prognostic model for AEG patients is important. Methods: Data of primary Siewert type II AEG patients from the SEER database from 2004 to 2015 were obtained and randomly divided into training and internal validation cohort. Additionally, data of primary Siewert type II AEG patients from the China Medical University Dandong Central Hospital from 2012 to 2018 were collected for external validation. Each variable in the training set underwent univariate Cox analysis, and variables with statistical significance (p < 0.05) were added to the LASSO equation for feature selection. Multivariate Cox analysis was then conducted to determine the independent predictive factors. A nomogram for predicting overall survival (OS) was developed, and its performance was evaluated using ROC curves, calibration curves, and decision curves. NRI and IDI were calculated to assess the improvement of the new prediction model relative to TNM staging. Patients were stratified into high-risk and low-risk groups based on the risk scores from the nomogram. Results: Age, Differentiation grade, T stage, M stage, and LODDS (Log Odds of Positive Lymph Nodes)were independent prognostic factors for OS. The AUC values of the ROC curves for the nomogram in the training set, internal validation set, and external validation set were all greater than 0.7 and higher than those of TNM staging alone. Calibration curves indicated consistency between the predicted and actual outcomes. Decision curve analysis showed moderate net benefit. The NRI and IDI values of the nomogram were greater than 0 in the training, internal validation, and external validation sets. Risk stratification based on the nomogram's risk score demonstrated significant differences in survival rates between the high-risk and low-risk groups. Conclusion: We developed and validated a nomogram for predicting overall survival (OS) in patients with Siewert type II AEG, which assists clinicians in accurately predicting mortality risk and recommending personalized treatment strategies.