1188 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 5, MAY2003 Third-Order Dispersion Compensation Using a Phase Modulator Erik Hellström, Henrik Sunnerud, Mathias Westlund, and Magnus Karlsson Abstract—Compensation of third-order dispersion in a fiber-optic transmission system using a phase modulator is studied both theoretically and experimentally. A sinusoidal signal is used as modulation function, where the amplitude and phase delay are optimized. The 2-ps input pulses (160-Gb/s compatible) were transmitted through a 626-km fiber link, where the characteristic oscillating tail was measured with a 1.6-ps resolution optical sam- pling system. When applying the phase modulation, the oscillating tail was significantly suppressed. The pulses were also used in a 160-Gb/s transmission experiment, where the eye diagrams were measured with the sampling system. Numerical simulations and practical experiments showed excellent agreement. Index Terms—Dispersion compensation, fiber-optic communi- cation, optical sampling, phase modulator, third-order dispersion, ultrahigh bit rates. I. INTRODUCTION T ODAY, standard single-mode fibers (SMFs) are up- graded with dispersion compensating fiber. This includes dispersion slope compensation and allows for broadband wave- length-division multiplexed transmission. However, the slope can be difficult to exactly cancel, and when the fiber is used for 160-Gb/s optical time-domain multiplexed (OTDM) trans- mission, this can be the major limiting factor. The net higher order dispersion can be compensated by phase modulation. The advantage of using a phase modulator to compensate for higher order dispersion is that a flexible system with efficient compensation using standard components is possible. Compensation of third- and fourth-order dispersion utilizing a phase modulator has been studied previously [1]–[5], but then for femtosecond pulses over short distances, rather than for 160-Gb/s transmission over relatively long distances (which is the object of this paper) but with comparable normalized third-order dispersion (TOD) magnitudes. However, the pre- vious work did not include studies of how different compensator parameters affect the optimum settings for the phase modu- lator. Nor did they show measurements of the characteristic third-order dispersion tail, which is done here with a 1.6-ps resolution optical sampling system [6]. Measurements using an optical sampling system to show the effects of TOD have, however, previously been presented in other studies [7], [8]. In this paper, compensation of TOD using a phase modu- lator is studied numerically and experimentally. A sinusodial Manuscript received August 27, 2002; revised February 3, 2003. This work was supported by the Swedish Strategic Research Foundation (SSF), Chalmers Center for High Speed Technology (CHACH), and Ericsson Telecom. The authors are with the Photonics Laboratory, Department of Microelec- tronics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden (e-mail: sunnerud@elm.chalmers.se). Digital Object Identifier 10.1109/JLT.2003.810563 phase modulation signal was applied, and the amplitude and phase delay were optimized by maximizing the energy inside the 160-Gb/s compatible 6.25-ps bit slot. The corresponding intersymbol interference (ISI) penalty is then calculated. Em- phasis is also put on characterizing the optical mux-factor of the OTDM system, i.e., the frequency at which the phase mod- ulation is applied in relation to the bit rate. The simulations were verified with experiments, where 2-ps pulses were trans- mitted through a 626-km-long transmission link. To measure the transmitted signal, a 1.6-ps resolution optical sampling system was used. The pulses were also used in a transmission experi- ment where clear 160-Gb/s eye diagrams after 500-km transmis- sion were demonstrated, which was not possible without TOD compensation. The simulated and experimental transmissions showed excellent agreement. II. THEORY The system used for dispersion compensation consisted of two optical fibers with an intermediate phase modulator, as shown in Fig. 1. First, the input signal (i) was dispersed linearly with time through a dispersion compensating fiber (DCF) (ii). Subsequently, the signal was passed through the phase modulator, where the modulation function was added to the phase of the signal. Finally, the modulated signal was compressed in a standard SMF (iii) with opposite sign of the compared to the prior DCF. Ideally, the characteristic tail induced by a positive dispersion slope of the transmission fiber should be fully compensated as indicated by (iv) in Fig. 1. However, this ideal case is not so easily achieved in practice, which will be discussed below. The calculations were made for the actual transmission link to be used in the experimental verification, but the results are generic and can be scaled to any -limited system and extrap- olated to any bit rate. The transmission link had a length of 626 km, where the effective length of the SMF was 540 km and DCF was 86 km. The group-velocity dispersion (GVD) in the transmission link was compensated by DCFs but a net TOD of ps km ps nm km remained. Hence, TOD is a limiting factor as the TOD length with the 160-Gb/s compatible 2-ps pulses is km, according to (1) where is the input pulse half-width at 1/e intensity point. When a pulse propagates through a transmission fiber of length with GVD and TOD coefficients and , the phase contribution added by the dispersion is given by (2) 0733-8724/03$17.00 © 2003 IEEE