IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 10, OCTOBER 2004 2365 Effectiveness of Fiber Lines With Symmetric Dispersion Swing for 160-Gb/s Terrestrial Transmission Systems J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin Abstract—We demonstrate theoretically and experimentally that a fiber line with a symmetric dispersion swing can substan- tially improve the performance of 160-Gb/s optical transmissions. The improvement lies in an increased transmission distance and reduction of the optimum input signal power by one order of magnitude compared with that of a conventional system. Index Terms—Dispersion management (DM), optical fiber com- munication, recirculating loop, ultrashort pulses. I. INTRODUCTION I T IS widely perceived that an appropriate management of the fiber chromatic dispersion is essential for both the designing of the next generation of transmission systems, and the upgrading of the already installed fiber-optic networks to higher time-division-multiplexed bit rates [1]–[5]. Various techniques of dispersion management have been proposed with a view to achieve ultrahigh-speed transmissions (at bit rate more than 40 Gb/s per channel). Hence, for terrestrial transmissions, one commonly makes use of conventional dispersion-managed (DM) systems, in which the map length is equal to (or more than) the amplifier span [4], [6]. In this letter, we demon- strate theoretically and experimentally that the performance of conventional DM systems, which are fundamentally built up from an asymmetric dispersion profile [6], can be substantially improved by using a symmetric profile of dispersion swing. II. THEORY Pulse dynamics in a periodically amplified DM fiber system can be described by the following nonlinear Schrödinger equa- tion (NLSE): (1) where is the normalized envelope of the axial electrical field . The function describes energy variations induced by losses and periodic amplification, and Manuscript received December 4, 2003; revised June 9, 2004. This work was supported by a contract between the University of Burgundy and the France Telecom R&D (Contract 42 56 26 63). The work of J. Fatome was supported by the Conseil Regional de Bourgogne and the Centre National de la Recherche Scientifique. J. Fatome, S. Pitois, P. Tchofo Dinda, and G. Millot are with the Labora- toire de Physique, Université de Bourgogne, Unité Mixte de Recherche, CNRS, 21078 Dijon Cédex, France (e-mail: spitois@u-bourgogne.fr). E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin are with France Telecom R&D RTA/OCN/TALE2, 22300 Lannion, France. Digital Object Identifier 10.1109/LPT.2004.834587 represent the group velocity dispersion and self-phase mod- ulation parameters, respectively. The usual dispersion param- eter is given by , where m is the transmission wavelength. The pulse energy along the line is given by , where is a constant of motion of (1). Using a Gaussian ansatz, one can express the NLSE (1) in terms of a set of ordinary differential equations for the dynamics of the pulse parameters [7] (2a) (2b) In (2), the over-head dot represents the derivative with respect to . The square root of , with , is proportional to the spectral bandwidth of the pulse, and is the cumulated dispersion. The parameter rep- resents the pulse chirp. The specific features of the transmis- sion systems under consideration come from the asymmetric and symmetric nature of their dispersion maps, as can be seen in Fig. 1(a1) and (a2), respectively. The asymmetric map (AM) is the standard map for the existing terrestrial transmission sys- tems. This map consists of two sections of fibers: a single-mode fiber (SMF) with the following typical parameters, dispersion ps/nm/km, dispersion slope ps/nm /km, length km, losses dB/km, effective core area m , followed by a dispersion compensating fiber (DCF), with typical parameters ps/nm/km, dB/km, and m . In the present study, we employ a double- stage amplification [6], in three distinct cases. The first case cor- responds to the classical situation, where the gain of the first amplifier (placed just before the DCF) is tuned so as to compen- sate for the total (distributed or lumped) losses over the first sec- tion of the map, while the second amplifier with gain com- pensates for the total losses over the second section of the map. This case (where ) corresponds to the classical asym- metric map (CAM) [4]. The second configuration corresponds to a “modified asymmetric map” (MAM) with . For the third configuration, we use a symmetric map (SM) that con- sists of three sections of fibers , as Fig. 1(a2) shows, and two amplifiers with equal gains. We have not con- sidered elements of precompensation and postcompensation of dispersion in any of the three systems. The length of the period of dispersion swing is km. Each period is repeated to build up the line associated with each configura- tion. 1041-1135/04$20.00 © 2004 IEEE