Fiber Nonlinear Effects Research Articles

Nonlinear Effect and MAI Impact on SAC-OCDMA System Based on 2D Multi-Diagonal Code and Laser Array

A new architecture for Spectral Amplitude Coding Optical Code Division Multiple Access (SAC-OCDMA) system based on two Dimensional Multi Diagonal (2D-MD) codes named 2D-MD SAC-OCDMA and utilizing a laser optical source is proposed for Long-Reach Passive Optical Network (LR-PON). In this work, a computer simulator tool is used, for the first time, as a SAC-OCDMA simulation set-up utilizing the unique combination of a coherent laser array and 2D-MD codes. In addition, the system performance is addressed numerically by taking into account Multiple Access Interference (MAI), optical coherent source noise, first, second and third order fiber dispersion, nonlinear effects and photo-detector noise. Simulation results indicate that for a single user (i.e., without considering MAI), the system can operate at a maximum bit rate of 55 Gb/s over 250 km of Single Mode Fiber (SMF), with a Bit Error Rate (BER) below 10−9 (Q-limit = 15.5 dB), when only first order fiber dispersion is considered. However, including the effects of second and third order fiber dispersion as frequency domain parameters, results in a reduction of the maximum bit rate to 40 Gb/s, while maintaining a Q-factor above the Q-limit under the same transmission distance. Furthermore, we demonstrate that the proposed architecture extends the SMF transmission reach up to 600 km and 480 km, when considering linear and nonlinear effects, respectively. Finally, we show that our proposed 2D-MD SAC-OCDMA system outperforms existing solutions presented in the literature for LR-PON configuration, in terms of both aggregate bit rate and transmission reach.

All-Optical Aggregation and De-Aggregation Between 8QAM and BPSK Signal Based on Nonlinear Effects in HNLF

An all-optical aggregation and de-aggregation scheme between one 8-ary quadrature amplitude modulation (8QAM) signal and three binary phase shift keying (BPSK) signals is proposed and theory simulated based on nonlinear effects in high nonlinear fiber (HNLF). In this scheme, the input 8QAM signal is de-aggregated into three BPSK signals by deploying self-phase modulation (SPM), cross-phase modulation (XPM), four wave mixing (FWM) and parameter amplification (PA) effect. Firstly, an improved amplitude compression loop (ACL) is designed based on SPM effect to convert 8QAM signal into quadrature phase shift keying (QPSK) signal. A degenerate phase sensitive amplifier (PSA) based on FWM effect is used to decompose QPSK signal into the first two BPSK signals (BPSK-1 and BPSK-2). The third BPSK signal (BPSK-3) can be extracted from the probe light modulated in its phase by the input 8QAM signal thanks to XPM and PA effect. Secondly, BPSK-3 is converted into an atypical on-off keying (OOK) signal through a 1-bit delay interference (DI). BPSK-1 and BPSK-2 are recombined into one QPSK signal through a coupler. Finally, the recombined QPSK signal and the atypical OOK signal are aggregated into one 8QAM signal by using XPM and PA effect. The error vector magnitude (EVM) and bit error ratio (BER) of the 8QAM and BPSK signal before and after de-aggregation and aggregation are calculated to analyse the performance of the scheme. The scheme can be applied in the network node to connect different networks which explore to use 8QAM and BPSK signal respectively.

A Comparative Study of SPM and XPM in Er-Yb Co-Doped Fiber

Optical fiber communication has been the most versatile and revolutionary medium of communication that has helped connect millions of people across the globe. These traits have seen tremendous development in the sector of optical fiber communication. There are now many desired qualities expected out of an optical fiber communication such as large transmission capacity and a smaller amount of loss. Communication systems operating with higher transmission rates have found an essential role of non-linear fiber optics. The behavior of light in non-linear media is described by non-linear optics. Cross-phase modulation (XPM) and self-phase modulation (SPM) are a few non-linearities occurring in the optical fiber. Non-linear effects reduce the performance of optical fibers. In this paper, a comparative study of non-linear effects in erbium-ytterbium co-doped fiber is reviewed using simulation. The results are compared with optical systems utilizing normal fiber. The benefits of using Er-Yb fiber have been demonstrated by analyzing effective systems comprising the Er-Yb co-doped fiber and their ability to mitigate the non-linearities.

Review on nonlinearity effect in radio over fiber system and its mitigation

Abstract Modern communication generation for high data rate requirement is fifth generation. The fifth generation has many advantages like low delay, high spectrum availability, high reliability, low jitter, and more capacity. To combat with the high capacity and high data rate requirement, optical fiber helps in the backhaul of 5G network. When fiber is used as a mode of propagation, many nonlinearities arises. This nonlinearity effect in the optical fiber communication is one of the most undesirable phenomena for the modern communication system which results in harmonic distortion, intermodulation distortion, phase distortion, and adjacent channel interference, etc. In most fiber optic communication systems, the major fiber nonlinear effect is the Kerr nonlinearity and Scattering effect that produced due to the variation of refractive index due to signal intensity. To minimize the effect of nonlinear distortion, some techniques are used which considerably improve the transmission capacity by reducing or compensating the effect of nonlinear distortion along with minimal infrastructure modifications and minimum cost for implementation. To overcome the effect of nonlinearity, fiber nonlinearity mitigation techniques are preferred to achieve the significant performance gains. Mitigation techniques can be implemented to improve and optimize the performance of optical communication network. In this paper, a brief description of the fiber nonlinearity effect and a review of various fiber nonlinearity compensation techniques are described.

Development of long‐distance power supply system with high power laser over single mode fiber

AbstractThe technology of long‐distance power supply with high‐power laser (HPL) over single‐mode fiber (SMF) is of great significance in specific environment. The nonlinear effect of fiber and photovoltaic conversion (PC) efficiency are the key factors restricting the application of this technology. The wide linewidth laser and cascaded long period fiber grating (CLPFG) band rejection filter are used to suppress the stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) effects, respectively, integrating sphere like, scattering light guide cone and thermoelectric power generation improve PC efficiency. A HPL over SMF remote power supply system is developed and tested. The injected fiber power is 10 W, the wavelength of 1550 nm laser is transmitted through 103 km single‐mode fiber, and then 26 mW power is converted for the sensor. This is also the highest level of the open literature. It is expected to be applied to the power supply of high voltage transmission line remote monitoring information system in remote areas.

Performance Analysis of a Full-Duplex TWDM-PON Using OFDM Modulation with Red LED Visible Light Communication System

Today’s access networks are in high demand to fulfill the high bandwidth requirement because of extensive improvement in high transmission rate applications for cloud computing, big data analytics, and other next-generation 5G smart applications. In this work, the symmetrical and bidirectional time and wavelength division multiplexing-passive optical network (TWDM-PON) system is proposed and demonstrated. Orthogonal frequency division multiplexing (OFDM) with 4-level quadrature amplitude modulation is used for downstream and upstream transmission. Also, 625 nm red light-emitting diode is utilized for visible light communication (VLC) using a wireless link to encourage the economic high transmission rate fiber/VLC optical network. The TWDM-PON employing OFDM with the VLC system has been analysed for downstream and upstream channels for variable fiber-wireless link range. Additionally, the impact of a high transmission rate and usage of digital signal processing (DSP) unit to reduce losses due to fiber nonlinearity effects in the proposed link has been investigated. The results show that the maximum faithful wireless and wired range for the proposed system is 140 m and 60 km respectively at 20 Gbps to attain the minimum 3.8 × 10−3 BER. The decrease in error vector magnitude (EVM%) by almost 52% with the use of DSP in the proposed system provides a high transmission rate of 200 Gbps in the proposed link. Further, comparative performance of the proposed system with previous latest works in literature reveals a superior performance of the proposed link. The proposed TWDM-PON system provides a next-generation access network from rural areas to urban areas.

Nonlinear Impairment Scaling in Multi-Mode Fibers for Mode-Division Multiplexing

The scaling of nonlinear effects in multi-mode fibers with the mode count has been investigated by analytical studies and by numerical simulations. Increasing the core radius results in larger effective mode field areas, which reduces the impact of nonlinear effects. On the other hand, the presence of more interaction partners for intermodal nonlinear interactions due to a higher number of propagating modes strengthens the impact of nonlinear signal degradations on data transmission. Our results indicate that these two trends are mostly balanced even for large mode counts. Transmission reaches and system performance comparable to standard single-mode fibers are achievable for at least 100 modes.

Optical Performance Monitoring in Mode Division Multiplexed Optical Networks

This article considers, for the first time, optical performance monitoring (OPM) in few mode fiber (FMF)-based optical networks. 1-D features vector, extracted by projecting a 2-D asynchronous in-phase quadrature histogram (IQH), and the 2D IQH are proposed to achieve OPM in FMF-based network. Three machine learning algorithms are employed for OPM and their performances are compared. These include support vector machine, random forest algorithm, and convolutional neural network. Extensive simulations are conducted to monitor optical to signal ratio (OSNR), chromatic dispersion (CD), and mode coupling (MC) for dual polarization-quadrature phase shift keying (DP-QPSK) at 10, 12, 16, 20, and 28 Gbaud transmission speeds. Besides, M-ary quadrature amplitude modulation (M = 8 and 16) is considered. Also, the OPM accuracy is investigated under different FMF channel conditions including phase noise and polarization mode dispersion. Simulation results show that the proposed 1D projection features vector provides better OPM results than those of the widely used asynchronous amplitude histogram (AAH) features. Furthermore, it has been found that the 2D IQH features outperform the 1D projection features but require larger number of features samples. Additionally, the effect of fiber nonlinearity on the OPM accuracy is investigated. Finally, OPM using the 2D IQH features has been verified experimentally for 10 Gbaud DP-QPSK signal. The obtained results show a good agreement between both simulation and experimental findings.

Towards Distributed Measurements of Electric Fields Using Optical Fibers: Proposal and Proof-Of-Concept Experiment.

Nowadays there is an increasing demand for the cost-effective monitoring of potential threats to the integrity of high-voltage networks and electric power infrastructures. Optical fiber sensors are a particularly interesting solution for applications in these environments, due to their low cost and positive intrinsic features, including small size and weight, dielectric properties, and invulnerability to electromagnetic interference (EMI). However, due precisely to their intrinsic EMI-immune nature, the development of a distributed optical fiber sensing solution for the detection of partial discharges and external electrical fields is in principle very challenging. Here, we propose a method to exploit the third-order and second-order nonlinear effects in silica fibers, as a means to achieve highly sensitive distributed measurements of external electrical fields in real time. By monitoring the electric-field-induced variations in the refractive index using a highly sensitive Rayleigh-based CP-φOTDR scheme, we demonstrate the distributed detection of Kerr and Pockels electro-optic effects, and how those can assign a new sensing dimension to optical fibers, transducing external electric fields into visible minute disturbances in the guided light. The proposed sensing configuration, electro-optical time domain reflectometry, is validated both theoretically and experimentally, showing experimental second-order and third-order nonlinear coefficients, respectively, of χ(2) ~ 0.27 × 10−12 m/V and χ(3) ~ 2.5 × 10−22 m2/V2 for silica fibers.

Low-complexity probabilistic shaping based on bit-weighted distribution matching in DMT-WDM-PON.

We introduce a novel probabilistic shaping (PS) scheme based on bit-weighted distribution matching (BWDM) into a discrete multi-tone wavelength division multiplexing passive optical network (DMT-WDM-PON) employing low-density parity-check-coded 16-ary quadrature amplitude modulation (16QAM). Unlike the prevailing arithmetic coding-class PS schemes with target symbol probability, such as arithmetic distribution matching and constant composition distribution matching, the proposed one realizes Gaussian-like symbol probability distribution emulation merely based on simple bit-class processing, having the advantage of much lower computational complexity. As the key operation in BWDM, the bit weight intervention is implemented in the process of PS-16QAM generation for elevated transmission probability of binary data '0' by cascaded operations of weight bit labelling and bit reconstruction. The experimental results show that, compared with uniformly-distributed signal with the same net rate, significantly-improved receiver power sensitivity and system tolerance to optical fiber nonlinear effect can be obtained in the DMT-WDM-PON system. The proposed PS scheme can be considered as one of promising practical solutions for more available optical network units due to enlarged system power loss budget for the optical distribution network.

Energy-efficient all optical wavelength converter for optical phase conjugation

Abstract All-optical wavelength converters (AOWCs) based on state-of-the-art highly nonlinear optical fibers (HNLFs) are best matched with future large-capacity optical networks because of their characteristic of fast response. AOWCs play important roles in wavelength-routed optical networks to alleviate the constraint of conflicted wavelengths and in optical phase conjugation networks to mitigate the effects of fiber nonlinearities. Generally, conversion efficiency (CE) is a key evaluation index of AOWCs and higher CE corresponds to better transmission performance. However, it is challenging to achieve higher CE because the launched pump powers into HNLFs are usually limited by their stimulated Brillouin scattering thresholds. Actually, the performance of AOWCs, i.e., that of the idlers, depends on both of their CEs and the signal powers. Thus, it is feasible to achieve good performance for AOWCs with lower CEs as that with higher CEs by optimizing the launched signal powers into HNLFs. Our experimental results verified the above proposal in the AOWCs with the CEs of –23.1 dB, −19.1 dB, −15.2 dB, −11.4 dB and −7.9 dB. The proposed AOWCs was used as optical phase conjugation in the 64-QAM coherent optical transmission experimental system and good compensation performances have been achieved under the above five operating conditions.

The Enhanced Gaussian Noise Model Extended to Polarization-Dependent Loss

We show how to extend the enhanced Gaussian noise (EGN) model to account for polarization-dependent loss (PDL) of optical devices placed along a fiber-optic link. We provide a comprehensive theory highlighting the relationships between the time, frequency, and polarization domains in the presence of fiber nonlinear Kerr effect and amplified spontaneous emission. We double-check the new model with split-step Fourier method (SSFM) simulations showing very good accuracy. The model can be efficiently exploited to estimate low values of outage probabilities induced by PDL with computational times orders of magnitude faster than the SSFM, thus opening new opportunities in the design of optical communication links.

Probabilistic Shaping 44QAM Based on Many-to-One Mapping in DMT-WDM-PON

We introduce a probabilistic shaping (PS) 44-ary quadrature amplitude modulation (44QAM) based on many-to-one (MTO) mapping into a discrete multi-tone wavelength division multiplexing passive optical network (DMT-WDM-PON) with maximum shaping gain of 0.46 dB. A low-density parity-check (LDPC) based bit-interleaved coded modulation and iterative decoding system is proposed to generate and transmit the PS-44QAM DMT signal without any extra PS redundancy. An extrinsic information (EI) is iteratively used between LDPC decoder and PS demapper to retrieve the PS-44QAM DMT signal including overlapped/ambiguous symbols. The experimental results show that the PS-44QAM DMT signal with improved receiver power sensitivity and system fiber nonlinear effect tolerance can be obtained in the power splitter based WDM-PON. Thus, the corresponding system loss budget can be significantly enlarged in the optical distribution network for the purpose of serving more optical network units.

LDPC-Coded Probabilistic Shaping PAM8 Employing a Novel Bit-Weighted Distribution Matching in WDM-PON

We propose and experimentally demonstrate a wavelength-division-multiplexing passive optical network (WDM-PON) employing low-density parity-check (LDPC) coded probabilistic shaping 8-level pulse amplitude modulation (PS-PAM8). In such a splitter-based WDM-PON system with direct detection, a novel probabilistic shaping (PS) method based on a bit-weighted distribution matching (BWDM) for near-Gaussian distribution (NGD) is proposed for the first time. For typical PS schemes based on typical arithmetic distribution matching (ADM) and constant composition distribution matching (CCDM), refining intervals continuously is needed to find the target symbol probability, which will necessarily introduce a plenty of additional redundant bits in the process of the target symbol probability distribution (SPD) emulation from data source. Different from ADM and CCDM, the PS scheme based on BWDM is realized by a simple bit-weight intervention algorithm with low hardware and calculation complexity, which only includes weight-marking bit insertion and bit inversion processes for adjustable SPD kurtosis. The experimental results show that by employing the proposed PS-PAM8, the receiver power sensitivity and system fiber nonlinear effect tolerance can be dramatically improved compared with the unshaped signal. Thus, the WDM-PON employing PS-PAM8 is of cost-effective advantage, which can serve more available optical network units due to the enlarged system loss budget for the optical distribution network.

Fiber impairments mitigation in OFDM based cognitive optical networks

An adaptive impairments assessment is necessary to evaluate the impact of various linear and nonlinear effects in future generation cognitive optical transport links. In this paper, an Adaptive Fiber Impairment Mitigation (AFIM) algorithm is proposed to identify a suitable mitigation scheme for the cognitive environment. The AFIM algorithm will assess fiber impairments and adaptively select a suitable mitigation scheme with minimum complexity based on the present network conditions and user performance target. The performance of AFIM algorithm is compared with Fixed Fiber Impairment Mitigation approach in terms of outage probability and outage capacity analysis. An Orthogonal Frequency Division Multiplexing based Mode Division Multiplexing system with Few Mode Fiber (FMF) is suggested as a solution to increase the nonlinearity threshold limit of the system. The $$\hbox {L}_2$$ -by-3 nonlinear transform based Peak to Average Power Ratio reduction technique is implemented to mitigate fiber nonlinear effects in FMF based backbone and backhaul links. The performance analysis of the FMF system has been evaluated and compared with that of Single Mode Fiber system. The proposed analytical model and mitigation schemes are integrated with the AFIM algorithm to realize the cognitive optical network. Further, the result shows that AFIM algorithm enhances the system capacity by more than 6-folds at an outage probability of 0.5 and reduces the outage probability to 0.6 at the capacity range of 20 Gbps.

Performance analysis of mode division multiplexing system in presence of nonlinear phase noise

Abstract The potential for higher spectral efficiency has increased interest in mode division multiplexing (MDM) systems. However, the sensitivity of MDM to fiber nonlinearity and mode coupling, which induces nonlinear phase noise (NLPN), forms the main penalty. In this work, we developed an analytical model that describes the effects of fiber nonlinearity on the performance of m-array quadrature amplitude modulation (mQAM) MDM system based few-mode fiber (FMF). The random NLPN is mainly induced when Kerr nonlinearities such as self-phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM) as well as their interaction with optical amplifiers noise occur over an optical fiber link. FMF is proposed and designed to carry six spatial modes. The parameters of proposed FMF are used with the analytical model for evaluating the NLPN versus power and distance. To verify the analytical results, an MDM system, that uses proposed FMF without any nonlinear compensation, is demonstrated by numerical simulation. Each spatial mode is modulated by a 4QAM format with a symbol rate of 20 Gsymbol/s. The results are obtained for single-, two- and six–mode propagations to show the influence of fiber nonlinearity on the system performance. The results reveal that the XPM phase noise is the dominant effect that degrades the system performance, specifically when two degenerate spatial modes or modes within the same mode group are co-propagated. In addition, for six-mode transmission, FWM insignificantly induces the NLPN. Finally, the results confirm that the numerical and analytical results in good agreement.

Controlling spatiotemporal nonlinearities in multimode fibers with deep neural networks

Spatiotemporal nonlinear interactions in multimode fibers are of interest for beam shaping and frequency conversion by exploiting the nonlinear interaction of different pump modes from quasi-continuous wave to ultrashort pulses centered around visible to infrared pump wavelengths. The nonlinear effects in multi-mode fibers depend strongly on the excitation condition; however, relatively little work has been reported on this subject. Here, we present a machine learning approach to learn and control nonlinear frequency conversion inside multimode fibers. We experimentally show that the spectrum of the light at the output of the fiber can be tailored by a trained deep neural network. The network was trained with experimental data to learn the relation between the input spatial beam profile of the pump pulse and the spectrum of the light at the output of the multimode fiber. For a user-defined target spectrum, the network computes the spatial beam profile to be applied at the input of the fiber. The physical processes involved in the creation of new optical frequencies are cascaded stimulated Raman scattering as well as supercontinuum generation. We show experimentally that these processes are very sensitive to the spatial shape of the excitation and that a deep neural network is able to learn the relation between the spatial excitation at the input and the spectrum at its output. The method is limited to spectral shapes within the achievable nonlinear effects supported by the test setup, but the demonstrated method can be implemented to learn and control other spatiotemporal nonlinear effects.

Effect of an input beam’s shape and curvature on the nonlinear effects in graded-index fibers

We present a general framework capable of describing the nonlinear propagation of pulsed optical beams of arbitrary shapes and phase fronts inside a graded-index (GRIN) fiber. The main assumption made is that the spatial self-imaging features of the beam are not affected by the temporal evolution of optical pulses. A propagation kernel known from the work done in the 1970s is used to obtain a distance-dependent nonlinear coefficient that captures all spatial effects within an effective nonlinear Schrödinger equation. We consider three specific beam shapes (Gaussian, circular, and square) to study the impact of the shape, position, and curvature of optical beams on the complex spatiotemporal dynamics specific to GRIN fibers. In particular, we focus on the impact of an input beam’s shape on the modulation-instability sidebands and the generation of multiple dispersive waves when higher-order solitons form inside a GRIN fiber. The results of our numerical analysis indicate that for beam widths chosen to yield the same value of the effective mode area at the input end of the fiber, the nonlinear effects are pronounced considerably when a Gaussian beam is launched into the fiber. We also found that even though the self-imaging period is doubled when an off-centered Gaussian beam is launched into a GRIN fiber, it does not affect the nonlinear evolution because the effective beam area still maintains the same periodicity, as long as the shift in the beam’s center is not so large that it does not remain confined to the fiber’s core.

Dispersion and Nonlinearity Distortion Compensation of the QPSK/16QAM Signals Using Optical Phase Conjugation in Nonlinear SOAs

We experimentally demonstrate the simultaneous compensation of both dispersion and nonlinear effects in a 100 km optical fiber link using optical phase conjugation of a 21 GB aud QPSK and 16QAM signal with nonlinear SOAs. Error-free performance is recorded for a launched power of up to 12 dBm, without any digital signal processing to compensate for distortions due to chromatic dispersion and nonlinear effects in fiber. The performance is verified for operation across the C-band.

Volterra Expansion Based Intra Channel Nonlinear Effect Equalization Method for Optical OFDM/OQAM Systems

Optical orthogonal frequency-division multiplexing offset quadrature amplitude modulation (O-OFDM/OQAM) system relaxes the orthogonal condition of the sub-carriers from the complex domain to the real field. Inter-symbol-interference (ISI) and inter-carrier-interference (ICI) could be suppressed by using filter banks with promising time-frequency-localization (TFL) properties. Therefore, cyclic prefix (CP) inserted between consecutive OFDM blocks could be removed for O-OFDM/OQAM system to improve system spectral efficiency. When passing through fiber channel, O-OFDM/OQAM faces serious intrinsic imaginary interference (IMI) induced by chromatic dispersion (CD), and fiber nonlinear effect, which would deteriorate system performance evidently. Fiber nonlinear effect induced interference is a great impairment for long haul transmission O-OFDM/OQAM system, and can not be equalized directly by using nonlinear equalization method designed for traditional optical OFDM. There is still much room for improvement of nonlinear equalization method for O-OFDM/OQAM. In this paper, we systematically study Volterra expansion based nonlinear equalization method (VENE) for O-OFDM/OQAM. We theoretically deduce simplified Volterra series expansion nonlinear transmission matrix (SVEM) for O-OFDM/OQAM based on mathematic deduction. With SVEM, intra channel nonlinear effect induced distortions could be modeled and estimated. By using specially designed pilot blocks, we obtain approximate solution of SVEM and perform effective VENE with very limited complexities. As shown in multiple Montel Carlo simulation results, nonlinear robustness for O-OFDM/OQAM has been improved significantly thanks to VENE, with various transmission distances and system parameters.