Introduction

Agrawal, Govind P.

doi:10.1016/b978-0-12-045140-1.50006-8

Cited by 81 publications

(138 citation statements)

References 50 publications

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“…Finally, optical fibers are weakly nonlinear which means that the refractive index of the fiber material changes as a function of the light intensity. The propagation of light pulses, taking all these effects into account, can be described by the coupled nonlinear Schrödinger equation [3], [4] (1) or equivalently (2) which are written in a form that is appropriate for a fiber with a randomly varying birefringence orientation. Here, is a column vector with elements and which are the complex envelopes of the two polarization components.…”

Section: Derivation Of the Manakov-pmd Equationmentioning

confidence: 99%

“…The parameter in (1) and (2) does not have a subscript since we are assuming that . A fundamental difficulty in solving (1) or equivalently (2) is that changes on a length scale of 0.3-100 m, while the length scales for PMD, chromatic dispersion, and the Kerr nonlinearity are hundreds or even thousands of kilometers. If one wishes to solve (1) accurately, taking into account rapid and random variations of the birefringence, one must do so on a very short length which is computationally expensive.…”

Section: Derivation Of the Manakov-pmd Equationmentioning

confidence: 99%

“…The development of communications technology has made it necessary to develop mathematical tools for describing light transmission in nonlinear optical fibers. Hasegawa and Tappert [1] showed that when the slowly varying envelope approximation applies, which is the case in communication signals to date [2], and fiber birefringence can be ignored, then the transmission is well-described by the nonlinear Schrödinger equation. Unfortunately, it is often impossible to ignore the fiber birefringence, particularly in modern-day NRZ (nonreturn-to-zero) communications, in which polarization scrambling is consistently used.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Studies on Signal Propagation in Optical Fibers with Randomly Varying Birefringence

Wai

Marcuse

Menyuk

et al. 1998

Solid-State Science and Technology Library

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Abstract-We report here on our investigations of the Manakov-polarization mode dispersion (PMD) equation which can be used to model both nonreturn-to-zero (NRZ) and soliton signal propagation in optical fibers with randomly varying birefringence. We review the derivation of the Manakov-PMD equation from the coupled nonlinear Schrödinger equation, and we discuss the physical meaning of its terms. We discuss our numerical approach for solving this equation, and we apply this approach to both NRZ and soliton propagation. We show by comparison with the coupled nonlinear Schrödinger equation, integrated with steps that are short enough to follow the detailed polarization evolution, that our approach is orders of magnitude faster with no loss of accuracy. Finally, we compare our approach to the widely used coarse-step method and demonstrate that the coarse-step method is both efficient and valid.

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Section: Derivation Of the Manakov-pmd Equationmentioning

confidence: 99%

Section: Derivation Of the Manakov-pmd Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Studies on Signal Propagation in Optical Fibers with Randomly Varying Birefringence

Wai

Marcuse

Menyuk

et al. 1998

Solid-State Science and Technology Library

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“…The two most commercially successful applications of nonlinear photonics have come from two fiber optic-based applications: optical fiber communications and mode-locked fiber lasers. 1 In both cases, the optical fiber serves as a nearly ideal waveguide whose dispersion and nonlinearity is used as the basis for controlling the light pulses, i.e. the optical bits.…”

Section: Introductionmentioning

confidence: 99%

“…The combination of high-repetition-rate data streams with a large number of WDM channels has pushed transmission rates to nearly 1 TB/s. 1 This has created a demand for all-optical transmission sources that can generate pico-second mode-locked pulses at various wavelengths. [3][4][5][6] Here, we develop a lowdimensional theoretical description of the dynamics of a multiple-wavelength mode-locked laser source.…”

Section: Introductionmentioning

confidence: 99%

Mode-locked laser pulse sources for wavelength division multiplexing

Farnum

Bale

Kutz

2010

Nonlinear Frequency Generation and Conversion: Materials, Devices, and Applications IX

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Recent theoretical investigations have demonstrated that the stability of mode-locked solution of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this paper, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple frequency channels.

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Consideration based on simulation for a DWDM system composed of a wide‐band optical phase conjugator and dispersion‐flattened transmission line

Yao

Hanawa

Takahara

et al. 2003

Electron. Comm. Jpn. Pt. I

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SUMMARYIn wavelength division multiplexing transmission, nonlinear effects such as cross phase modulation between the pulses of channels with different wavelengths due to overtaking causes pulse distortion and timing jitter. In particular, deterioration of the transmission characteristics caused by cross phase modulation becomes more conspicuous when the incident peak power becomes larger. In order to realize a wavelength division multiplexing transmission system with a higher bit rate over a longer distance, a high incident peak power that maintains a high SNR is indispensable and a technique to compensate the effect of cross phase modulation is needed. In this paper, computer simulation demonstrates that, by placing a broadband phase conjugator at the center of the dispersion-flattened transmission line, the cross phase modulations caused in the first half and the latter half are canceled and its effect can be reduced. It is further shown that the transmission system with the present configuration can increase the incident peak power by 5 dB over that using nonlinear transmission, which is considered effective for high densities in the case of wavelength division multiplexing transmission with a frequency use efficiency of 0.32 bit/s/Hz.

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Introduction

Cited by 81 publications

References 50 publications

Studies on Signal Propagation in Optical Fibers with Randomly Varying Birefringence

Studies on Signal Propagation in Optical Fibers with Randomly Varying Birefringence

Mode-locked laser pulse sources for wavelength division multiplexing

Consideration based on simulation for a DWDM system composed of a wide‐band optical phase conjugator and dispersion‐flattened transmission line

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