TAILIEUCHUNG - Optical Networks: A Practical Perspective - Part 78

Optical Networks: A Practical Perspective - Part 78. 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. | 740 Pulse Propagation in Optical Fiber Figure The magnitude of the pulse envelope of the second-order soliton. Agr97 G. P. Agrawal. Fiber-Optic Communication Systems. John Wiley New York 1997. Mar80 D. Marcuse. Pulse distortion in single-mode fibers. Applied Optics 19 1653-1660 1980. Mar81 D. Marcuse. Pulse distortion in single-mode fibers. 3 Chirped pulses. Applied Optics 20 3573-3579 1981. appendix Nonlinear Polarization The linear equation for the relationship between the induced polarization P and the applied electric field E holds when the power levels and or bit rates are moderate. When this is not the case this must be generalized to include higher powers of E r t . For an isotropic medium and an electric field polarized along one direction so that it has a single component E r this relationship can be written as follows P r t c0 x l r t - ti. E r t dt J 00 eoi i X 2 G - tj t - Q r t E r t2 dt dt2 J oo J oo e I i x 3 t-ti t-t2 t-t3 E r t E r t2 E r t3 dhdt2dt3 J oo J oo J oo Now x l r t is called the linear susceptibility to distinguish it from x i r t i 2 3 . which are termed the higher-order nonlinear susceptibilities. Owing to certain symmetry properties of the silica molecule x 2 r t 0. The effect of the higher-order susceptibilities x 4 X 5 - is negligible in comparison with that of x 3 . Thus we can write El as P r i PL r t PNL r. t . 741 742 Nonlinear Polarization Here Pl x t is the linear polarization given by . The nonlinear polarization PniAp t is given by Pnl i t fo i i i x t -ti t -t2 t -t3 J 00 J oo J 00 E r ti E r t2 E r t3 dt dt2dt3 . The nonlinear response of the medium occurs on a very narrow time scale of less than 100 fs much smaller than the time scale of the linear response and thus can be assumed to be instantaneous for pulse widths greater than 1 ps. Note that even if the pulse occupies only a tenth of the bit interval this assumption is satisfied for bit rates greater than 100 Gb s. We will consider only this .

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