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286                                                               Fiber Optic Communications


                                200




                                150
                               Pump power (mW)  100







                                 50




                                  0
                                   0       10        20       30       40       50
                                                      Length (km)

                      Figure 6.26 Decay of the Raman pump. The parameters are the same as those of Fig. 6.24.


                               35


                               30
                                                                       P s (0) = –6 dBm
                               25
                                                                        P s (0) = 0 dBm
                               G (dB)  20                              P s (0) = 6 dBm


                               15

                               10

                                5
                                 20       22        24       26        28        30
                                                   Pump power (dBm)

            Figure 6.27  Dependence of gain on the pump power. Gain saturates as the signal power increases. The parameters are
            the same as those of Fig. 6.24.



              For the backward-pumping scheme, the evolution of signal and pump powers is given by
                                             dP s  g r
                                                 =   P P −  P ,                            (6.209)
                                                            s s
                                                      p s
                                              dz   A p
                                             dP p    g
                                                     p
                                           −     =−     R  P P −  P .                      (6.210)
                                                                p p
                                                          p s
                                              dz     A
                                                      s  s
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