We show, using nonlinearity management, that the optimal performance in high-bit-rate dispersionmanaged fiber systems with hybrid amplification is achieved for a specific amplifier spacing that is different from the asymptotically vanishing length corresponding to ideally distributed amplification [Opt. Lett. 15, 1064Lett. 15, (1990]. In particular, we prove the existence of a nontrivial optimal span length for 40-Gbit͞s wavelength-division transmission systems with Raman -erbium-doped fiber amplification. Optimal amplifier lengths are obtained for several dispersion maps based on commonly used transmission fibers. © 2005 Optical Society of America OCIS codes: 060.4510, 060.4370, 060.2320. During the late 1990s, erbium-doped fiber amplif iers (EDFAs) had a strong effect on the performance and design of optical networks, resulting in the deployment of a large number of high-capacity long-distance optical transmission systems. In this context, the optimization of the amplifier spacing allows one to control the amplif ied spontaneous emission (ASE) noise generated by the cascade of EDFAs. In fact, the finest amplif ication span length is one that facilitates the best trade-off between the low-cost requirements (a low number of amplifiers, ensuring satisfying cost efficiency) and stringent system performance constraints (a large number of amplifiers, ensuring good performance of the transmission system because of the reduction of accumulated ASE noise). Nonlinear effects also have a strong inf luence on overall system performance. In particular, long amplif ier spans result in high input average powers (to maintain a good optical signal-to-noise ratio), leading in turn to an increase in the effects of nonlinearities. In these conditions the goal of transmission-system designers is to find the best balance between the requirements of a high optical signal-to-noise ratio (OSNR) and few nonlinear impairments. Yariv demonstrated 1 that the highest OSNR of an ideal optically amplified system is obtained for a transmission system that produces a perfectly distributed amplif ication or asymptotically vanishing span length. This result is incompatible with the modern necessity for cheaper system design. Fortunately, the recent availability of reliable high-power laser pumps has made possible a comeback of distributed Raman amplif ication (DRA) in dense wavelength-division multiplexing (WDM) transmission systems.
-4Compared with traditional lumped amplifier schemes, DRA significantly improves the link's OSNR. The margins released can then be used for extending the transmission distance and (or) decreasing the signal power injected into the fiber span (thus limiting the effects of nonlinearities). Combined with dispersion management and EDFA amplification, distributed Raman amplif ication can be used to better control the evolution of signal power inside the amplif ication spans, and thus nonlinear effects along the optical line, effectively performing nonlinearity management.
-7The properties of the fibers used (Rama...