Pulse Confinement in Optical Fibers with Random Dispersion

Abstract

Short-range correlated uniform noise in the dispersion coefficient, inherent in many types of optical fibers, broadens and eventually destroys all initially ultra-short pulses. However, under the constraint that the integral of the random component of the dispersion coefficient is set to zero (pinned), periodically or quasiperiodically along the fiber, the dynamics of the pulse propagation changes dramatically. For the case that randomness is present in addition to constant positive dispersion, the pinning restriction significantly reduces average pulse broadening. If the randomness is present in addition to piece-wise constant periodic dispersion with positive residual value, the pinning may even provide probability distributions of pulse parameters that are numerically indistinguishable from the statistically steady case. The pinning method can be used to both manufacture better fibers and upgrade existing fiber links. The effect of random perturbations in optical fibers increasingly attracts attention as the demand for the quality of transmission grows daily (1, 2). The impact of randomness on signal transmission in a single-mode fiber is negative; it causes degradation of the signal and lowers transmission capabilities. In particular, amplifier noise (3-6) and random fiber birefringence (7-11) lead to random shifts in the pulse position (timing jitter) and to pulse broadening, respectively. Both effects eventually cause a destruction of bit patterns and lead to an increase of the bit-error-rate (BER), the most important parameter describing performance in fiber communications systems (12).In the present paper, we consider the effect of random dispersion, which is, for ultrashort pulses, one of the major causes of bit-pattern destruction. However, we propose a way to significantly reduce the pulse deterioration and eventually reduce the BER caused by the noise in dispersion by using passive (independent of pulse properties) periodic control of the accumulated dispersion of the fiber link. The method may even provide statistically steady propagation of the pulse along the fiber and gives insight into general understanding of control mechanisms for nonlinear systems with randomness.Chromatic dispersion is an important characteristic of a medium and can significantly degrade the integrity of wave packets. In practice, chromatic dispersion is not uniformly distributed and often exhibits random variations in space and time. On the other hand, wave propagation through the medium is usually much faster than temporal variations of the chromatic dispersion. Therefore, these random variations can be treated as ''spatial'' multiplicative noise that does not change in time. This multiplicative noise is conservative, and the wave energy remains constant during propagation through the medium. Recently, high-precision measurements of fiber chromatic dispersion as a function of a fiber length experimentally demonstrated the significance of the dispersion randomness (13,14).The overall chromatic dispersion in an optical fiber...

Dissipative soliton fiber lasers with higher-order nonlinearity, multiphoton absorption and emission, and random dispersion

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“…25. The major difference is due to the matrix character of the process: What was an exponential of an integral over a random process now turns into a z-ordered exponential Ŵ .…”

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“…The effect of a random variation of GVD on MI has been studied extensively [25][26][27][28][29] for the particular case where the GVD is perturbed by a Gaussian white noise, which is explicitly solvable. Under these conditions a deformation of the conventional MI gain profile due to the random perturbation was found when the unperturbed fiber has an anomalous dispersion.…”