Fundamental equations of nonlinear fiber optics

Wei, Haiqing; Plant, David V.

doi:10.1117/12.506444

Cited by 4 publications

(27 citation statements)

References 17 publications

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“…On one hand, transmission fibers and DCFs may be combined into fiber spans with zero dispersion slope, then OPC is able to equalize the residual dispersion and the slope of dispersion slope among such spans. On the other hand, the flexible designs and various choices in the dispersion parameters of specialty fibers, in particular DCFs, make it possible to construct fiber transmission lines that manifest "scaled symmetries" about the OPC, which are desired properties to effectively suppress fiber nonlinearities [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

“…Based on the nonlinear Schrödinger equation (NLSE), it has been shown that OPC enables one fiber transmission line to propagate inversely (thus to restore) an optical signal that is nonlinearly distorted by the other, when the two fiber lines are mirror-symmetric about the OPC in the scaled sense [11,15,17]. Preliminary experiments have confirmed such effect of nonlinear compensation [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…12 No. 9 / OPTICS EXPRESS 1940 of nonlinearity compensation using scaled translational symmetry requires that the conjugating fiber segments have the same sign for the loss/gain coefficients, opposite second-order dispersions, and the same sign for the third-order dispersions [16,17]. Such conditions are naturally satisfied, at least approximately, in conventional fiber transmission systems, where, for example, a standard single-mode fiber (SMF) may be paired with a DCF as conjugating counterparts.…”

Section: Introductionmentioning

confidence: 99%

“…In Refs. [16,17], we have briefly touched upon the basic idea and feasibility of nonlinearity compensation using scaled translational symmetry. In this paper, we shall present an extensive and systematic study of the theory and practical applications of scaled translational symmetry in fiber transmission systems for nonlinearity compensation.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation

Wei¹,

Plant²

2004

Opt. Express

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Optical phase conjugation is demonstrated to enable simultaneous wide-band compensation of the residual dispersion and the fiber nonlinearities in dispersion-managed fiber transmission lines employing slope-compensating fibers. When the dispersion slope of transmission fibers is equalized by slope-compensating fibers, the residual dispersion and the slope of dispersion slope are compensated by middle-span optical phase conjugation. More importantly, fiber nonlinearity may be largely suppressed by arranging the fibers into conjugate pairs about the phase conjugator, where the two fibers of each pair are in scaled translational symmetry. The translational symmetry is responsible for cancelling optical nonlinearities of the two fibers up to the first-order perturbation, then a mirror-symmetric ordering of the fiber pairs about the conjugator linearizes a long transmission line effectively.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation

Wei¹,

Plant²

2004

Opt. Express

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“…Especially for a single-mode fiber, there is only one guided mode (actually two if counting the different polarizations), optical energy in all other spatial modes are not wellconfined in the fiber and eventually get lost into the environment. With a fixed polarization, it is customary to represent an information-carrying optical pulse by, 6,7 …”

Section: Introductory Quantum Fiber Opticsmentioning

confidence: 99%

Quantum noise in optical communication systems

Wei

Plant

2004

Optical Modeling and Performance Predictions

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It is noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, which, as an extra source of noise, could become comparable to the amplified-spontaneous-emission noise of optical amplifiers. The optical noise in random loss/gain has a quantum origin, as a manifestation of the corpuscular nature of electromagnetic radiation. This paper adopts the Schrödinger representation, and uses a density matrix in the basis of photon number states to describe the optical signals and their interaction with the environment of loss/gain media. When the environmental degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism provides an intuitive interpretation of the quantum-optical noise as the result of a classical Markov process in the space of the photon number states. The formulism would be more convenient for practical engineers, and should be sufficient for fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Even better, the model admits analytical solutions to the photon-number distribution of the optical signals.In modern fiber transmission lines, the optical signals experience alternating loss and gain. The amplified spontaneous emission (ASE) of the in-line amplifiers is usually blamed and considered as the sole source of noise that corrupts the optical signals. However, it should be noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, namely, an extra source of noise, which could become comparable to the commonly blamed ASE noise. It is therefore necessary to understand and include this noise in system design and performance evaluation. Fundamentally, the optical noise in random loss/gain has a quantum origin, incurred as a result of the corpuscular nature of electromagnetic radiation. Such quantum noise is often treated in the Heisenberg representation, and interpreted as the result of a Langevin noise operator, 1 or vacuum field operators, 2, 3 added to the Heisenberg field operator of the signal. This paper adopts the Schrödinger representation, and uses a density matrix in the basis of photon number states to describe the signal field, the medium reservoir, and their interactions. When the medium degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism is sufficient for practical fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Furthermore, our formulism...

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Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations

Zhang

Wei

et al. 2006

J. Opt. Soc. Am. B

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Fundamental equations of nonlinear fiber optics

Cited by 4 publications

References 17 publications

Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation

Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation

Quantum noise in optical communication systems

Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations

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