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Journal ArticleDOI

Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems

01 Jul 2006-Journal of Lightwave Technology (IEEE)-Vol. 24, Iss: 7, pp 2806-2826
TL;DR: In this paper, the Manakov-PMD equation was derived using multiple-length-scale techniques and it was shown that the scalar nonlinear Schro/spl uml/dinger equation is valid when the signal is initially in a single polarization state.
Abstract: Aspects of the interaction of the Kerr nonlinearity and polarization mode dispersion (PMD) are reviewed. The basic equation that governs this interaction on the length scale of interest in optical fiber communications systems is the Manakov-PMD equation. This equation is derived using multiple-length-scale techniques. The focus of the derivation is the elucidation of common misunderstandings and pitfalls rather than mathematical rigor. It is shown that the scalar nonlinear Schro/spl uml/dinger equation is valid when PMD is absent and the signal is initially in a single polarization state. Two examples are then presented that illustrate the complexity of the interaction between nonlinearity and PMD. The first example considers the interaction of a nonlinearly induced chirp with PMD. As the power increases, one can obtain an improved eye opening relative to the case when PMD is absent. The second example considers the effect of nonlinear polarization rotation in a wavelength-division-multiplexed system. When nonlinear polarization rotation is important, the principal states of polarization become time dependent and PMD compensation becomes ineffective. This problem can be mitigated through the use of line codes.

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Citations
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Book
01 Dec 2010
TL;DR: In this article, a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field is presented. But the focus is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion and the dynamical and statistical properties of the dynamics when it is chaotic.
Abstract: This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

996 citations

Journal ArticleDOI
Zhenning Tao1, Liang Dou1, Weizhen Yan1, Lei Li1, Takeshi Hoshida1, Jens C. Rasmussen1 
TL;DR: In this paper, a low-complexity intrachannel nonlinear compensator operating at the symbol rate is proposed based on the nonlinear perturbation predistortion for the dual-polarization quadrature phase-shift keying (DP-QPSK) systems.
Abstract: Intrachannel nonlinearity is considered a major distortion in high-capacity transmission systems particular for the case without inline optical chromatic dispersion compensation. In this paper, a low-complexity intrachannel nonlinear compensator operating at the symbol rate is proposed based on the nonlinear perturbation predistortion for the dual-polarization quadrature phase-shift keying (DP-QPSK) systems. Compared with the widely studied backpropagation algorithm, the proposed algorithm achieves comparable performance with significantly reduced complexity and halved sampling speed in digital signal processing and digital-to-analog converters. The proposed algorithm is demonstrated in a 43 Gb/s DP-QPSK transmission experiment over 1500 km. In addition to the experimental demonstration, numerical simulation verifies that the proposed algorithm is quite robust by tolerating significant uncertainties of link parameters and span-by-span inhomogeneity in the links.

205 citations


Cites methods from "Interaction of polarization mode di..."

  • ...Then, we extend the perturbation analysis to the DP transmission by considering the Manakov equation that describes the optical field evolution through the fiber links where the nonlinear effective length is much longer than the fiber birefringent beating length [22]...

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Journal ArticleDOI
Ling Liu1, Liangchuan Li1, Huang Yuanda1, Kai Cui1, Qianjin Xiong1, Fabian N. Hauske1, Changsong Xie1, Yi Cai1 
TL;DR: In this paper, a new electronic nonlinearity compensation scheme based on inverse Volterra series transfer function (VSTF) is proposed, which shows 1 dB improvement in Q-factor with a 256 Gb/s polarization-division-multiplexed 16-level quadratic amplitude modulation format.
Abstract: The Volterra series transfer function (VSTF), in which the input-output relationship of a nonlinear system is represented by a series of nonlinear kernel functions, is an elegant tool to model nonlinear systems. The inverse of a nonlinear system can be constructed by analyzing VSTF. We propose a new electronic nonlinearity compensation scheme based on inverse VSTF. We show 1 dB improvement in Q-factor with a 256 Gb/s polarization-division-multiplexed 16-level quadratic amplitude modulation format, and 50% reduction in complexity by lowering the processing rate.

149 citations


Cites background or methods from "Interaction of polarization mode di..."

  • ...total power of x and y polarization contributes to the intrachannel nonlinearity, and a modified accounts for the effect of fiber nonlinearity averaging over the fiber birefringence assumes the value of [13], [14]....

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  • ...The simple Manakov equations that describe the evolution of the 2-D vector electromagnetic field envelope in a nonlinear optical fiber with some random birefringence are given by [13], [14]...

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Journal ArticleDOI
TL;DR: A paper on long-haul analog photonics is presented using theory and experimental results, including intensity modulation with direct detection, phase modulation with interferometric demodulation, and suppressed-carried techniques.
Abstract: A paper on long-haul analog photonics is presented using theory and experimental results. Various analog fiber-optic modulation formats are reviewed, including intensity modulation with direct detection, phase modulation with interferometric demodulation, and suppressed-carried techniques. Modulation linearization methods are reviewed. The limitations of and requirements for photodiode detectors are described.

125 citations


Cites background from "Interaction of polarization mode di..."

  • ...mode dispersion [118], [119], polarization chromatic dispersion [120], [121], and cross-polarization modulation [122]....

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Journal ArticleDOI
TL;DR: In this article, a simple but accurate analytical model for the fiber-optic channel affected by cross-phase modulation (XPM) is proposed and validated through numerical simulations, which describes XPM as a time-varying and frequency-selective complex fading, whose impact and statistical properties can be analyzed.
Abstract: A simple but accurate analytical model for the fiber-optic channel affected by cross-phase modulation (XPM) is proposed and validated through numerical simulations. The model describes XPM as a time-varying and frequency-selective complex fading, whose impact and statistical properties can be analytically investigated. As an example, the proposed model is applied to derive an analytic lower bound to the channel capacity and to investigate the coherence properties of the channel.

119 citations


Cites methods from "Interaction of polarization mode di..."

  • ...The extension of the proposed model to polarization division multiplexing systems requires the application of the LP method to the Manakov equation [15], accounting for both polarizations and including in (2) the additional cross-polarization term, that is still linear with respect to the observed signal....

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References
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Book
Govind P. Agrawal1
01 Jan 1989
TL;DR: The field of nonlinear fiber optics has advanced enough that a whole book was devoted to it as discussed by the authors, which has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field.
Abstract: Nonlinear fiber optics concerns with the nonlinear optical phenomena occurring inside optical fibers. Although the field ofnonlinear optics traces its beginning to 1961, when a ruby laser was first used to generate the second-harmonic radiation inside a crystal [1], the use ofoptical fibers as a nonlinear medium became feasible only after 1970 when fiber losses were reduced to below 20 dB/km [2]. Stimulated Raman and Brillouin scatterings in single-mode fibers were studied as early as 1972 [3] and were soon followed by the study of other nonlinear effects such as self- and crossphase modulation and four-wave mixing [4]. By 1989, the field ofnonlinear fiber optics has advanced enough that a whole book was devoted to it [5]. This book or its second edition has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field of nonlinear fiber optics.

15,770 citations

Book
01 Jan 1978
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Abstract: This book gives a self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations. Parts and chapter titles are as follows: fundamentals - ordinary differential equations, difference equations; local analysis - approximate solution of linear differential equations, approximate solution of nonlinear differential equations, approximate solution of difference equations, asymptotic expansion of integrals; perturbation methods - perturbation series, summation series; and global analysis - boundary layer theory, WKB theory, multiple-scale analysis. An appendix of useful formulas is included. 147 figures, 43 tables. (RWR)

4,776 citations


"Interaction of polarization mode di..." refers background in this paper

  • ...Why then should the nonlinear Schrödinger equation, which completely ignores polarization effects, ever hold? The answer to this question lies in a multiple-scale analysis [24], [25]....

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  • ...What is meant by “most” in this context can be made rigorous by applying the concepts of perturbation theory [24], [25]....

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Book
01 Dec 1981
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
Abstract: : Under appropriate conditions, ocean waves may be modeled by certain nonlinear evolution equations that admit soliton solutions and can be solved exactly by the inverse scattering transform (IST). The theory of these special equations is developed in five lectures. As physical models, these equations typically govern the evolution of narrow-band packets of small amplitude waves on a long (post-linear) time scale. This is demonstrated in Lecture I, using the Korteweg-deVries equation as an example. Lectures II and III develop the theory of IST on the infinite interval. The close connection of aspects of this theory to Fourier analysis, to canonical transformations of Hamiltonian systems, and to the theory of analytic functions is established. Typical solutions, including solitons and radiation, are discussed as well. With periodic boundary conditions, the Korteweg-deVries equation exhibits recurrence, as discussed in Lecture IV. The fifth lecture emphasizes the deep connection between evolution equations solvable by IST and Painleve transcendents, with an application to the Lorenz model.

3,415 citations

Book
22 Dec 2012
TL;DR: Eventually, you will enormously discover a supplementary experience and execution by Spending more cash by spending more cash.
Abstract: Eventually, you will enormously discover a supplementary experience and execution by spending more cash. still when? reach you tolerate that you require to get those every needs taking into consideration having significantly cash? Why don't you try to get something basic in the beginning? That's something that will guide you to understand even more a propos the globe, experience, some places, once history, amusement, and a lot more?

1,311 citations

Journal ArticleDOI
TL;DR: In this paper, the results of a series of experiments in which a giant pulsed ruby laser is used to study several different nonlinear optical effects arising from an induced optical polarization third order in the electric field strength are presented.
Abstract: This paper presents the results of a series of experiments in which a giant pulsed ruby laser is used to study several different nonlinear optical effects arising from an induced optical polarization third order in the electric field strength. The various phenomena studied are special cases of either frequency mixing or intensity-dependent changes in the complex refractive index, including Raman laser action at a focus. A wide range of crystalline and isotropic materials was studied. The theory for these effects is extended to cover resonant interactions. The experimental results are interpreted in terms of simplified models, and quantitative values for the nonlinear polarizability coefficients are given. The rather large experimental uncertainties in these coefficients are discussed.

1,154 citations