824 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 11, NO. 7, JULY 1999 Dependence of Self-Phase Modulation Impairments on Residual Dispersion in 10-Gb/s-Based Terrestrial Transmissions Using Standard Fiber Giovanni Bellotti, Member, IEEE, Alain Bertaina, and S´ ebastien Bigo, Member, IEEE Abstract—We carry out, by computer simulation, an extensive investigation of the impact of residual dispersion on power margins induced by self-phase modulation in typical 5 100- km-long terrestrial transmission systems at 10 Gb/s, using stan- dard single-mode fiber and modular dispersion compensation. We show that the most performing compensation technique is postcompensation, with positive residual dispersion, and that pre- compensation must be avoided in case of dual-stage amplification. We also propose a design rule to perform optimal dispersion compensation in multichannel transmissions. Index Terms— Crosstalk, dispersion compensation, intensity modulation, optical fiber nonlinearity, wavelength-division mul- tiplexing. I. INTRODUCTION T HE MOST effective and practical strategy for upgrading the already-installed transmission systems, using stan- dard single-mode fiber (SMF), is the periodical insertion of dispersion-compensating fiber (DCF) for suppressing the linear distortion induced by group-velocity dispersion (GVD). In presence of nonlinear effects, such as self-phase modulation (SPM) and cross-phase modulation (XPM), the signal distor- tion cannot be fully suppressed, because the generation of nonlinear phase modulation, which induces intensity distortion through GVD [1], [2], is distributed during the propagation. The transmission performance is thus dependent on the posi- tion of the DCF and the zero residual dispersion is not the best choice anymore. The dependence on the DCF position has been already studied [3]–[5] and it has been shown that, in the case of full compensation, the precompensation technique achieves the best results. As shown in Fig. 1, we define pre- or postcompensation when the DCF is located before or after the transmission fiber, respectively. In this letter, we generalize the results in [3]–[5] by ana- lyzing the dependence of the performances of both schemes on the residual dispersion. The study is concentrated on realistic terrestrial transmission links, which typically reach 500 km, periodically compensated at every span with DCF’s of equal length. This modular architecture facilitates practical Manuscript received December 23, 1998; revised March 17, 1999. G. Bellotti was with Alcatel Corporate Research Centre, 91461 Mar- coussis Cedex, France. He is now with the Dipartimento di Ingegneria dell’Informazione, Universit` a di Parma, 43100 Parma, Italy. A. Bertaina and S. Bigo are with Alcatel Corporate Research Centre, 91461 Marcoussis Cedex, France. Publisher Item Identifier S 1041-1135(99)05124-1. (a) (b) Fig. 1. Modular post- and precompensation schemes in the case of (a) single-stage and (b) dual-stage in-line amplification. realization. We show by simulation that, if we also consider the cases of partial compensation, the most performing technique turns out to be, differently from what asserted in [3]–[5], the postcompensation. We also show that precompensation is not a valid technique when the dual-stage strategy is adopted for span amplification. Moreover, we propose a prac- tical design rule for wavelength-division-multiplexed (WDM) SPM-limited transmission systems, and we show that the presence of multiwavelength nonlinear effects, substantially XPM, does not change the essence of the obtained results. II. RESULTS We present the results of computer simulations performed using the split-step Fourier method [6] for the system plotted in Fig. 1. A single channel, modulated with a 10-Gb/s nonreturn- to-zero (NRZ) 2 -long bit sequence, is generated through a chirp free transmitter (extinction ratio 13 dB) and is launched into a link composed of five spans of 100 km of SMF and km of DCF. The length is varied from 13 to 19 km, in order to change the residual dispersion, that is the disper- sion accumulated from the transmitter to the receiver. Fiber dispersion, dispersion slope, attenuation, nonlinear coefficient, and effective area are 17 ps/nm/km, 0.07 ps/nm /km, 0.22 dB/km, 2.7 10 m /W, and 80 m , respectively, for SMF, and ps/nm/km, 0.09 ps/nm /km, 0.6 dB/km, 2.6 10 m /W, and 20 m for DCF. is the power launched at the input of every span. The in-line erbium-doped fiber amplifiers (EDFA’s) are supposed flat and noiseless, with gain equal to span loss. To accommodate the additional loss of the DCF modules while meeting signal-to-noise ratio (SNR) 1041–1135/99$10.00  1999 IEEE