Signal linewidth broadening due to nonlinear Kerr effect in long-haul coherent systems using cascaded optical amplifiers

Ryu, Shiro

doi:10.1109/50.166789

Cited by 30 publications

(16 citation statements)

References 11 publications

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“…Consequently, higher bit rate modulation can broaden optical field linewidth significantly. Under white phase noise, (15) reduces to (8) in [18]. Fig.…”

Section: Phase Noise Spectral Density and Equivalent Linewidthmentioning

confidence: 95%

“…From Fig. 7, pt (5.5dBm in this case) is insensitive to D, hence (18) can be used to estimate the optimal optical power even when Compare Figs. 7 and 5 reveals that in D O fibers phase noise can be evidently enhanced by fiber nonlinearity, while intensity noise will not.…”

Section: Phase Noise Spectral Density and Equivalent Linewidthmentioning

confidence: 97%

“…From (11) these frequencies are 6.2GHz, 18.7GHz, 25.7GHz, 31 .2GHz and 35.9GHz. .., which agree well with Fig.…”

Section: Noise Transmission Matrix In a Cascaded Optical Amplifier Chainmentioning

confidence: 98%

“…differential phase shift keying (DPSK) or continuous phase frequency shift keying (CPFSK) in coherent optical systems), performance degradation is determined by the phase noise, which is quantified by linewidth [10], [18]. In coherent systems, laser linewidth is generally quite narrow (for instance, <0.1MHz), hence the laser phase noise can be ignored in long-haul systems with chained optical amplifiers [1 8].…”

Section: Phase Noise Spectral Density and Equivalent Linewidthmentioning

confidence: 99%

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<title>Rigorous analysis of noise evolution in nonlinear dispersive optical fiber</title>

Jiang

Fan

2001

SPIE Proceedings

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Based on the weak intensity/phase modulation transfer matrix H, a matrix V for intensity noise (IN) and phase noise (PN) evolution along nonlinear, dispersive and lossy fiber is derived, while matrix description makes it especially useful in noise evolution analysis in systems with chained optical amplifiers. Evolution oftwo noise sources, laser phase noise and ASE of EDFA, is examined in detail through V. IN, PN and optical field noise spectral densities are studied uniformly. Correspondingly, electrical signal-to-noise ratio (SNR), equivalent linewidth (L\Veq) and optical signal-to-noise ratio (SNR) are used to characterize system performance. It is found that for TM systems, an optimal Po corresponding to minimum SNR exists in positive dispersion fibers, and input optical power cannot be arbitrarily increased to improve SNRe even though only noise is considered. On the contrary, in negative dispersion fibers, SNR is improved with increasing P0 monotonously. For PM systems with negligible laser phase noise and regardless of the sign of fiber dispersion, an optimal optical power also exists to ensure minimum phase noise. SNRO, a combined contribution from intensity and phase noise, is better in fibers with negative dispersion than that in fibers with positive dispersion under the same P0.

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“…Consequently, higher bit rate modulation can broaden optical field linewidth significantly. Under white phase noise, (15) reduces to (8) in [18]. Fig.…”

Section: Phase Noise Spectral Density and Equivalent Linewidthmentioning

confidence: 95%

Section: Phase Noise Spectral Density and Equivalent Linewidthmentioning

confidence: 97%

“…From (11) these frequencies are 6.2GHz, 18.7GHz, 25.7GHz, 31 .2GHz and 35.9GHz. .., which agree well with Fig.…”

Section: Noise Transmission Matrix In a Cascaded Optical Amplifier Chainmentioning

confidence: 98%

Section: Phase Noise Spectral Density and Equivalent Linewidthmentioning

confidence: 99%

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<title>Rigorous analysis of noise evolution in nonlinear dispersive optical fiber</title>

Jiang

Fan

2001

SPIE Proceedings

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“…When optical amplifiers are used periodically to compensate the fiber loss, the interaction of optical amplifier noise and fiber Kerr effect induced nonlinear phase noise, often called Gordon-Mollenauer effect [17], or more precisely, nonlinear phase noise induced by self-phase modulation. Added directly into the signal phase, Gordon-Mollenauer effect is a quadratic function of the electric field and degrades DPSK signal [11,14,[17][18][19][20][21][22][23].Previous studies found the variance or the corresponding Q-factor of the quadratic phase noise [11,17,[24][25][26][27] or the spectral broadening of the signal [14,18,28]. Recently, quadratic phase noise is found to be non-Gaussian distributed both experimentally [20] and theoretically [29,30].…”

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confidence: 99%

Performance of DPSK Signals With Quadratic Phase Noise

2005

IEEE Trans. Commun.

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Nonlinear phase noise induced by the interaction of fiber Kerr effect and amplifier noises is a quadratic function of the electric field. When the dependence between the additive Gaussian noise and the quadratic phase noise is taking into account, the error probability for differential phase-shift keying (DPSK) signals is derived analytically. Depending on the number of fiber spans, the signal-to-noise ratio (SNR) penalty is increased by up to 0.23 dB due to the dependence between the Gaussian noise and the quadratic phase noise. 1 this paper, the additive phase noise is quadratic function of the electric field. When the electric field is contaminated with additive Gaussian noise, although the quadratic phase noise is uncorrelated with the linear phase noise, both non-Gaussian distributed, the phase noise weakly depends on the additive Gaussian noise.Differential phase-shift keying (DPSK) signals [6][7][8][9][10][11][12][13][14][15][16] have received renewed attention recently for long-haul or spectrally efficiency lightwave transmission systems. When optical amplifiers are used periodically to compensate the fiber loss, the interaction of optical amplifier noise and fiber Kerr effect induced nonlinear phase noise, often called Gordon-Mollenauer effect [17], or more precisely, nonlinear phase noise induced by self-phase modulation. Added directly into the signal phase, Gordon-Mollenauer effect is a quadratic function of the electric field and degrades DPSK signal [11,14,[17][18][19][20][21][22][23].Previous studies found the variance or the corresponding Q-factor of the quadratic phase noise [11,17,[24][25][26][27] or the spectral broadening of the signal [14,18,28]. Recently, quadratic phase noise is found to be non-Gaussian distributed both experimentally [20] and theoretically [29,30]. As non-Gaussian random variable, neither the variance nor Q-factor is sufficient to completely characterize the phase noise. The probability density of quadratic phase noise is found in [30] and used in [23] to evaluate the error probability of DPSK signal by assuming that quadratic phase noise and Gaussian noise are independent of each other. However, as shown in the simulation of [22,23], the dependence between Gaussian noise with quadratic phase noise increases the error probability.Using the distributed assumption of infinite number of fiber spans, the joint statistics of nonlinear phase noise and Gaussian noise is derived analytically by [19,21,31]. The characteristic function of nonlinear phase noise becomes a very simple expression with the distributed assumption [29]. The error probability of DPSK signal has been derived with [22] and without [21,32] the assumption that nonlinear phase noise is independent of the Gaussian noise. Based on the distributed assumption, it is found that the dependence between linear and nonlinear phase noise increases both the error probability and SNR penalty [21,32].The distributed assumption is very accurate when the number of fiber spans is larger than 32 [21,29]. For a typical fiber span...

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Advanced Lightwave Systems

Agrawal¹

2010

Fiber‐Optic Communication Systems

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Lightwave systems discussed so far are based on a simple digital modulation scheme in which an electrical binary bit stream modulates the intensity of an optical carrier inside an optical transmitter (on-off keying or OOK). The resulting optical signal, after its transmission through the fiber link, falls directly on an optical receiver that converts it to the original digital signal in the electrical domain. Such a scheme is referred to as intensity modulation with direct detection (IM/DD). Many alternative schemes, well known in the context of radio and microwave communication systems [l]-[3], transmit information by modulating both the amplitude and the phase of a carrier wave. Although the use of such modulation formats for optical systems was considered in the 1980s [4]-[9], it was only after the year 2000 that phase modulation of optical carriers attracted renewed attention, motivated mainly by its potential for improving the spectral efficiency of WDM systems [10]- [16]. Depending on the receiver design, such systems can be classified into two categories. In coherent lightwave systems [14], transmitted signal is detected using homodyne or heterodyne detection requiring a local oscillator. In the so-called self-coherent systems [16], the received signal is first processed optically to transfer phase information into intensity modulations and then sent to a direct-detection receiver.The motivation behind using phase encoding is two-fold. First, the sensitivity of optical receivers can be improved with a suitable design compared with that of direct detection. Second, phase-based modulation techniques allow a more efficient use of fiber bandwidth by increasing the spectral efficiency of WDM systems. This chapter pays attention to both aspects. Section 10.1 introduces new modulation formats and the transmitter and receiver designs used to implement them. Section 10.2 focuses on demodulation techniques employed at the receiver end. The bit-error rate (BER) is considered in Section 10.3 for various modulation formats and demodulation schemes. Section 10.4 focuses on the degradation of receiver sensitivity through mechanisms such as phase noise, intensity noise, polarization mismatch, and fiber dispersion. Nonlinear phase noise is discussed in Section 10.5 together with the techniques used for its compensation. Section 10.6 reviews the recent progress realized with emphasis on improvements in the spectral efficiency. The topic of ultimate channel capacity is the focus of Section 10.7.

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Signal linewidth broadening due to nonlinear Kerr effect in long-haul coherent systems using cascaded optical amplifiers

Cited by 30 publications

References 11 publications

<title>Rigorous analysis of noise evolution in nonlinear dispersive optical fiber</title>

<title>Rigorous analysis of noise evolution in nonlinear dispersive optical fiber</title>

Performance of DPSK Signals With Quadratic Phase Noise

Advanced Lightwave Systems

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