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The stochastic generalized nonlinear Schrödinger equation (SGNLSE) of third order in the Stratonovich sense is examined here. New elliptic, hyperbolic, trigonometric, and rational stochastic solutions are obtained using a modified mapping method. Because the GNLSE is extensively used in nonlinear optical phenomena, optical fiber communication systems, communication and heat pulse propagation in materials, the obtained solutions may be used to study a broad range of relevant physical phenomena. In order to interpret the effects of multiplicative noise, the dynamic performances of the various obtained solutions are displayed utilizing 3-D and 2-D graphs. We infer that multiplicative noise impacts and stabilizes the behavior of SGNLSE solutions. [ABSTRACT FROM AUTHOR]

This paper leverages the Ginzburg–Landau equation, a fundamental model for elucidating the dynamics of dissipative optical solitons, in conjunction with the Markov Chain Monte Carlo method and the Lilliefors normality test, to precisely identify key parameters such as dispersion coefficient, nonlinear coefficient, and gain coefficient. Our comprehensive analysis yields not only posterior mean estimates and confidence intervals for these parameters but also their corresponding posterior probability density functions. These findings offer valuable statistical insights and theoretical underpinnings for the design and optimization of fiber lasers, with implications for enhancing the performance of fiber-optic communication systems. [ABSTRACT FROM AUTHOR]

This research explored optical soliton solutions for the (2+1)-dimensional generalized fractional Kundu-Mukherjee-Naskar equation (gFKMNE), which is a nonlinear model for explaining pulse transmission in communication structures and optical fibers. Two enhanced variants of (G'/G)- expansion method were employed, namely, extended (G'/G)-expansion method and the generalized (r + G'/G)-expansion method, based on the wave transformation of the model into integer-order nonlinear ordinary differential equations (NODEs). By assuming a series-form solution for the resultant NODEs, these strategic methods further translated them into a system of nonlinear algebraic equations. Solving these equations provided optical soliton solutions for gFKMNE using the Maple-13 tool. Through 3D and contour visuals, it was revealed that the constructed soliton solutions are periodically arranged in the optical medium, forming dark soliton lattices. These dark soliton lattices are significant in several domains, such as optical signal processing, optical communications, and nonlinear optics. [ABSTRACT FROM AUTHOR]

This manuscript elaborate a novel characteristic of stochastic multi breather type, periodic, hybrid periodic and different type of waves solutions for the Shrödinger–Hirota (SH) equation. The mentioned equation is studied by a Wiener process and white noise which is used for the sudden and large-scale fluctuation. By applying the wave transformation technique the considered equation is transformed into ordinary differential equations, gives meaningful analysis. From the solution of the SH equation various type of results, including breather like waves, hybrid periodic waves, and singular solitons. Breather waves are applied in optical fiber communications, oceanography, and plasma physics. Singular waves find use in medical imaging, seismic research, and nonlinear optics. Hybrid singular-periodic waves have applications in photonics, acoustics, and material science, enabling advancements in diverse fields. To visually capture these intricate behaviors, we used Mathematica software to generate 2D and 3D graphs of the analytical stochastic solutions. This combination of mathematical rigor and numerical simulations provides a comprehensive understanding of the phenomena under study, making a valuable contribution to the field of nonlinear wave equations and stochastic processes. [ABSTRACT FROM AUTHOR]

The concern of this study is to investigate the optical solitons pluses. The (2 + 1) -dimensional Kundu–Mukherjee–Naskar (KMN) mathematical model in birefringent fibers is taken under consideration for this sake because this model has great importance in optics and delineate the propagation of soliton dynamics in optical fiber communication system and the rogue waves in the oceans and the bending of the light beam. Two newly developed approaches first extended rational sinh-Gordon method which is formulated from the well-known sinh-Gordon equation and second exp (− ϕ (ϖ)) -expansion function method are manipulated for the construction of optical solitons in distinct formats. Bright, dark, and singular along their combined forms, periodic and plane wave solutions are extracted with the aid of proposed methods. Moreover, the modulation instability of investigated model is also carried out via linear stability theory. To endorse the physical compatibility of the results, the 2D, 3D, contour, and density plots have been delineated using appropriate parametric values. According to our literature research, these two methods that we are working on have not been applied to the KMN equation in birefringent fibers before, and we believe that the new solutions we have obtained will be useful to researchers working in modeling in this field. The evaluated results suggested that the techniques employed in this research to recover inclusive and standard solutions are approachable, efficient, and speedier in computing and can be considered a handy tool in solving more complex phenomena with the assistance of symbolic computation. [ABSTRACT FROM AUTHOR]

This study explores optical soliton solutions within the framework of the Caudrey–Dodd–Gibbon equation (CDGE) and the ( 1 + 1 )-dimensional Boussinesq equation, utilizing the modified Sardar sub-equation method (MSSEM). The derived solutions are meticulously verified using symbolic software Mathematica and encompass a rich array of mathematical functions, including trigonometric, hyperbolic, and exponential functions. Visualization techniques, such as 3D plots, 2D plots, density graphs, and contour graphs, effectively illustrate the diverse behaviors exhibited by these soliton solutions. These equations have been studied previously, their comprehensive traveling wave solutions are relatively unexplored. By employing the modified Sardar sub-equation method, which has demonstrated effectiveness in solving nonlinear evolution equations, this study aims to bridge this gap. The soliton solutions obtained encompass a wide spectrum of behaviors, including bright, dark, periodic, singular, dark-periodic, bright-periodic, dark-singular, compactons, and bright-singular soliton solutions, as well as other complex phenomena. The comprehensive exploration of soliton solutions not only enhances our understanding of fundamental wave phenomena but also provides valuable insights for addressing nonlinear equations across various scientific disciplines, including optical fiber communications, plasma physics, and nonlinear dynamics. [ABSTRACT FROM AUTHOR]

The use of optical fiber for communication has grown at a rapid pace due to the demands of the modern information era. In this paper, the modified extended direct algebraic method is implemented to explore optical solitons and other exact wave solutions for the coupled system of perturbed highly dispersive complex Ginzburg–Landau equation with polynomial nonlinearity law which describe the transmission of solitons in birefringent fibers. The obtained solutions include bright solitons, dark solitons, singular solitons and combo dark-singular solitons. Additionally, Jacobi elliptic function solutions, exponential solutions, and singular periodic solutions are also offered. To ensure the existence of the obtained soliton solutions, we set some constraints on the parameters. In addition, some selected solutions are visually shown to demonstrate the physical properties of the exact solutions. [ABSTRACT FROM AUTHOR]

In this work, we realised the soliton solutions of nonlinear Schrödinger equation (NLSE) that arise from optical fibers, we considered the modified Sardar sub-equation method (MSSEM) to find solitary solutions analytically. The stability of the retrieved soliton solutions realised from the NLSE are investigated. We demonstrate the soliton solutions that are stable and can last for a very long time without losing its form or energy under specific circumstances and those soliton solutions that are unstable. The MSSEM is a frequently employed technique in research for addressing specific mathematical modeling or physical phenomena problems. Its selection in this specific study might stem from its proven efficacy in handling the particular problem under investigation. The decision to utilize MSSEM could be driven by several considerations, including its precision, computationally efficient, effectiveness, greater accuracy and capability to manage intricate systems. Finally, our method offers greater flexibility in modeling various physical phenomena, which makes it particularly useful in applications in diverse fields such as quantum mechanics and nonlinear optics. The findings have ramifications for the architecture of optical fiber communications and offer significant new insights into the behavior of solitons in optical systems. The NLSE has proven to be an effective tool for understanding wave behavior in fiber optics. Its applications have helped engineers and scientists optimize the design of optical fibers and predict the behavior of various conditions. Moreover, our study provides insights into the fundamental properties of solitary solutions in the NLSEs and their practical implications in physical systems. [ABSTRACT FROM AUTHOR]

In this paper, we take into account the coupled stochastic Korteweg–De Vries (CSKdV) equations in the Itô sense. Using the mapping method, new trigonometric, rational, hyperbolic, and elliptic stochastic solutions are obtained. These obtained solutions can be applied to the analysis of a wide variety of crucial physical phenomena because the coupled KdV equations have important applications in various fields of physics and engineering. Also, it is used in the design of optical fiber communication systems, which transmit information using soliton-like waves. The dynamic performance of the various obtained solutions are depicted using 3D and 2D curves in order to interpret the effects of multiplicative noise. We conclude that multiplicative noise influences the behavior of the solutions of CSKdV equations and stabilizes them. [ABSTRACT FROM AUTHOR]

In this research, a dynamical (3 + 1)-dimensional nonlinear Schrödinger model (NLSM) is under consideration which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This aforementioned model has been widely applied in Bose–Einstein condensates, nonlinear optical fiber communication plasma physics, hydrodynamics, elastic media and other diversified areas of mathematical physics and engineering. This study has two main objectives. Firstly, to obtain some novel solutions in the shape of singular, dark, periodic and plane wave solutions that are innovative and not previously found in the literature. Secondly, an amended extended tanh-function method with modulation instability (MI) is used for this model. As far as we know, this has never been investigated in this manner. The 2-D, 3-D and contour plots have been defined using the required parametric values to support the results of physical compatibility. According to the examined results, the method used in this study to retrieve consisting and conventional solutions is efficient and more immediate in computing and can be thought of as a useful tool in resolving more difficult problems that arise in the field of engineering, physics, mathematics and fiber optics. [ABSTRACT FROM AUTHOR]

The object of the research is deleting the interaction of the higher order soliton interaction by introducing the third and fourth order dispersions inside an optical fiber. The results are obtained by the simulation of the nonlinear Schrödinger equation, which models the propagation of solitons in the optical fiber using the method of Fast Fourier Transform. The interaction of two higher order solitons due to the attraction of their electric field can lead to losing the solitons’ properties. Hence, this can prevent the use of solitons in high-bit-rate optical fiber communication systems because it increases the bit error rate, significantly limiting the potential of the communication system. To resolve this problem, we should diminish the bit rate error by avoiding the interaction of the co-propagative solitons when they are too close. It is well known that, during higher order soliton propagation in the presence of the third order dispersion, the irregular shape of the higher order soliton disappears, and a splitting towards its fundamental constituents occurs after a considerable propagation. As for the fourth order, dispersion gives rise to two dispersive wave sidebands on the red or blue side. Our results reveal that bringing two higher order solitons together in the presence of the fourth order dispersion, a series of interactions between the components generated after their fission is obtained. In the third-order distribution, besides the fourth-order diffusion, the rare form and the supercontinuum generated by the fission of the higher-order solitons disappear, and we get two fundamental solitons propagating in parallel with a temporal shift and some inconsiderable dispersive waves. The most important aspect is that both higher-order dispersions are able to suppress the interactions of higher-order solitons thanks to the time shift induced by the third-order distribution and the intermittent compression caused by the fourth-order scattering. These results can be obtained in practice inside the dispersion-engineered photonic crystal waveguide (PhC-wg), which allows for manipulating the high order dispersion. [ABSTRACT FROM AUTHOR]

We demonstrate a silicon photonic transmitter for soliton-based communications enabling the interleaving of QPSK and APSK modulated soliton pulses overlapping in both the time and frequency domains. The nonlinear Fourier transform is used to both determine adequate soliton launch conditions and facilitate nonlinear equalization at the receiver. A spectral efficiency of 0.5 b/s/Hz per polarization is reached over a 5400 km transmission distance and constitutes, to the best of our knowledge, a record for soliton transmission over such long distances. Linear and nonlinear minimum mean square error and artificial neural network-based equalizers are also experimentally benchmarked, with artificial neural networks resulting in particularly effective equalization in this system. [ABSTRACT FROM AUTHOR]

This article negotiates the investigation of optical pulses with the Biswas-Arshed equation in birefringent fibers that involves a two-component form for vector solitons in an optical fiber communication system. Various optical pulses are recovered in single and combo shapes like bright, dark, singular, bright-dark, and dark-singular solitons by the uses of the extended Fan-sub equation method (EFSEM). In addition, the hyperbolic, singular periodic waves, Jacobi's elliptic function solutions are also derived. This method is beneficial for solving the nonlinear partial differential equations (NLPDEs), because this method is not only useful for finding the new solitary wave solutions, but also gives us the solutions obtained previously by the usage of other techniques (Riccati equation, or first kind elliptic equation, or the generalized Riccati equation as mapping equation, or auxiliary ordinary differential equation method) in a combined approach. The constraints conditions to ensure the existence criteria of reported optical soliton solutions are also listed. The stability analysis of the studied model is also examined by utilizing linear stability theory. In addition, by selecting different parametric values, the physical representation of some achieved solutions is plotted in 3D and contour graphs with the help of Mathematica. The reported results show that the proposed method is effective, concise, straightforward, powerful, and it can be used to tackle some more complex nonlinear systems. [ABSTRACT FROM AUTHOR]

This paper studies Radhakrishnan-Kundu-Laksmannan equation which is used to describe the pulse propagation in optical fiber communications. By using improved modified extended tanh-function method various types of solutions are extracted such as bright solitons, singular solitons, singular periodic wave solutions, Jacobi elliptic solutions, periodic wave solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some of the obtained solutions are represented graphically. [ABSTRACT FROM AUTHOR]

Eigenvalue-based communication technologies using inverse scattering transform (IST) have gained attention as a new transmission strategy in optical fiber communications. In recent years, several studies on artificial neural network (ANN)-based equalization and demodulation schemes for eigenvalue-modulated signal have been conducted to enhance the receiver sensitivity. However, in the case of a presence of a carrier frequency offset (CFO) at receiver, the effects of the CFO on ANN receiver of eigenvalue-modulated signal is yet to be reported. In this study, we numerically and experimentally investigated the generalization performances of eigenvalue domain ANN-based demodulator on CFO. Furthermore, we propose to combine an ANN-based demodulator with a CFO compensation method based on IST and a relation between frequency and eigenvalue shifts. The proposed method, based on an appropriate soliton pulse, achieves a high CFO estimation accuracy of submegahertz order even if the CFO reaches $\pm$ 2.5 GHz under the noiseless condition. In the presence of noise and a large CFO of 2.5 GHz, the method attains a CFO estimation accuracy below 60 MHz for OSNR = 10 dB with a low pilot pulse rate, such as 0.064%. We show the simulation results obtained after applying the proposed CFO compensation to the ANN demodulator, which is valid for 2.5 GHz CFO and long-haul transmission over 5000 km. Experiments performed in this study demonstrate successful demodulation of an eigenvalue-modulated signal with OSNR penalty $< $ 1 dB in the presence of CFO within 1 GHz at 2.5 Gb/s. [ABSTRACT FROM AUTHOR]

This paper builds exact optical solitons to the coupled of nonlinear equations which describes the pulse propagation in birefringent optical fibers with the effects of ellipticity angle and coupling coefficient. By adopting the new Sardar sub-ODE method, diverse optical solitons as W-shaped bright, dark optical solitons, trigonometric function and singular function solutions have been secured. To show out the warranty of the stability of the acquired results, we examine the effects of the ellipticity angle and coupling coefficient on modulation instability. It is noted beside of the linear and circular birefringence, for θ = 45 o , it is exhibited unstable zone where MI growth rate. To enroll the effects of the coupling coefficient on MI growth rate, we fixed a value of the ellipticity angle θ = 45 o . In Figs. 6 and 10, we acquired some new behavior of the MI gain compared to Houwe et al. (2021). These results show out stable/unstable zones compared to Ablowitz and Horikis (2017), Houwe et al. (2021). Moreover, these results will be helpful in nonlinear optical fibers to explain the communication over long distance and optical fibers design. [ABSTRACT FROM AUTHOR]

Optical eigenvalue communication is a promising technique for overcoming the Kerr nonlinear limit in optical communication systems. The optical eigenvalue associated with the nonlinear Schrödinger equation remains invariant during fiber-based nonlinear dispersive transmission. However, practical applications involving use of such systems are limited by the occurrence of fiber loss and amplified noise that induce eigenvalue distortion. Thus, several time-domain neural-network-based approaches have been proposed and demonstrated to enhance receiver sensitivity toward eigenvalue-modulated signals. However, despite the substantial improvement in power margin realized using time-domain neural-network-based demodulators compared to their conventional counterparts, these devices require rigorous training for each transmission distance owing to changes in time-domain pulses during transmission. This paper presents a method for demodulation of eigenvalue-modulated signals using an eigenvalue-domain neural network and demonstrates its utility through simulation and experimental results. Simulation results obtained in this study reveal that the proposed demodulator demonstrates superior generalization performance compared to its time-domain counterpart with regard to the transmission distance. Moreover, experimental results demonstrate successful demodulation over distances from zero to 3000 km without training for each distance. [ABSTRACT FROM AUTHOR]

Spectral efficiency (SE) is one of the key metrics for optical communication networks. An important building block for its maximization are optical superchannels, channels that are composed of several subchannels with an aggregate bandwidth larger than the bandwidth of the detector electronics. Superchannels which are routed through the network as a single entity, together with flex-grid routing, allow to more efficiently utilize available bandwidth and eliminate the guard-bands between channels, thus increasing spectral efficiency. In contrast to traditional wavelength division multiplexing (WDM) channels, subchannel spacing and thus superchannel SE is governed by the linewidth and stability of the frequency spacing of the transmitter lasers. Integrated optical frequency combs, particulary the parametrically generated so-called microcombs, which provide optical lines on a fixed frequency grid are a promising solution for low power superchannel laser sources that allow to minimize the SE loss from suboptimal channel spacing. However, it is extremely challenging to realize microcombs with sufficient line power, coherence and line spacing that is compatible with electronic bandwidths. Because the line-spacing generated by most devices is above 40 GHz, demonstrations often rely on additional electro-optic frequency shifter or divider stages to avoid digital-to-analog-converter (DAC) performance degradation when operating at high symbol rates. Here we demonstrate a 52-line superchannel from a single 22 GHz line spacing soliton microcomb. We demonstrate 12 Tb/s throughput with > 10 bits/s/Hz SE efficiency after 80 km transmission and 8 Tb/s throughput (SE > 6 bits/s/Hz) after 2100 km, proving the feasibility and benefits of generating high signal quality, broadband waveforms directly from the output of a micro-scale device with a symbol rate close to the comb repetition rate. [ABSTRACT FROM AUTHOR]

The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear Fourier transform (PNFT) has been much less investigated compared to its counterpart based on vanishing boundary conditions. In this article, we design a first experiment based on the PNFT in which information is encoded in the invariant nonlinear main spectrum. To this end, we propose a method to construct a set of periodic waveforms each having the same fixed period, by employing the exact inverse PNFT algorithm developed in Part I. We demonstrate feasibility of the transmission scheme in experiment in good agreement with simulations and obtain a bit-error ratio of 10−3 over a distance of 2000 km. It is shown that the transmission reach is significantly longer than expected from a naive estimate based on group velocity dispersion and cyclic prefix length, which is explained through a dominating solitonic component in the transmitted waveform. Our constellation design can be generalized to an arbitrary number of nonlinear degrees of freedom. [ABSTRACT FROM AUTHOR]

In the fiber communication domain, people are facing the challenges due to the rapidly growing requirement on the capacity from new functions and services. Multi-hump solitons are therefore noticed and studied on the feasibility of improving the capacity of the optical fiber communication. In this paper, we study the vector bright solitons and their interaction properties of the coupled Fokas–Lenells system, which models the femtosecond optical pulses in a birefringent optical fiber. We derive the so-called degenerate and nondegenerate vector solitons associated with the one and two eigenvalues, respectively, and the latter admits the symmetric profile. Asymptotically and graphically, interaction patterns of such solitons are classified as follows: Interactions between the degenerate solitons can be elastic or inelastic, reflecting the intensity redistribution between the two components; Interactions between the degenerate and nondegenerate solitons are inelastic, which make the nondegenerate solitons maintaining or losing the profiles in the different situations; Interactions between the nondegenerate solitons do not cause the intensity redistribution, while their shapes change slightly or remain unchanged. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic links to analyze fundamental properties of such nonlinear communication channels. Transmission of a signal in nonlinear channels is conceptually different from linear communications. We use here the NLSE channel model to explain and illustrate some new unusual features introduced by nonlinearity. In general, NLSE describes the co-existence of dispersive (continuous) waves and localized (here in time) waves: soliton pulses. The nonlinear Fourier transform method allows one to compute for any given temporal signal the so-called nonlinear spectrum that defines both continuous spectrum (analog to conventional Fourier spectral presentation) and solitonic components. Nonlinear spectrum remains invariant during signal evolution in the NLSE channel. We examine conventional orthogonal frequency-division multiplexing (OFDM) and wavelength-division multiplexing (WDM) return-to-zero signals and demonstrate that both signals at certain power levels have soliton component. We would like to stress that this effect is completely different from the soliton communications studied in the past. Applying Zakharov–Shabat spectral problem to a single WDM or OFDM symbol with multiple sub-carriers, we quantify the effect of statistical occurrence of discrete eigenvalues in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission, an OFDM symbol with high probability has a soliton component. [ABSTRACT FROM AUTHOR]

Optical frequency combs have established their presence in many fields among which is microwave photonics. Here, we briefly introduce optical frequency comb generators, focusing on high repetition rate combs. Examples of comb-based signal processing are highlighted, including Brillouin mitigation, beamforming, RF-filtering, sub-sampling and RF-channelizers. [ABSTRACT FROM AUTHOR]

Kerr media are applied in the photonic lattices and optical fibers, while optical fiber communication becomes one of the main pillars of modern communication. In this letter, we study a (3 + 1)-dimensional nonlinear Schrödinger equation with distributed coefficients for the spatiotemporal optical solitons or light bullets in a diffractive nonlinear Kerr medium with anomalous dispersion. The N-dark soliton solutions in terms of the Gramian is obtained via the Kadomtsev–Petviashvili hierarchy reduction, where N is a positive integer. Via the graphic analysis, we observe the interaction of the two dark solitons. Effects from the diffraction/dispersion coefficient β (z) and gain coefficient γ (z) are also discussed on the amplitudes and oscillations of the two dark solitons, as well as on the interaction of the two dark parabolic shape solitons. [ABSTRACT FROM AUTHOR]

The soliton, the eigen-solution of nonlinear Schrodinger equation (NLSE), has been investigated in many branches of physics. The first prediction of a soliton in optical fiber could be dated back to 1973. Since then, numerous theoretical and experimental works on solitons have been carried out, including soliton communication and soliton generation in fiber lasers. However, due to the constraints of hardware and digital signal processing methods, research on solitons have been stalled for decades. Recently, the nonlinear Fourier transform (NFT) has attracted significant attention in the field of optical fiber communications and soliton-based signal processing, which provides a powerful mathematical framework for analyzing and understanding the behavior of solitons in optical fibers, enabling the development of novel signal processing techniques. The NFT technique has brought the soliton back to life. It has been widely recognized that in nonlinear frequency domain, the nonlinear crosstalk resulting from the Kerr effect is practically negligible, and fiber nonlinearity damage caused by the Kerr effect can be accounted for as a linear transform factor. Moreover, NFT has been demonstrated for the analysis of laser radiation, highlighting its potential in characterizing ultrafast pulses in the nonlinear frequency domain. In this submission, we review the advancements of NFT concerning both in soliton communication and characterization, focusing on practical implementation aspects. With many practical implementation aspects still being open, our mini review is aimed to assist researchers in evaluating the potential, identifying challenges, and envisioning future directions in NFT-based signal processing technologies. And wake up the sleeping beauty – the soliton! [ABSTRACT FROM AUTHOR]

Abstract We investigate the Kaup-Newell equation that represents one of the forms of derivative nonlinear Schrödinger equation. The model applies to the description of sub-pico-second pulse propagation through an optical fiber. A special complex envelope traveling-wave method is applied to find a nonlinear equation with a fifth-degree nonlinear term describing the dynamics of field amplitude in the nonlinear media. It is shown that the phase associated to the obtained pulses has a nontrivial form and possesses two intensity dependent chirping terms in addition to the simplest linear contribution. A class of soliton solutions of the bright, dark and singular type are derived for the first time. The requirements concerning the optical material parameters for the existence of these chirped structures are also discussed. [ABSTRACT FROM AUTHOR]

We report on the experimental investigations of various self-organized structures of soliton molecules in a thulium-doped fiber laser mode-locked by a monolayer MoS2 saturable absorber. With the alteration of cavity parameters, soliton pairs, soliton triplets, and soliton quartets were successively generated, and the short-term and long-term stabilities were tested, exhibiting potential coding alphabet extension from the traditional binary coding scheme to higher coding scheme in fiber communication. Soliton pairs with the phase-difference of $\pi $ , $\pm \pi /2$ , and 0 have been observed systematically in the same thulium-doped fiber cavity, for the first time. Our results might benefit the fundamental physics research of nonlinear dynamics in fiber lasers at the mid-infrared region. [ABSTRACT FROM AUTHOR]

A self-started stable tunable mode-locked soliton fiber laser in a linear cavity structure composed by commercial passive elements is presented in this paper. It is based on the combination of an erbium-doped fiber as the active medium, and a saturated fiber Bragg grating (FBG) as a partial mirror of the cavity. The other side of the cavity consists of a semiconductor saturable absorber mirror acting also as the mode-locking device. The central wavelength of the FBG is selected by the application of axial strain giving rise to a tunable soliton over 8.6 nm on the C band with a variable spacing of 0.01 nm. The laser delivers 18.9 ps long pulses with a 0.14 nm bandwidth, an 8.2 MHz repetition rate, a pulse energy of 89 pJ, and a peak power of 4.71 W. [ABSTRACT FROM PUBLISHER]

This paper investigates the capacity of signaling on the continuous spectrum (CS) of optical fibers as defined by the nonlinear Fourier transform (NFT). The channel model of such NFT-based optical fiber communication systems is studied based on the behavior of the propagated optical signal in the time domain for an asymptotically long fiber length. The derived channel model is validated using simulation for different scenarios of practical interest. An important characteristic of the channel in the nonlinear spectral domain is the strong dependence of noise to signal. A variance normalizing transform is applied as a tool to obtain an estimate on the capacity of the underlying channel. The results predict a remarkable capacity for signaling on CS, which can be utilized as an extra degree of freedom along with discrete spectrum (i.e., soliton transmission). It is further observed that the channel capacity of signaling on CS saturates at high signal power despite the linearizing capability of the NFT. [ABSTRACT FROM PUBLISHER]

Optical communication system is a kind of communication system using the light wave as the carrier. It has been widely used in recent years with the advantages of the long distance. Optical solitons have some merits for high stability, amenable to generate and low cost, it is an ideal carrier of optical communication system. In this paper, the regulation of pulse characteristics of the optical soliton is studied theoretically. The influence of high-order dispersion and high-order nonlinear effects on the amplitude, shape and other transmission characteristics of the optical soliton is studied by using the bilinear method with the high-order variable coefficient nonlinear Schrödinger (NLS) equation in the nonuniform fibers, and the regulation problems such as the maintenance and excitation of the optical soliton are analyzed. The waveform and amplitude control of the optical soliton and the change of optical soliton characteristics with the dispersion management are studied profoundly, and the nonlinear dynamic processes in their respective intracavity are analyzed. A feasible scheme for avoiding and utilizing the optical soliton is proposed, which has the significance for the investigation of the parameter regulation and dynamic control of the optical soliton in practical inhomogeneous optical fiber communication systems. [ABSTRACT FROM AUTHOR]

The coordinated multipoint transmission/reception aided collocated antenna system (CoMP-CAS) and the mobile relay assisted fractional frequency reuse distributed antenna system (MR-FFR-DAS) constitute a pair of virtual-MIMO-based technical options for achieving high spectral efficiency in interference-limited cellular networks. In practice, both techniques have their respective pros and cons, which are studied in this paper by evaluating the achievable cell-edge performance on the uplink of multicell systems. We show that, assuming the same antenna configuration in both networks, the maximum available cooperative spatial diversity (or the multiplexing gain) inherent in the MR-FFR-DAS is lower than that in the CoMP-CAS. However, when the cell-edge mobile stations (MSs) have a low transmission power, the lower complexity MR-FFR-DAS relying on the simple single-cell processing may outperform the CoMP-CAS by using the proposed soft-combining-based probabilistic data association (SC-PDA) receiver, despite the fact that the latter scheme is more complex and incurs a higher cooperation overhead. Furthermore, the benefits of the SC-PDA receiver may be enhanced by properly selecting the MRs' positions. Additionally, we show that the performance of the cell-edge MSs roaming near the angular direction halfway between two adjacent remote antennas (i.e., the “worst-case direction”) of the MR-FFR-DAS may be more significantly improved than that of the cell-edge MSs of other directions by using multiuser power control, which also improves the fairness among cell-edge MSs. Our simulation results show that, given a moderate MS transmit power, the proposed MR-FFR-DAS architecture employing the SC-PDA receiver is capable of achieving significantly better bit error rate (BER) and effective throughput across the entire cell-edge area, including even the worst-case direction and the cell-edge boundary, than the CoMP-CAS architecture. [ABSTRACT FROM AUTHOR]

Optical soliton is a nonlinear wave with huge information or data which travels over larger distance in optical fibers. This paramount application of optical soliton forced many mathematicians and physicians to focus on it which initiates to study the soliton solutions of mathematical model in optical fiber communication characterized by nonlinear Schrodinger equation (NLSE) along with its important applications. Nonlinear Schrodinger equation represents propagation of light pulse through an optical fiber. In this paper NLSE is solved numerically by using exponential cubic B-spline differential quadrature method. In this method leave-one out cross validation strategy is being used to find optimal value of parameter p which enhances accuracy and efficiency of its results which are near to exact solutions and approximate to available numerical solutions in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we use the unified method to research the variable coefficients Sasa-Satsuma model equation, which describes the nonlinear phenomenon of pulse propagation in optical fiber communication. Optical soliton, elliptic function, rogue waves, bright and dark soliton solutions of Sasa-Satsuma equation have been obtained to study nonlinear phenomena in related fields. With the aid of symbolic calculation, the exact solutions that complex soliton solutions, complex elliptic solutions and complex rational function solutions of the equation are needed to deal with more related phenomena. Later on, two-dimensional and three-dimensional graphics plots of the resulting solutions are made using Maple, and we discuss the symmetric soliton wave, periodic wave and kinky symmetric periodic wave formed by distinct solutions. [ABSTRACT FROM AUTHOR]

Abstract: Using a variational method, we analyze the residual frequency shifts due to cross-channel interactions in wavelength division multiplexed dispersion managed soliton transmission systems. We put forward a simple criterion for the optimal location of the amplifier based on the results of this analysis. This conclusion is explained in terms of the dependence of the propagation properties of a single pulse on the position of the amplifier and the optimality of the criterion is assessed, for some specific parameter values, using a commercial simulation software. [Copyright &y& Elsevier]

Abstract: We study the interplay between bit pattern randomness, cross phase modulation (XPM) and delayed Raman response in massive on–off-keyed (OOK) multichannel optical fiber transmission lines. We find that the interplay between Raman-induced crosstalk and XPM-induced position shift is the dominant mechanism for error generation at intermediate propagation distances, while at longer distances, the interplay between Raman-induced cross frequency shift and Raman crosstalk is dominant. For systems with a jump in the number of channels at a distance z = z 1, we observe a rapid change in the frequency profile of the bit-error-rate (BER) for z >z1. As a result of this change, the BER for z > z 1 is highest for the outermost frequency channels. We attribute the change in the frequency profile of the BER to Raman crosstalk effects, whose strength increases as the square of the number of channels and channel index. Our results quantitatively illustrate that analysis of pulse dynamics in a few central channels is unlikely to provide an accurate evaluation of system performance in massive OOK multichannel transmission. [Copyright &y& Elsevier]

Optical fibers are used in the optical sensing and optical fiber communication. In this paper, we investigate a variable-coefficient coupled Hirota system which describes the vector optical pulses in an inhomogeneous optical fiber. With respect to the slowly varying normalized envelopes of the electric fields, we construct the one-fold solutions which describe the two breather-like solitons and one breather, and two-fold solutions which describe the four breather-like solitons and two breathers. We obtain the one- and two-fold breather-to-soliton conversion conditions which are both related to α (t) and β (t) , the coefficients of the group velocity dispersion and third-order dispersion. Based on the one-fold breather-to-soliton conversion condition, we present several types of the nonlinear waves and the corresponding relations on α (t) and β (t). Interaction between the Akhmediev breather/Kuznetsov–Ma breather and breather-like soliton is shown. Maximum amplitudes of the Akhmediev breather/Kuznetsov–Ma breather and breather-like soliton are related to δ (t) , where δ (t) denotes the coefficient of the nonlinear terms corresponding to the self-phase modulation and cross-phase modulation. When α (t) and β (t) meet the one-fold breather-to-soliton conversion condition, interaction between the periodic wave/anti-dark/multi-peak/ M -shaped soliton and breather-like soliton is presented. Interaction between the two-Kuznetsov–Ma breather and two-breather-like soliton is shown. Maximum amplitudes of the two-Kuznetsov–Ma breather and two-breather-like soliton are related to δ (t). When α (t) and β (t) meet the two-fold breather-to-soliton conversion conditions, interaction between the two-anti-dark and two-breather-like soliton is shown. [ABSTRACT FROM AUTHOR]

This paper looks back at the beginnings of nonlinear optics in fibers and some of the subsequent work that forms the basic underpinnings of the modern field. There is a brief look at some of the major applications and current trends. [ABSTRACT FROM PUBLISHER]

Abstract: Taking into account many developments in fiber optics communications, we propose a higher nonlinear Schrödinger equation (HNLS) with variable coefficients, more general than that in [R. Essiambre, G.P. Agrawal, Opt. Commun. 131 (1996) 274], which governs the propagation of ultrashort pulses in a fiber optics with generic variable dispersion. The study of this equation is performed using the Painlevé test and the zero-curvature method. Also, we prove the equivalence between this equation and its anomalous integrable counterpart (the so-called Sasa–Satsuma equation). Finally, in view of its physical relevance, we present a soliton solution which represents the propagation of ultrashort pulses in a dispersion decreasing fiber. [Copyright &y& Elsevier]

It was shown that one can improve transmission performance in ultra-long-haul wavelength-division-multiplexed (WDM) systems by matching the input pulsewidth to the path-averaged dispersion (PAD) in the line. Wider pulses should be used for higher values of PAD, and vice versa. It was also noted that this pulsewidth selection is only effective in the dispersion-managed soliton (DMS) propagation regime but not in the chirped return-to-zero (CRZ) regime. [ABSTRACT FROM PUBLISHER]

In fiber links with a bit rate greater than 100 Gb/s per wavelength channel, the third-order dispersion (TOD), known as the dispersion slope, becomes a major factor that limits transmission capabilities. This paper presents a numerical study on the propagation of picosecond pulses in anomalous dispersion fibers, the dispersion slope of which is periodically compensated for by lumped compensators. In particular, pulse propagation is discussed in comparison with path-averaged solitons in a dispersion-flattened fiber. Simulations of single-pulse transmission reveal that pulses in the slope-compensated link can be easily dispersed. The dispersive component can be effectively eliminated by introducing inline bandpass filters, the bandwidth of which is smaller than that suitable for solitons in a dispersion-flattened fiber. The transmission of a pulse pair is also considered and is predicted to be stabilized for transmission power larger than that which is optimum for solitons in a dispersion-flattened fiber. These predictions are confirmed by demonstrating system analyses using a pseudorandom bit stream, showing that the penalty of the slope compensation is due to an increase in timing jitter. [ABSTRACT FROM PUBLISHER]

Performance of fiber-based optical signal regenerators consisting of a synchronous amplitude modulator, a highly nonlinear fiber, and an optical bandpass filter is analyzed. The regenerators are operated in two different schemes: one utilizes solitonlike pulse compression in anomalous-dispersion fiber and subsequent filtering, and the other utilizes spectrum broadening in normal-dispersion fiber and subsequent spectrum slicing. Regeneration performance is compared for the two schemes in terms of the shape of energy transfer function and abilities of noise and timing-jitter reduction. Although both types of regenerators show good regenerator performance, the one based on spectrum broadening and slicing has better ability to stabilize signal amplitude while requiring larger signal power launched into the nonlinear fiber. The effectiveness of the regenerators in single-channel quasi-linear highly dispersed pulse transmission and dispersion-managed soliton transmission is also numerically examined. [ABSTRACT FROM PUBLISHER]

We show that, in addition to a stable single soliton, a dispersion-managed (DM) system can also support stable bisolitons. The system parameters in which the bisolitons can exist are also studied. In addition, we propose novel error preventable line-coding schemes in which binary data are assigned to bisolitons and single DM solitons. By using the schemes, impairments arising from intrachannel interactions can be drastically reduced compared with the conventional scheme for the same bit rate. The compatibility of bisoliton to wavelength-division-multiplexed system is also discussed [ABSTRACT FROM PUBLISHER]

The moment method is used to calculate the Raman-induced timing jitter generated by amplifier-induced fluctuations in the energy, frequency, and position of optical pulses propagating inside dispersion-managed fiber links. Using a Gaussian form for chirped optical pulses in combination with the variational analysis, we obtain an analytic expression for the timing jitter whose predictions agree well with the numerical results obtained by solving the nonlinear Schrodinger equation directly. The effects of third-order dispersion are also included in the analysis. We also apply the moment method to standard solitons propagating inside dispersion-decreasing fiber as well as to chirped return-to-zero (CRZ) lightwave systems. We apply our results to a specific 160-Gb/s system and find that the Raman jitter resulting from intrapulse Raman scattering limits the transmission distance in all three cases [ABSTRACT FROM PUBLISHER]

The optical fiber communication system is one of the components of a supporting system in the modern Internet fields. Under investigation in this paper is a coupled fourth-order nonlinear Schrödinger system, which describes the ultrashort optical pluses in a birefringent optical fiber. By virtue of the existing Lax pair, generalized Darboux transformation, two- and three-soliton solutions are derived, with respect to the polarization components of the electric field. Based on such solutions, we graphically display (1) the elastic interactions between/among the two/three solitons on a zero-intensity background, where amplitudes of the solitons remain unchanged; (2) the inelastic interactions between/among the two/three solitons, where amplitudes of the solitons change; (3) the bound state among the three solitons; (4) the higher-order linear and nonlinear effects, represented by β , on the polarization components of the electric field: The interval between two peaks becomes smaller and the numbers of the peaks increase when the value of β increases; The three solitons move along the positive time direction when the value of β decreases; The distances between the adjacent peaks become smaller when the value of β increases. [ABSTRACT FROM AUTHOR]