15 April 1998 Ž . Optics Communications 149 1998 261–266 Reduction of Gordon-Haus jitter in a dispersion compensated optical transmission system: analysis Takao Okamawari, Akihiro Maruta 1 , Yuji Kodama Graduate School of Engineering, Osaka UniÕersity, 2-1 Yamada-oka, Suita, Osaka 565, Japan Received 4 November 1997; accepted 7 January 1998 Abstract We theoretically analyze the Gordon-Haus timing jitter in an optical transmission system with dispersion compensation. The enhanced power obtained in such a system reduces the frequency shift induced by noise, and choosing an appropriate position of the receiver further reduces the timing jitter converted from the frequency shift. Based on these results, we can obtain the reduction of the Gordon-Haus timing jitter in a dispersion compensated system, compared with a conventional soliton having equal pulse width and path-average dispersion. q 1998 Elsevier Science B.V. Keywords: Soliton; Dispersion compensation; Timing jitter; Perturbation method 1. Introduction Ž . Recently, a new soliton-like RZ Return to Zero pulse transmission technology using periodic dispersion compen- w x sation has been developed 1–3 . Inserting the normal Ž dispersion fiber which is called dispersion compensation . fiber: DCF into an anomalous dispersion fiber, the path- average dispersion of the system is reduced. Moreover, the pulse propagating in such a system has a Gaussian-like shape with periodical change of amplitude, pulse width and chirp, and the peak power of the pulse is enhanced when compared with a soliton in a uniform anomalous dispersion fiber with equal pulse width and path-average w x dispersion 3,4 . By using these properties of the pulse, it is possible to make a new transmission line with higher bit-rate andror longer transmission distance compared to a conventional soliton transmission system. Another applica- tion of this technology is to upgrade an installed transmis- sion line into a high-speed system. This is because the enhanced power improves the signal-to-noise ratio at the 1 Corresponding author. E-mail: maruta@comm.eng. osaka-u.ac.jp wx receiver 3 , and the small path-average dispersion achieved by the dispersion compensation technique reduces the Gor- wx don-Haus timing jitter 2 . Recently, it has been observed numerically that there is an extra timing jitter reduction in w x such a system 5–7 . In this paper, we theoretically explain the reduction of the Gordon-Haus effect in a periodic dispersion compensated system. According to the original theory given by Gordon and wx Haus 8 , the noise at each amplifier induces the frequency shift of the pulse, and this frequency shift is converted into the timing jitter through dispersion. So we have to examine the dynamics of frequency and position of the pulse under the influence of amplifier noise. We use the variational method, and we choose a Gaussian pulse as a trial func- tion. This then enables us to analyze the Gordon-Haus timing jitter in a dispersion compensated system. This paper is organized as follows. Section 2 gives a Ž brief explanation of the model equation perturbed nonlin- . ear Schrodinger equation for a transmission system with ¨ periodic perturbation of dispersion compensation and lumped amplification. Then we apply the variational method for the model equation and derive equations of motion for the pulse parameters describing its amplitude, pulse width, chirp, frequency, center position, and phase. 0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. Ž . PII S0030-4018 98 00006-6