Optical Networks: A Practical Perspective - Part 11. 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. | 70 Propagation of Signals in Optical Fiber Figure A negatively chirped Gaussian pulse. Here and in all such figures we show the shape of the pulse as a function of time. unchirped pulses to acquire a chirp. It then becomes important to study the effect of chromatic dispersion on such pulses. The third reason is that the best transmission performance is achieved today by the use of Gaussian pulses that are deliberately chirped. We will discuss these systems in Section and in Chapter 5. Pulses with a Gaussian envelope are used in high-performance systems employing RZ modulation see Section . For most other systems the pulses used tend to be rectangular rather than Gaussian. However the results we derive will be qualitatively valid for most pulse envelopes. In Appendix E we describe mathematically how chirped Gaussian pulses propagate in optical fiber. The key result that we will use in subsequent discussions here is that after a pulse with initial width To has propagated a distance z its width Tz is given by II To Here k is called the chirp factor of the pulse and is proportional to the rate of change of the pulse frequency with time. A related parameter which depends on both the chirp and the pulse rise-time is called the source frequency chirp factor a in the Telcordia SONET standard . Broadening of Chirped Gaussian Pulses Figure shows the pulse-broadening effect of chromatic dispersion graphically. In these figures the center or carrier frequency of the pulse a o has deliberately been shown greatly diminished for the purposes of illustration. We assume is negative this is true for standard single-mode fiber in the gm band. Figure a shows an unchirped x 0 Gaussian pulse and Figure b shows the same pulse after Chromatic Dispersion 71 a b c d Figure Illustration of the pulse-broadening effect of chromatic dispersion on unchirped and chirped Gaussian pulses for 2 0 . a An unchirped Gaussian pulse at z 0. b The pulse in
