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Optical Networks: A Practical Perspective - 37

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Optical Networks: A Practical Perspective - Part 37. This book describes a revolution within a revolution, the opening up of the capacity of the now-familiar optical fiber to carry more messages, handle a wider variety of transmission types, and provide improved reliabilities and ease of use. In many places where fiber has been installed simply as a better form of copper, even the gigabit capacities that result have not proved adequate to keep up with the demand. The inborn human voracity for more and more bandwidth, plus the growing realization that there are other flexibilities to be had by imaginative use of the fiber, have led people. | 330 Transmission System Engineering velocity difference is greater when the channels are spaced farther apart in systems with chromatic dispersion . To quantify the power penalty due to four-wave mixing we will use the results of the analysis from SBW87 SNIA90 TCF 95 OSYZ95 We start with 2.37 from Section 2.4.8 3cAe This equation assumes a link of length L without any loss and chromatic dispersion. Here P Pj and Pk denote the powers of the mixing waves and P k the power of the resulting new wave n is the nonlinear refractive index 3.0 x 10-8 zm2 W and dijk is the so-called degeneracy factor. In a real system both loss and chromatic dispersion are present. To take the loss into account we replace L with the effective length Le which is given by 5.24 for a system of length L with amplifiers spaced I km apart. The presence of chromatic dispersion reduces the efficiency of the mixing and we can model this by assuming a parameter rjjjk which represents the efficiency of mixing of the three waves at frequencies a j and a k- Taking these two into account the preceding equation can be modified to Pijk Vjk PiPjPkL2e. 3cAe For on-off keying OOK signals this represents the worst-case power at frequency Dijk assuming a 1 bit has been transmitted simultaneously on frequencies a j and a k- The efficiency jk goes down as the phase mismatch A J between the interfering signals increases. From SBW87 we obtain the efficiency as a2 4e al sin2 A 2 mjk a2 A.0 2 1 1 -e- 2 Here A 3 is the difference in propagation constants between the different waves and D is the chromatic dispersion. Note that the efficiency has a component that varies periodically with the length as the interfering waves go in and out of phase. In our examples we will assume the maximum value for this component. The phase mismatch can be calculated as Aß ßi ßj -ßk- ßijk 5.8 Fiber Nonlinearities 331 where represents the propagation constant at wavelength Xr. Four-wave mixing manifests itself as intrachannel crosstalk. .