Very high capacity long-haul optical comIf amplifiers with gain G = exp(-d) are munication systems can be designed by using inserted after each of N fiber segment of length erbium-doped fiber amplifiers, wavelength diviI, the power of channel i at the receiver can be sion multiplexing (WDM) and dispersion-shifted found to be fiber. The use of dispersion-shifted fiber allows higher bit-rates, but enhances the efficiency of Pi(NI) = Pi(O) e"'Pij~(N~) , four-wavc milcing (FWM) wave generation by reducing the phase-mismatch naturally provided by the fiber dispersion [l], thus causing FWM to become the dominant nonlinear effect [2]. FWM is a nonlinear process in which three waves of frequencies f i , fj, and fb (k # i ,j) interact through the third-order electric susceptibility of the optical fiber to generate a wave of frequency f i j b = fi + fj fb [3]. In this process power is transferred (in approximately equal amount) from channels i and j to channel k and to the FWM wave at f i j b , causing depletion of channels i and j. The power lost by channel i can be computed by adding the power that has been transferred at frequency f i j b at the end of the fiber to the power lost by the FWM wave during propagation. Denoting with P ; j b ( z ) the power of the FWM wave at the point z in the fiber, the power of channel i, Bi(z), is given by
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